Science topic

# Numerical Analysis - Science topic

Numerical Methods
Questions related to Numerical Analysis
Question
i want to study impact test of adhesively SLJ using abaqus, but
i couldnt know how to define adhesive material and interaction properties,
E(MPa) 1520
G (MPa) 565
σu (MPa) 46.93
τu (MPa) 46.86
GIC (N/mm) 4.05
GIIC (N/mm) 9.77
thickness: 0.2mm
1-is it sufficient?
2-is it correct way to analyze it, edit material> Maxs damage + Elastic>traction-->entering values.
3-if it is true, program wants from me this values for maxs damage;--> nominal stress normal-only and first and second direction
how can i put this values? How can i calculate or find? any suggestions
4- should i also do interaction properties-->contact-->cohesive properties , if yes, how can i calculate or find the Kss,Ktt,Knn values
5- Lastly there are limited information about repeated impact test for this topic on internet, how can analyze the repeated test, like, impact to deformed SLJ joint (including its previous stress values)
if someone helps, i would really appreciated..
The best software for impact simulation is just ls-dyna. Don' waste your time with abaqus.
Question
I am an M.Tech structural engineering student working on the project ' Numerical analysis of Kath-kuni architecture ( a common masonry typology ) in Himachal Pradesh region of India subjected to earthquake loading in ABAQUS software' . The question of concern is that I am finding it difficult to input plasticity parameters for timber/ wood material that I have used in my model even after searching in various research papers. I have got only elasticity parameters and wood being an orthotropic material requires plasticity parameters and a plasticity damage model to be defined in order to understand the actual material behavior in ABAQUS software. So, kindly help me in finding the plastic properties and a damage model for timber, it would be very helpful to proceed in my current project.
Thanks and regards
hi Nayak,
did you find a solution to your problem? i am also trying to define solid wood in abaqus cae. i have elastic data but plastic data and i can't find how to define this data in abaqus. I have limited time left for my master thesis. I need serious help from you and other friends.
Regards.
Question
📢 #specialissue #CallforPapers Calling all researchers and experts in numerical analysis and meshless methods! CMES-Computer Modeling in Engineering & Sciences new special issue “New Trends on Meshless Method and Numerical Analysis” is open for submission now.
👨‍🎓 Guest Editors Prof. Ji Lin, Hohai University, China. Prof. Fajie Wang, Qingdao University, China.
📚In recent years, in the category of numerical analysis, the meshless method has witnessed a research boom to free engineers and scientists from the difficult task of mesh generation and to reduce mesh sensitivity of solutions. Meshless methods include the kernel methods, the moving least square method, the radial basis functions, etc, such as the well-known smoothed particle hydrodynamics, the diffuse element method, the element-free Galerkin, the method of fundamental solution, the reproducing kernel particle method. The meshless method has become an attractive alternative for problems in computational mechanics, computational physics, computational chemistry, computational biology, computational materials science, etc.
🔍The main target of this special issue is to focus on the latest developments of meshless methods, such as theoretical analysis, applications, development of new methods, fast solution techniques, etc. The applications of advanced techniques such as isogeometric analysis, artificial intelligence, the physical-based numerical model, etc, in meshless methods are also welcomed.
#NumericalAnalysis #MeshlessMethods #CallForSubmissions #ResearchOpportunity
I may write on "How to simulate Physical-Based Numerical Models with Meshless Methods"
Question
Do obstacles in a channel change the regime from laminar to turbulent while the Reynolds number is under 2300 (approximately 1000)?
The Reynolds number UD/nu=2300 is based on a smooth circular pipe of diameter D, with STEADY mean flow velocity U and fluid of kinematic viscosity nu. Below this critical Reynolds number any perturbation due to an obstacle will not cause persistent turbulence to occur far downstream of the obstacle. Of course locally the wake of a blunt body placed in the pipe can be turbulent, but soon the flow will relaminarize if we travel further downstream. Above Re=2300 the flow does not need to be turbulent. It can be turbulent if there is a sufficiently large initial upstream perturbation. In principle the flow can remain laminar if the inlet is very smooth and care is taken to avoid vibrations. Experimentally fully developed laminar pipe flows have been achieved for Re=500. 000. It is important to realize that this critical Reynolds number does depend on the geometry of the cross-section of the channel. For a rectangular channel of height h and width w >>h, usually one considers a Reynolds number Re=Uh/nu based on the channel heigth. The critical Reynolds number for allowing turbulence is around Re=hU/nu=1100. There is however much less literature on flows through slit shaped channels than circular pipes. If you consider an open channel flow, clearly the critical Reynolds number will be quite different from Re=2300 and of course it does depend on the length scale used in the definition of this Reynolds number!
Question
I want to simulate a discrete random  media with FDTD method.
the simulation environment is air that is filled with random spherical particles (that are small to the wavelength) with defined size distribution.
what is an efficient  and simple way to create random scatterers in large numbers in FDTD code?
i have put some random scatterers in small area but i have problem producing scatterers in large numbers.
any tips, experiences and suggestions would be appreciated.
Are you asking how to make your particles a helix/spiral shape? First, before doing that, I recommend running simulations that will just use the effective properties that your helices should give. That will let you explore device ideas without needed the complexity and inefficiency of having to resolve the spirals in your grid. Second, you will want to create a small simulation of a helix to retrieve the effective properties. This is usually called homogenization or parameter retrieval. Third, if you need to, move on to your more complicated 3D simulation.
That still leaves the question of how to build a helix in a 3D grid. One way you can do this is to create the helix in a CAD software such as SolidWorks or Blender. You can export that model as an STL file, which is just a surface mesh that MATLAB (or whatever software you are using) can import. From there, there are codes available that can import those STL files and "voxelize" them into a 3D array. If you are using MATLAB, search the MathWorks website for "voxelize" and you will find multiple solutions. Once you have that, you can create copies of the spiral in your FDTD grid. This approach will let you import even more complicated shapes relatively easily. Alternatively, you can create the spiral directly in your grid. I would do this by creating a array that has a list of points along the center of your spiral. From there, you can calculate what points your FDTD grid should be assigned to that spiral by calculating their distance to the points on the spiral. If they are within a certain distance, assign the material properties of your spiral. Otherwise, assign the material properties of whatever medium the spirals are residing in.
I am sure there are plenty of other ways to do this. If you are interested, I dedicated almost all of Chapter 1 to describing techniques for building geometries into arrays for simulation using the finite-difference method. I do not specifcally talk about spirals, but you may find some of that chapter very helpful. Here is a link to the book website:
Hope this helps!!
Question
As it is impossible to use equations here, I am posting the link to my question here.
It would be better if you give an example that covers your problem more precisely. Can you share the code you used it for solving the problem?
Question
I want to simulate mixing two fluids with different inlets and velocities in COMSOL. I used "Laminar Flow" and "Transport of Diluted Species" physics to do it, and my problem is that I cannot select both fluids for my domain. I have two fluids and one domain for mixing. How can I do it? Should I use "Multiphase Flow" physic?
Yes, you have to define a multi-phase model, e.g., VOF or Euler-Euler.
Question
My combustion simulation is fully converged. The mass imbalance that Fluent calculates is 3×10^-9. However, if i calculate the mass imbalance from the average surface integrals, as (density×velocity)_avg xArea is the mass flux from inlet and outlet, the resulting mass imbalance is the order of 10^-7. What causes this deviation as its order is around 10^2. Thank you.
Mass weighted averages are more meaningful. For combustion simulations, local density and mass depend on temperature... Area weighted average is based on the mesh...
Question
Hello,
We are working on the optimisation of the natural frequency of the composite beams. And using DOE L27 array has been created. Now to enter response variables' of 27 test cases, is it correct to use numerical software like ANSYS ??
Yah. No issues.
Question
I have a system of non-linear differential equations that explains the behaviour of some of the cancer cells.
Looking for help identifying the equilibrium points and eigenvalues of this model in order to determine the type of bifurcation present.
Well it's a good idea to find some of them, first. The first equation implies that y=0 is an equilibrium, so a class of equilibria is of the form (x,0,z). That reduces the problem. From the last equation it then should be possible to solve for z and, from the second, for x.
Then look at the other factor of the first equation; and so on.
Question
I need a collaborator with experience in code development and, if possible, numerical analysis too.
I am currently developing an open source code in python that can be used to solve different kinds of Integral Equations.
In the last one and half years I have done some work in numerical Algorithms for integral equations with some papers already published. It has culminated to several python codes which I have used to produce the results.
The codes are all private but the results are published so I am inclined to make these codes publicly available so that others can use them at no cost and minimum effort.
I, therefore, need a fellow Researcher who has good skills in software engineering and numerical analysis to join me in this line.
A minimum requirement is the knowledge of git and python.
You can email me at nwaigwe.chinedu@ust.edu.ng
Chinedu Nwaigwe Great, Interested, In fact, 'm pleased to learn you're working on open-source programs to solve integral equations. Publish your code to make your study more publicly available and to allow others to build on your work.
A partner with skills in code development and numerical analysis would be ideal. As you indicated, knowledge of Git and Python would be a must. However, further knowledge of numerical techniques for solving integral equations would be advantageous.
Question
I simulate a periodic structure placed on a lossy, dispersive half-space whose relative permittivity is smaller than zero at some frequencies. Using CST 2020, I apply open boundary condition (without adding space) in the direction filled with the mentioned medium.
However, the simulation doesn't progress due to the errors. These errors are as follows:
1) "The Floquet port boundary at Zmin must be homogeneously filled with isotropic loss-free and non-dispersive material. For non-dispersive materials, please consider using the option to "Ignore losses" in the solver specials.".
2)"The Floquet port boundary at Zmin has negative material coefficients, which are not supported."
Curious to know the reason. Does it belong to the software limitations or sth?
Any suggestions or ideas are appreciated.
Thanks
Libi Mol V.A
Yes I've used this technique to get the results. But, as I mentioned i want to know why Floquet ports can't model lossy (as well as dispersive) half-space medium without using the Open add space boundary condition (BC).
Because, by considering a quarter wavelength space between the medium and Floquet port (via using Open add space BC ), we don't model a half-space anymore. Accordingly, we can obtain results approximately by considering sufficient thickness for the lossy medium.
Question
Hello ResearchGate Community,
I am working on composite laminate analysis. Need to do a numerical analysis and the stacking sequence is given by the supervisor in the attached photo.
- If there is a + and - sign together (as in the case for 45 degree), then what to do?
- What to do during (0,90)?
- How the symmetry will work here?
I have some options (options given below), but not sure and don't have a clear explanation. Can anyone please help me and confirm it?
(1) 45/0/90/45/45/90/0/45/45/0/90/45/45/90/0/45
(2) 45/0/0/45/45/0/0/45/45/0/0/45/45/0/0/45
(3) 45/0/45/0/45/0/45/0/45/0/45/0/45/0/45/0
I thought to use only +45, so I have come up with these 3 options, but not sure~
Thank you a bunch in advance for your effort and time :)
To stack the plies of a composite material in numerical analysis, you will need to use a software that is capable of modeling composite materials, such as finite element analysis (FEA) software. The specific steps will depend on the software you are using, but in general, you will need to follow these steps:
1. Create a new model in the software.
2. Define the material properties for each ply of the composite. This will typically involve specifying the material type (e.g. glass fiber reinforced polymer), the properties of the matrix material (e.g. Young's modulus and Poisson's ratio), and the properties of the fiber reinforcement (e.g. fiber volume fraction, fiber orientation, and fiber modulus).
3. Define the geometry of the composite structure. This will typically involve creating a 2D or 3D representation of the composite structure, such as a flat panel or a cylindrical tube.
4. Assign the material properties to the different plies of the composite. In most software, this will involve selecting the plies and assigning the appropriate material properties to each one.
5. Define the loading and boundary conditions for the composite structure. This will typically involve specifying the applied loads and the supports or constraints that are applied to the structure.
6. Run the analysis to calculate the stress and strain distribution within the composite structure.
7. Review the results of the analysis, such as the stress and strain contours or the failure criteria.
To stack the plies in the specific stacking sequence of [(±45)/(0,90)]4s, you will need to define the orientation of each ply relative to the previous ply. For example, if the first ply is oriented at 45 degrees, the second ply would be oriented at -45 degrees, the third ply would be oriented at 0 degrees, and so on. The software will automatically calculate the resulting ply orientations based on the specified stacking sequence.
Question
I am currently doing my dissertation and I am trying to check the reliability for sub-scales I have newly created. The items comes from multiple measures as my data is from a data archive (so were collected from different studies). I have re-coded them all onto the same Likert scale but keep getting the error message "too few cases analysis not run". All missing values are coded the same (999-888) but from the help online, I am thinking it is as the missing values are scattered over numerous analysis variables? Is there any way round this? Any advice would be appreciated.....
Coefficient alpha is based on correlations, so you be having a problem with missing data for "complete" cases. But you should also check to see if your problem is structural in the sense that you are including items from two (or more) different surveys in the same analysis, because it would be impossible to calculate correlations when the variables are drawn from different data sets.
Question
I'm modeling a steel concrete composite beam in ABAQUS software using shell elements for the I section and solid elements for the concrete slab. Please explain me how to use tie constraint to make the contact in between these two surfaces.
Akila Dulanjalee Wijethunge Can you share your Abaqus model (.inp format)?
Question
How can I import 2D sketches from CATIA into COMSOL Multiphysics?
The formats that COMSOL reads in 2D geometry are not available in CATIA.
You can import your 2D model from CATIA software into AutoCAD software and write output DXF.
Good luck!
Question
I have generated 16 variable probability distributions in the form of a 16 dimensional NumPy array in python. How could I determine all the peaks in this function in python or using some software?
Thank you all for the clarifications
Question
Consider the Newtonian n-body problem. An initial condition must specify the initial positions and velocities for each of the n point masses. Thus the space of initial conditions has dimension 6n. I am interested in the subset G of initial conditions which yield solutions that:
1. Are global (defined for all t > t_0)
2. Do not have have collisions or any particle escaping into infinity
3. Are real analytic: at each t there is a neighbourhood U(t) such that each position component of each particle is given by a convergent power series in t.
Note that real analytic functions which are real analytic on the whole R need not be given globally by a convergent power series as in the complex analytic case (of entire functions).
For if we extend a real analytic function to the complex numbers, such as 1 /1 + x^2, then it may well have a pole. We call such real analytic functions piecewise-entire.
What can be said about G topologically ?
When are the coeficients of the convergent power-series computable (possibly different for each member of a countable cover of the reals) ?
Are there examples of solutions which satisfy 1 and 2 but not 3, i.e. are smooth but not real analytic ?
I do not think such a general question can have a definite answer. A particular question to classify the initial data leading to closed periodic trajectories (without collisions) for 3 body case makes sense and is of importance. I guess the most appropriate person to discuss all that is R Montgomery from UC Santa Cruz.
Question
I am trying to model excavation procedure of tunnel (D-shaped) in Abaqus (CAE). I have obtained the RF1 and RF2 from an independent analysis as given in Abaqus example (Abaqus example problem guide/1.1.11 Stress-free element reactivation). Now, my problem is that how to apply those concentrated forces ((2n+1)*2) on corresponding nodes?... Because, in my model total number of nodes (2n+1) on tunnel periphery are 129 (in the abaqus example, there are only 13 nodes). And, its changing with each trial/variation of mesh size.
So, how should I apply the concentrated forces?
i) one by one clicking each node, creating each node a set and then applied the loads from load module ? (it's tedious/repetitive. I don't want to do it) or
ii) Doing some editing in *.inp file? (But, when I tried with following format, ABAQUS is simply neglecting my edited lines:
node number, direction, magnitude) or
Regards,
Dipaloke
So your input file looks like something like this ? (CLOAD statements for each node ?) :
node number, direction, magnitude
node number, direction, magnitude) or
node number, direction, magnitude) or
...
Question
In order to represent our observations or sight of a physical process and to further investigate it by conducting experiments or Numerically models? What are basics one need to focus ? Technically, how one should think? First, thing is understanding, you should be there! If we are modeling a flow we have to be the flow, if representing a let's say a ball, you have to be the ball! To better understand it! What are others?
Aditya Kumar Mishra replication is tough though i do agree with the expert comments above that physical replication like visualization is a must one of the important criteria I feel is to To assess applicability one must always specify the requirements along with exact what attribute of a previous results of interest.
Question
when I tried to simulate a tesla valve with the compressible turbulent fluid flow for hydrogen (single-phase standard k-ε turbulent physic and heat transfer in fluid physic are used, and the study is stationary), I got the following error:
"Undefined value found.
- Detail: NaN or Inf found when solving linear system using SOR line."
What is the problem?
Bonjour, one of the reasons is the type of mesh implemented and the computer processor you use. To solve these types of equations your computer must be powerful. I recommend you to work with as few meshes as possible.
Question
Hello everyone,
• So, as he mentioned in his paper that he neglected the Marangoni effect. Up until now, one can control the fluid flow with changing surface tension gradient. But since he neglected this effect, I don't know how I can enhance my fluid flow. I am having exactly the opposite fluid flow that he showed in the paper. (please see the attached screenshot of my simulation). His fluid flow is having curls in the molten pool clockwise but mine is anticlockwise. How else I can affect the fluid flow (Marangoni is out of discussion since he neglected and surface tension coefficient is assumed to be constant)?
• He also neglected the latent heat in this paper and used recoil pressure to deform the free surface. But in order to apply the saturated vapor pressure in mass flux, latent heat of vaporization is used. You can comment on it too.
I have implemented all the boundary conditions and equations mentioned in the paper. Still, not able to generate the same results. If anyone can help me with it, I would really appreciate it. I am open to discussion as well through chat system or zoom.
as I explained in my previous answers, all these effects are considered, at least in the manuscript you refer to, as volume forces and their magnitude is obtained from empirical expressions. Both phenomena, the recoil pressure, and the vapor-induced shear stress occur due to the same physical effect, namely the rapid evaporation of material. Thereby, the recoil pressure is simply a pressure acting on the keyhole surface and directed in the inward normal direction of the free surface. The shear stress, however, acts in the tangential direction, which can be obtained with/from the normal inward vector.
Best,
Antoni Artinov
Question
I am trying to solve a time-dependent diffusion equation with finite-difference discretizations using the Newton–Raphson method. However, I encountered some problems in convergence--the solution result changes when changing time step size. Here I want to find some coding examples to refer to. Thank you.
In general, the name diffusion equation (time dependent or not) identifies a linear PDE, whose finite difference discretization leads to a linear algebraic problem that does not require a nonlinear solver like Newton Raphson. This means that your problem is a nonlinear one, for example with nonlinear viscosity (porous media equation and such), and that an implicit method is being used for the time discretization. The correct way to approach these problems is to write the space and time discretization (there is no mention of what time discretization method is used) which leads to a (potentially large) nonlinear system to be solved
at each time step. Then at each time step a nonlinear solver is used to compute the solution of thie algebraic problem. Any of these steps might have been coded incorrectly leading to the problem you mention. One simple way to check what is going on is to compare with the results of a simple explicit method (say forward Euler) employed with a very small time step, such a method would not require NR iterations and therefore any incorrectness in the NR solver would not affect it.
Question
Re: ARTICLE: "Should Type Theory replace Set Theory as the Foundation of Mathematics?" BY
Thorsten Altenkirch
Type Theory is indicated (by the author) to be a sometimes better alternative and a sometimes-replacement for regular set theory AND thus a sometimes better replacement for the logical foundations for math (and Science). It seems to allow turning what is qualitative and not amenable to regular set theory into things that can be the clear particular objects of logical reasoning. Is this the case? (<-- REALLY, I am asking you.)
It is very rarely, if ever, I have addressed anything that I did not have a good understanding of; BUT, here is the exception (and a BIG one). (I HAVE VERY, VERY little understanding of this Article -- even from the most crude qualitative standpoint. You would say I should have researched this more, but it in not my bailiwick , only more confusion, on my part would likely occur, "shedding no light". My sincere apologies. ANYHOW:
:
If indeed things are as the author, Thorsten Altenkirch, says: it seems different things (other than those related to standard propositions in regular set theory) could widen the use of set theory itself yet retaining (including) all of regular set theory (with all of its virtues, as needed). BUT, in addition it is indicated it could be applied to areas (PERHAPS, like biological and behavior science) where present set theory (and the math founded on it) cannot now be applied.
"[ The ] type theoretic axiom of choice hardly corresponds to the axiom of choice as it is used in set theory. Indeed, it is not an axiom but just a derivable fact."
More Quoting of the author: "Mathematicians would normally avoid non-structural properties, because they entail that results are may not be transferable between different representations of the same concept. However, frequently non-structural properties are exploited to prove structural properties and then it is not clear whether the result is transferable." .... "And because we cannot talk about elements in isolation it is not possible to even state non-structural properties of the natural numbers. Indeed, we cannot distinguish different representations, for example using binary numbers instead." ... "we can actually play the same trick as in set theory and define our number classes as subsets of the largest number class we want to consider and we have indeed the subset relations we may expect. ... Hence Type Theory allows us to do basically the same things as set theory" ... as far as numbers are concerned (modulo the question of constructivity) but in a more disciplined fashion limiting the statements we can express and prove to purely structural ones."
"we cannot talk about elements in isolation. This means that we cannot observe intensional properties of our constructions. This already applies to Intensional Type Theory, so for example we cannot observe any difference between two functions which are pointwise equal." ...
"...Hence in ITT (regular set theory) while we cannot distinguish extensionally equal functions we do not identify them either. This seems to be a rather inconvenient incomplete- ness of ITT, [ (common set theory)] which is overcome by Type Theory (HoTT)"
"[It] reflects mathematical practice to view isomorphic structures as equal. However, this is certainly not supported by set theory which can distinguish isomorphic structures. Yes, indeed all structural properties are preserved but what exactly are those. In HoTT all properties are structural, hence the problem disappears. ..."
"While not all developments can be done constructively it is worthwhile to know the difference and the difference shouldn’t be relegated to prose but should be a mathematical statement." [AND}: ...
"Mathematicians think and they often implicitly assume that isomorphic representations are interchangeable, which at closer inspection isn’t correct when working in set theory. Modern Type Theory goes one step further by stating that isomorphic representations are actually equal, indeed because they are always interchangeable."...
..."The two main features that distinguish set theory and type theory: con- structive reasoning and univalence are not independent of each other. Indeed by being more explicit about choices we have made we can frequently avoid using the axiom of choice which is used to resurrect choices hidden in a proposition. Replacing propositions by types shows that that the axiom of choice in many cases is only needed because conventional logic limits us to think about propositions when we should have used more general types."
Oh, here's the link to THE ARTICLE:
The answer is simply no. Additionally, considering "realist (platonic)" and "non-realist (non-platonic)" doesn't actually help with the answer I am going to provide, and the article also begs the question. It's like asking why you like music, is it because it sounds good, or is it because it makes you feel good? Well, that depends on what you mean! Equally, asking a working mathematician about the independence of math, or the construction of math will get you very confused looks. They way one treats math, is ever which is the most convenient, or the most sensible to the person. As such, the article in question does not particularly respect nor delineate the historical and functional differences between these two foundations of mathematics very well. Mathematics is a very broad, messy, overlapping subject. In fact, most of the math I regularly use does not really involve calculations, or functions per se. But, as the article is a pre-print, I assume it simply represents a scribbling of his thoughts.
In order to elucidate my answer better, some background in the cartography of mathematics is needed. There are many different universes (formal distinct foundations of mathematics as unique fields) of mathematics that have their own level of reasoning, and focuses. To name a few, category theory, abstract group theory, analysis, proof theory, many-valued logic, and the list just keeps going. All of which are employed at different levels to ascertain certain properties of math, or even to articulate certain questions. For instance, if one wants to study the different universes of mathematics, category theory is generally involved, and the object considered is called a topos. Or if one wishes to study how numbers work, one can employ number theory to study them as unique things, or you can employ analysis and study them as functions, or you can study them with group theory and consider them as action as well. In this view, no field of mathematics has a primacy over other mathematics, only advantages to the inquiries at hand.
Here is a simple question that I think illustrates the point I am making: is two an element of four, or not? That is to ask, in the construction of numbers, are they considered logically unique (aka type theory), or as informal primitives so that numbers are just simply numbers (set theory)? It is in fact this very question that helps separate type theory and set theory. This question, is akin to asking is meaning found in words or what the words represent? However both are true to a certain degree, and from different perspectives. If we are partial to the former, we are essentially asking, does the construction of words form the meaning they express? Yes, but only if we consider meaning as inherent to language alone (intensional). That is language makes meaning, not the world outside of our minds. If we are partial to the latter however, then words denote things, they are analogs to events, and point to common descriptions that we see (extensional). In the same manner, type theory considers numbers as things in themselves, to say "there are two dogs" is to say two dogs. Because the number two is different then dogs. Equally, computer scientists often employ type theory because it logically constructs things, whereas, mathematicians like set theory because its very good at describing things, and there relationships. It would be very burdensome for a mathematician if we had to logically construct everything from the bottom up. Instead of saying, let us consider a sequence of integers. The computer scientist would have to define every part of that sentence.
I hope this helps clarify the question.
Question
Consider the powerful central role of differential equations in physics and applied mathematics.
In the theory of ordinary differential equations and in dynamical systems we generally consider smooth or C^k class solutions. In partial differential equations we consider far more general solutions, involving distributions and Sobolev spaces.
I was wondering, what are the best examples or arguments that show that restriction to the analytic case is insufficient ?
What if we only consider ODEs with analytic coeficients and only consider analytic solutions. And likewise for PDEs. Here by "analytic" I mean real maps which can be extended to holomorphic ones. How would this affect the practical use of differential equations in physics and science in general ? Is there an example of a differential equation arising in physics (excluding quantum theory !) which only has C^k or smooth solutions and no analytic ones ?
It seems we could not even have an analytic version of the theory of distributions as there could be no test functions .There are no non-zero analytic functions with compact support.
Is Newtonian physics analytic ? Is Newton's law of gravitation only the first term in a Laurent expansion ? Can we add terms to obtain a better fit to experimental data without going relativistic ?
Maybe we can consider that the smooth category is used as a convenient approximation to the analytic category. The smooth category allows perfect locality. For instance, we can consider that a gravitational field dies off outside a finite radius.
Cosmologists usually consider space-time to be a manifold (although with possible "singularities"). Why a manifold rather than the adequate smooth analogue of an analytic space ?
Space = regular points, Matter and Energy = singular points ?
For a function describing some physical property, when complex arguments and complex results are physically meaningful, then often the physics requires the function to be analytic. But if the only physically valid arguments and results are real values, then the physics only requires (infinitely) smooth functions.
For example, exp(-1/z^2) is not analytic at z=0, but exp(-1/x^2) is infinitely smooth everywhere on the real line (and so may be valid physically).
One place where this happens is in using centre manifolds to rigorously construct low-D model of high-D dynamical systems. One may start with an analytic high-D system (e.g., dx/dt=-xy, dy/dt=-y+x^2) and find that the (slow) centre manifold typically is only locally infinitely smooth described by the divergent series (e.g., y=x^2+2x^4+12x^4+112x^6+1360x^8+... from section 4.5.2 in http://bookstore.siam.org/mm20/). Other examples show a low-D centre manifold model is often only finitely smooth in some finite domain, again despite the analyticity of the original system.
Question
Can anyone please help me write a MATLAB program to find the temperature distribution (By numerical method) across a composite building wall subjected to periodic boundary conditions?
Dear Debashish,
You may find the Matlab code for chapter 2 of my book:
A Compendium of Partial Differential Equation Models, CUP
can be adapted to your problem. It is based on the "Method of Lines".
I hope this helps.
Regards,
Graham W Griffiths
Question
I'd like to draw a simple model on Plaxis LE designer but I did not find any guideline video that could help me to design it.
The model sample I attached. Please I hope any one can help me as fast as you can
Thanks
Nesrine El Houari Thank you but already check the manual and did not mention it
Question
I am trying to model a fault plane within an infinite soil/rock medium with a prescribed in-situ stress state to see its impact. How can I input my in-situ stresses into ABAQUS? any help appreciated thanks!
Hello,
Proceed according to the attachment.
Question
Dear all,
What are the factors to be taken into consideration when modeling stone columns in FLAC 3D? Are there differences between the modeling of stone columns and piles?
For using piles in FLAC 3D, alot of parameters of every pile element should be determined such as bending moment and shearing force.
If you use stone columns in FLAC 3D, only some parameters of stone zone should be determined, but bending moment and shearing force of every pile element can not be obtainedobtained and the infill materials of stone columns are totally different with that for RC piles.
Best regards,,,
Question
my numeric data is in 1, 0 & 0.5. how can I perform structure analysis?
Question
I want to solve a nonlinear equation G(W)=0 via Newton-Krylov-hookstep method, which comes from the attempt of finding a periodic orbit of the 2D flows in a rectangle。
I had found a possible approximate value W0, and |G(W0)| is about 7. But now the Newton-Krylov didn't lead to a fast decrease of |G(W)|, and it stagnates around 6.9~7.
Is there some remedy I can do to make |G(W)| decreases fast enough?
Thank you very much.
P.S. The variable 'W' represents the FFT coefficients of w(x,y) in MATLAB, thus the real residual should be |G(W0}|/N^2, and the corresponding values of w(x,y) is quite satisfactory for the attempt of finding a periodic orbit. In my opinion, it's a pity to discard this value, though I have to agree that it may be a bad initial guess in reality.
My advice is to find better starting point using simple approaches (golden rate etc) and to read the theory of Newton's methods. Regards
Question
To the best of my knowledge, the first rigorous approach was presented here
and all studies followed that approach.
But I wonder what about the approach to follow in case of an integral equation that is discretized?
Have you ever seen some study wherein the modified integral equation is illustrated?
Paolo I know that paper and the answer is yes and not... The local truncation error is expressed in terms of pointwise derivatives but I mean an expression of the LTE wherein the integrals appear explicitly, congruently to the initial integral equation.
Ok, let me say that we could think to start from any MDE derived in a classic way for a PDE and integrate its LHS and RHS to generate the integral modified equation.
But if we start from the original idea that the weak equation does not require the differentiability, we should not introduce any Taylor expansion in space. Otherwise we should regularize the variable and define the Taylor expansion for the smooth averaged function.
Question
Dear Colleagues,
Are You by any chance familiar with any data/papers on the subject of RC or prestressed circular hollow sections (in columns, beam-columns, beams) subjected to preferably both axial force and bending moment or maybe under pure bending at worst. If Yes please share the links in the comments below.
I am interested mostly in experimental research but numerical analyses would also be appreciated.
Best Regards,
Bartosz Grzeszykowski
Question
Hello friends
Nowadays I am trying to use Code_Aster to simulate CABLE . I want to know how to add a force like this F=0.5*velocity^2 on selected nodes?
And how can people add a triangle distributed force on a moving cable whose coordinate is changing with time .
if you have a time-dept simulation, you can create a multiplyiting function with LIST_REEL and DEFI_FONC.
Franco
Question
Hi
I wanna solve partial differential equation in terms of x and t (spatial and time), As I know one of the most useful way for solving pde is variable separation. well explained examples about mentioned way are wave equation, heat equation, diffusion....
wave equation is Utt=C^2 .Uxx
in other word; derivatives of displacement to time, equals to derivatives of displacement to spatial multiplied by constant or vice versa.
however my equation is not like that and derivatives are multiplied to each other.for example : Uxx=(1+Ux)*Utt
Im wondering how to solve this equation.
I will be thankful to hear any idea.
Dear Alireza Akbari looks like your equation is a nonlinear PDE, there are tables for those:
However I could not find yours, but don't worry, I tell you a trick we use in MHD.
1. You linearized it, i.e., you solve the PDE as a function of ei(k.r - omega t)
2. You get a complex polinom, but I don't see any parameters in your equation.
3. Anyway you can try an algebraic manipulator such as math or maple and find the roots. However, I find it strange that there is not a parameter, you need it to scan the complex solution.
Best Regards.
Question
I want to solve analytically a coupled 2nd order space-time problem, originated from an optimal control problem. One of the problems is forward, another is backward in time. For example, (i) $y_t-y_{xx}=u, y(x,0)=0, y(0,t)=0, y(1,t)=g(t)$ (ii) $-p_t-p_{xx}=y, p(x,T)=0,p(0,t)=0, p(1,t)=h(t)$ with the coupling condition $p(x,t)+c*u(x,t)=0$ in $(0,1)\times (0,T)$. I have tried separation of variables, but it is getting complicated, any suggestions?
PDE's can be solved with the software Mathematica. They have a free version online.
Question
I'm planning to perform a low-velocity impact analysis on a sandwich composite consisting of top and bottom face sheets (Unidirectional fibre reinforced) with 4 plies each and a core (aluminium). The thicknesses are small relative to the other dimensions. After going through various materials, I'm still confused whether which one among the following combinations of elements I should go for -
1) SC8R (Core and face sheets)
2) SC8R (Core) and C3D8R (Face sheets)
3) SC8R (Face sheets) and C3D8R (Core)
4) C3D8R (Core and face sheets)
SC8R - Continuum Shell Element
C3D8R - Solid Element
Question
Hi
I'm using three different performance criteria for evaluating my model:
1.Nash–Sutcliffe (NSE)
2.Percent bias (PBIAS)
3.Root mean square error (RMSE)
You can suppose that I used a regression model to estimate a time series data such as river mean daily discharge or something like that.
But for a single model and a single dataset, we saw difference performances for each criteria.
Is this possible? I expected that all of these three criteria have same results.
You can see the variation's diagram of these criteria in appendix pic.
Thanks
Due to different factors
Question
Dear friends
I am trying to use CODE_ASTER , a finite element software to simulate a fish cage‘s movement. I am using HHT method to solve the problem with alpha=-1/3. My force is added with Morison equation like this : fn=0.5ρCdLDV|V| and it is added at each selected time step(defined before calculation).
When the velocity is under 0.5m/s, my job seems well ,but when I change a higher velocity, the deformation become pretty bad, the cage is oscillating . In my job, there is no structural damping ,only the numerical damping is added. I am wondering what will cause this problem? If it is the problem of implicit solver or the way I add the force?
There is a GIF of the problem. I hope to get some ideas.
Dear friend,
This problem you describe has been known for a long time and can be due to several causes.
Firstly, the use of FEM for the calculation of mesh cages is not always recommended. This is due to the fact that the shape changes of the netlike structure can be relatively large. This is due to the fact that the hydrodynamic loads are relatively large compared to the tensile forces in the mesh bars.
A second reason may be the discretisation of the netlike structure. A discretisation that is too fine-meshed can lead to numerical problems, a discretisation that is too coarse may be physically impermissible. Here you could try a little - also in conjunction with the hydrodynamic loads.
And last but not least, you should allow a slight stretching of the net material. You will see that this has a positive effect on the peak loads in the mesh bars (they become smaller), which are ultimately responsible for the structural vibrations.
If all this does not help, you need to test what frequencies of the waves are allowed, that means also in the hydrodynamic loads (you mentioned the Morison equation, which is known to consist of the Froude-Krylov force, the hydrodynamic inertia force and the viscous load).
Good luck, Mathias Paschen
Question
when the analysis is done by the Axisymmetry model, the out put of force vs displacement is obtained by the kN/rad. simply we multiply 2pi and get force in kN. in this case square footing (150x150mm) is half.
but when the same analysis is done the Plain stain model, the output is obtained kN/m. so which length of width is multiply to get force or how to get bearing capacity. use square footing 150x150
Note:
for rectangular footing if your conducting plane strain condition it will become strip footing?
Question
In a flow over rotating cylinder simulation, if the cylinder keeps changing its shape with respect to different angular position during rotation. How to specify the shape changes of the cylinder in the transient analysis case?
Ramarajan J. If the motion is prescribed or can be described by formula, than the approach will be no FSI simulation needed.for purely the rotational motion it would be sufficient to assign the calculated surface velocity as a boundary condition to the walls of the rotational spherical body. For the additional axial displacement, the body real needs to be displaced with regard to the originally generated mesh and this could be accomplished by mesh morphing (in CFX) or the so-called "moving-deforming mesh" algorithm in Fluent.In contrary, if the rotational spherical body can freely move in the fluid under the influence of acting hydrodynamic forces, then a description of the body motion is not possible by simple formula. In this case not a FSI, but a 6DOF (6-degree-of-freedom) simulation would be required. The body itself is not deformable, I assume. So its motion can be described as the motion of a rigid body under the influence of the acting hydrodynamical force and moment on its center of mass. Combining 6DOF with moving-deforming mesh would then do the work.
take this video as an example: https://youtu.be/pn0J_XSOkds
Question
Dear researchers.
I am studying the vibration of a blade in function of rotational velocity.
the blade feedback through ANSYS is presented in the attached picture.
Why the feedback is instantaneous in the numerical study while in the experimental it is a continuous sinusoidal (Measure with Laser vibrometry)?
is there any thing wrong I am doing in the numerical analysis? how to compare in this case
There are two behavior values that you need to set, one for the "reference" and the other one is for the "mobile" that needs to be "Rigid" in your case. Attached please find a sample analysis that I did long time ago. Two joints are applied in this model. The top joint is Revolute joint and the bottom one is Planar that enables applying side displacement while the part is rotating.
By the way, in addition to rotational velocity, rotational acceleration is available with joint load that can simulate the impact part of your simulation (sudden start).
In my opinion, the stationary solution you got right now is good enough and performing a transient analysis as I said earlier is more expensive and time consuming but it is still an option.
Question
Hello dear colleagues,
I couldn't figure out what are the required material properties to perform fatigue simulation using ANSYS SMART. What should I add to predefined structural steel to proceed with the simulation?
Thank you very much for your help.
I hope you can find what you are searching for concerning "deltas".
Question
Dear scholars,
my topic of interest is the numerical analysis of weldments with special interest in material heterogeneitiy (base material, coarse- & fine-grain-zone, filler material). For this purpose, i modeled a quarter of a 3D-butt-welded sample under displacement load. Each particular zone was modelled with specific material-data (for all in general: multilinear-plasticity; isotropic hardening), Hollomon-extrapolation was used to obtain realistic results.
The results of the numerical simulation show huge discontinuities in zones of material transition when it comes to the internal stresses (for von-Mises-stress, see the attached PDF). In my opinion, these discontinuities have their origin in the simple fact, that the nodes on the borders between two different materials can't "smooth out" the two differing material behaviours. This arises from the fundamentals of FEA and can't be "improved" by ANSYS-specific modelling steps.
Am I right with my conclusion or does anyone have any advice for me in this context? Any advice is highly appreciated. In case there are still questions, I have attached my APDL script. Otherwise don't hesitate to ask, if more information is needed.
The basic facts of my numerical approach:
- Calculation using APDL script in ANSYS
- Notch stress analysis on 2D/3D bodies
>>> 2D: Plane183
>>> 3D: Solid186 & Solid 187
- Multilinear-plasticity material models with isotropic hardening
- Due to lack of experimental data: stress-strain diagrams of the 4 material domains from secondary source.
>>> Hollomon extrapolation already performed there
Many thanks for any help.
Timo Siemer
Your output is a result of FEM theory, which ensures only force equilibrium at nodes and displacement compatibility across adjacent elements, but not equilibrium of stress. Given a deformed mesh, the stress in a node changes depending on whether that node belongs to one element or to the adjacent one.
In addition, it seems that yor model has a geometrical singularity (zero notch radius), where the theoretical stress is clearly infinite (whilst the FE stress is finite, no matter how fine is the mesh).
Finally, it is not clear to me the purpose of your analysis and what result you expect from it.
Question
Is there a best method for simulating a tensile test with a strain rate of 1mm/min that experimentally took minutes while obtaining accurate break results? Is it necessary to run at a specific strain rate like when testing experimentally, or could I run any displacement in any end time and get an accurate stress-strain curve?
Hello, I am attempting to use ANSYS to simulate the tensile testing of a polymer according to ASTM D638. This entails a strain rate of 1mm/min.
I'm having the following issues:
- resources do 1 of the following: a) use explicit dynamics using very fast strain rates eg. displacement = 0.01m, time = 0.001s, or b) they use static structural with a displacement and get a result with no fracture, though it seems much more common in literature.
Following a), my imported material causes an error when break would be expected, where time step goes too small or energy error is too high, but no break happens. Then, if I try to apply the displacement over a long study time, like 1mm/min by applying a displacement and increasing the end time to ~60s, or by applying a velocity of 1mm/min and setting a 60s end time, I get computation times of nearly days and then it fails quite early while saying "energy error too large" or "time step too small".
To reiterate, is there a better, more time-efficient method for performing this? Am I understanding end time and strain rate wrong? Pictures can be added for clarification if requested.
Dear Nate Tran ,
It is a bit difficult to understand how you setup your numerical model. I mean you did not say anything regarding how the material is setup (it is setup with Stress-Strain curve or ...) and what nonlinear model is used for this simulation (e.g., Multilinear Kinematic Hardening, Bilinear Kinematic Hardening and etc. ). For that reason I can suggest general guidelines for this type of simulation.
Also, if you haven't considered any fracture concept (e.g., XFEM, etc.) you can't visually see the breakage happening in your model. Therefore, you only see that the analysis is not converged and consequently terminated.
Another important thing is that, you are trying to see the effect of different strain rate in your analysis. If this is the case, then I suggest you use transient structural analysis instead of static structural analysis. Static structural analysis doesn't consider time integration in the numerical analysis and you won't be able to see the effect of different strain rate.
Question
When solving Ordinary Differential Equations in time using, say R, is common to find ourselves in a part of the parameter space that does not allow for correct solutions. For simple models it is easy to derive parameter conditions in a way that we only end up with appropriate solutions.
Consider a complex ecological system with many species, that is, multiple ODEs. It can be difficult or impossible to arrive analytically at the intervals for parameters that lead to proper states (i.e. all species abundances should be positive for example). We can try to choose random parameter combinations until we get results that make sense, but often times we get hyper-exponential blow-ups in growth.
Is there any numerical or analytical trick that can help in avoiding these solutions?
For me, too, it is a bit unclear if your question is about divergence in numerical time integration, or about determination of stability boundaries.
Adding to what the Gabriel Thomas wrote, if the question is about stability boundaries, then as an alternative to a brute force grid algorithm you could also consider numerical continuation and bifurcation analysis. There exist a number of freely available software implementations. One of these is MatCont, co-developed by Yuri Kuznetsov from Utrecht. (If you need pointers, feel free to let me know.)
Question
We are trying to establish a method to calculate the diffusion coefficient of resin materials. What methods are available to derive the diffusion coefficient of composites from the diffusion coefficient of matrix? The filler we are using is glass and the resin is PPS. I know that the Springer method exists, but are there any other formulas that take into account the angle, volume, and particle size of the filler?
Please, share with me any report on Springer method for derivation of the diffusion coefficient of composites from the diffusion coefficient of matrix...
Question
Dear Researchers, I ask for help;
This is in COMSOL Muliphysics ver.5.6
I am tryring to solve a model of an Energy Power Cable which is burried in the soil, is a 2D model
I choose to couple the phenomena of: -Electrostatics, -Electric Currents and -Heat Transfer in Solids (this last one is coupled using the 'Electromagnetic Heating' sub-module within the AC/DC module).
I already could solve the Electric Potential and the Electric Field (both, E and D) distribution,
But as much as I tried, I cannot understand how to solve correctly the Heat Transfer part of the model
The coupled phenomenon of Heat Transfer is due to the Joule Effect, due to the Electric Current/Voltage passing across the conductor.
When I solve for the Temperature Distribution I get :
- All the model is at the same temperature
- The value of the Temperature is negative, and
- This value is x10^18 K
Defenitevely something is wrong, very likely with the boundary condition of the Heat Source I'am trying to stablish.
It could be an evident-to detect mistake, but I cannot understand it
I am attaching the pictures
The first one is of the view 100% zoomed out, to see the complete geometry (I am including the seccion of the soil in my model),
and the second image is the view zoomed in of the geometry of the Cable
Please, does any know, and can help me, Why I cannot solve this model correctly ?
I will really appreciate it,
Best Regards !
I see, I did find the imput for the Volumetric loss density, electromagnetic (ec)
But, when I fix the Heat Source with this source, I got no Temperature (see attached image please)
Question
Dear Researchers :
Recently I asked an official quotation (with all the requiered concepts) from ANSYS and from COMSOL to implement the same type of License and the same set of modules, the scheme of the License are not exactly the same , but very close ,
For both software I'm interested in being able to solve applications with the Structural Mechanics Module and the Electromagnetic Module
But in general, If I place both final prices in the same footage, I realise ANSYS is always more expensive (at least today) than COMSOL (roughly between 35 - 40 % more)
Does anyone with experience in this may know one of the reasons why this is so ?
Regards !
Since I got more experience with scripting, I want to share my opinion from scripting point of view.
I found ANSYS more interesting than COMSOL because of its outstanding scripting capabilities. Depending on the module you want to use, ANSYS either uses JavaScript (e.g., DesignModeler and Mechanical) or IronPython (Workbench interface, Fluent etc.) in the background. In addition, Ansys provided APIs in IronPython programing language for almost all its modules (e.g., DesignModeler and Mechanical) which makes automation very easy. I mean you are not going to be limited to go with only one programming option and different gateways are provided for programing.
whereas, in COMSOL you will be limited to APIs provided in Java only, which is fine too.
This is my two cents and hope other people can share more great opinions from other perspectives.
Thanks,
Question
Dear.
Since I am interested ;ore in understanding the way sensors work, so I would like to start a numerical analysis for several sensors to try to combine that with experimental results.
an example of the sensors I would like to simulate is:
My aim is to use the simulation to understand at the first place and a starting point toward the development of those sensors.
any tools and any advice are welcome.
Question
Hello everyone
Recently, I've been working on constructing the waveform for the simple PCB interconnect by means of existing algorithm, which means I don't want to use the commercial software.
To be simple, I suppose the topology is just TX + transmission line + RX (See Fig. 1)
At the beginning, I just wanted to quickly estimate the waveform with ideally initial waveform (See Fig. 2)
Unfortunately, I had no idea to estimate the TX output impedance and RX input impedance.
Eventually, I thought I had to build the waveform by means of interpreting the IBIS models.
There are [Pullup], [Pulldown], [POWER Clamp], [GND Clamp],... in the IBIS.
However, I don't know how to use them to construct the waveform and get the internal impedance.
My question : How to do that with the IBIS information?
(Suppose the IBIS is 4.2 version)
Sir Szuhsien:
You are welcome, and i wish you good health and happiness....
Question
I am analyzing two adjacent interconnected rectangular channel flow patterns. The image of my numerical model is attached below.
The fluent solver was pressure based, and velocity formation was absolute. The SIMPLE algorithm was used. Laminar regime was selected and energy equation was kept on. Boundary conditions were checked carefully. Inlet velocity and pressure outlet conditions were applied. Uniform Heat flux was applied at the bottom face. Solid fluid interfaces are thermally coupled. Second order upwind equations were used for energy and momentum equations. The residuals were kept 10^−5 range, and the solution was fully converged.
I have drawn a centerline inside a mini-channel for observing velocity distribution. Is my solution right? and velocity profile having zigzag is okay? if not, pls explain.
Wish you all the best luck!
KHOA
Question
I want to do comprehensive study of errors in variables from both numerical analysis and statistical viewpoint and compare the results with regression for selected parameter estimation problems in my domain where it is expected to perform better in terms of accuracy. These problems are of type linear and non linear regression. I want to check if the method under study is an improvement over generalized least squares. I am including multiple factors like accuracy, computational efficiency, robustness, sensitivity in my study under different combinations of stochastic models. What kind of statistical analysis/ experimental design/metric/hypothesis test is required for a study of this nature to establish superiority of one method over another(to make a recommendation of one method over another for a particular class of problems)
Maybe you wan to consider the recursive least squares algorithm (RLS). RLS is the recursive application of the well-known least squares (LS) regression algorithm, so that each new data point is taken in account to modify (correct) a previous estimate of the parameters from some linear (or linearized) correlation thought to model the observed system. The method allows for the dynamical application of LS to time series acquired in real-time. As with LS, there may be several correlation equations with the corresponding set of dependent (observed) variables. For the recursive least squares algorithm with forgetting factor (RLS-FF), adquired data is weighted according to its age, with increased weight given to the most recent data.
Years ago, while investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the RLS-FF algorithm to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer, hence giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). The proposed (adaptive) control algorithm compared favourably with PID. Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):
Question
I am simulating a rectangular water channel. To validate my numerical results, I want to present a graph containing the enhancement of Nu for this channel with several Re. Then, I compared this variation with another's study where the hydraulic diameter is not the same, however, both channels are mini-channels.
For example:
In this paper - Under Section 3.1:
The authors validated their model with Fan et al., Ho et al, and Moraveji et al. However, their hydraulic diameters are not same. How is this comparison valid?
To understand how to compare your results with an experiment or literature results, please learn the theory of Dimensional Analysis. According to this theory, a phenomenon is governed by dimensionless numbers. For example, in one case, the Nusselt number is affected by the Reynolds and Prandtl numbers. Therefore, when you compare the Nusselt numbers you get with the Nusselt numbers from the literature, you must compare them to the same Reynolds and Prandtl numbers. For the case you are comparing, you need to equate the definitions of Re, Pr, and Nu between your case and the case in the literature. For example, if the Re and Nu numbers are defined by involving the hydraulic diameter in the literature, then you calculate your results at the same Re and Pr.
Good luck....
Question
I am doing 3pt bending test in LS-Dyna with a glassfibre-epoxy sample. So it is a non-linear dynamic (quasi static) problem. I assume it is a implicit problem since the event is slower and the effects of strain rates are minimal. But my professor used explicit control card to solve this. what difference can it give?
Explicit solver can be used for modelling slow problems if you use appropriate time scaling or mass scaling.
Without the scaling, the run time will be very long since the load is applied at a very slow rate. And with too much scaling, the results will be incorrect.
When you say he used Explicit, I assume that he used explicit solver with the actually loading rate.
Strain rate effects are related to the rate of displacement or deformation....not whether it is implicit solver or explicit. You still can simulation dynamic problems with implicit analysis and model quasi-static events with explicit, but you need to know what are the suitable keywords to add in both cases.
Here is how I did 3-point bending. I used explicit because I wanted to apply a dynamic load
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Hi
Simon Smith Thank you so much for your explanation 🙏
Question
While performing numerical analysis using Ansys workbench software. I have performed compression analysis in both static structural and transient structural analysis. In both the cases of the results. I have observed the stress concentration is high at the boundaries of the cylinder sample. why the stress concentration is high in the compressive samples ?
Fluids interact with the boundary and cause stresses and strains. In fact, the flow of fluid through a cylinder experiences increasing drag as you approach the edge of the cylinder. In compression, which is just another way of analyzing fluid flow, the interface is still causing an increase in strains. Additional effects are involved, like, surface tensions, &c.
Question
Dear
I am performing a series of structural analysis test through software, for some model I already have the experimental results so the selection of mesh is related to this results, the good mesh is the one who gives the best approximation to the desired results but....
In Case we are testing a new design or a new structure without any previous knowledge , how to know the correct mesh?
Can you describe your desired research and the numerical approach and corresponding software in more detail so that I may help you?
Kindest regards,
Question
I want to solve a second-order non-linear and non-homogenous order differential equation using the non-linear shooting method and fourth-order Runk Gutta using Python?
This is a typical two-point boundary values ​​problem. It's best to replace the second-order equation with two first-order equations. Then you just need to use any method of minimizing the function and integrating the equations. The possible stiffness of the equations can make numerical calculations difficult. In the case of strong non-linearity, multiple solutions can also be expected.
Question
I would like to know if the SUPG method has any advantages over the least squares finite element method?
Dear Zmour,
It can be better in term of diffusion convection reaction. My opinion is little different, the least-squares method has better control of the streamline derivative than the SUPG.
Ashish
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I am currently working on PCF design and numerical analysis to achieve high negative chromatic dispersion and low confinement for high-speed optical telecommunication networks. Any simulation assistance as to how to use the COMSOL multiphysics tool to achieve these objectives?
Best regards,
LC
Question
Dear Colleagues and Authors,
plenty of problems in mathematics, economics, physics, biology, chemistry, and engineering, e.g., optics, radar, acoustics, communication theory, signal processing, medical imaging, computer vision, geophysics, oceanography, astronomy, remote sensing, natural language processing, machine learning, non-destructive testing, and other disciplines, can be reduced to solving an inverse problem in an abstract space, e.g., in Hilbert and Banach spaces. Inverse problems are called that because they start with the results and then calculate the causes. Solving inverse problems is a non-trivial task that involves many areas of Mathematics and Techniques. In cases where the problem is ill-posed, small errors in the data are greatly amplified in the solution, and therefore, regularization techniques using parameter choice rules with optimal convergence rates are necessary.
Currently, I am editing a special issue on "Numerical Analysis: Inverse Problems – Theory and Applications 2021" with a Switzerland-based "Mathematics" MDPI Journal.
I would like to draw your attention to this possibility of submitting research articles:
Please let me know if you need any help.
Thank you for your kind consideration,
Christine Böckmann
Dear Prof. Christine Böckmann, that's great. Feel free to invite me as a Reviewer.
Animasaun Isaac. L. (PhD)
Department of Mathematical Sciences,
Fluid Dynamics and Survey Research Group, Center for Research and Development,
The Federal University of Technology, Akure, PMB 704, Nigeria, West Africa.
Tel.: +2348034117546
Question
Multi-step methods implicitly use one-step methods as a starter, but we still expect better approximation using the multi-step method. I want to know why?
There is no reason why a method to solve numerically ODEs should have better accuracy if it is multistep. There are methods of the same order of accuracy both in the multistep and multistage - single step class. In general, multistep methods have smaller computational cost per time step, since they re-use previously computed right hand side values, while multi-stage methods are more flexible, especially as far as time step adaptation is concerned. While traditionally multistep methods were preferred, since the 1970 multi stage, Runge-Kutta methods have become more popular (most, but not all, MATLAB ODE solvers are based on multi stage methods). For very large scale applications, where memory occupation is a concern, multistep methods have in many cases been abandoned due to excessive memory requirements (this has happened for example in numerical weather prediction). This classical book
Lambert, J. D. (1991). Numerical methods for ordinary differential systems (Vol. 146). New York: Wiley.
provides a clear presentation of both classes of methods.
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