# Civil Engineering

Why can't an Initial value Problem (IVP) be solvable using the Finite Element method?

It is accepted that given a 2nd order linear or nonlinear ODE au'' + bu'  + cu where a, b,c can be functions of x,u,u' with the prime denoting derivative wrt x  and that if initial values are prescribed then the solution can be obtained using Runge-Kutta methods etc while if boundary values are prescribed then the ODE could be solved using the Finite Element or Finite difference Method. My question is why can't an Initial value Problem (IVP) be solvable using the Finite Element method?

Daniel Nunez · University of Kansas

There are several different Finite Element Methods, not just one. ALL of these methods can be classified in 2 groups: (1) F.E. methods based on fundamental Lemma of Calculus of Variations (Galerkin method, Petrov-Galerkin, Weighted residual, Galerkin method with weak form) and (2) F.E. method based on a residual functional associated with the differential equation (least-squares method).

There are several types of differential equations. Hyberbolic, Elliptic, Parabolic, First order, Second order, etc. HOWEVER, ALL differential equations have a differential operator associated with them and ALL differential operators can be classified in 3 groups: (1) self-adjoint (2) non-self adjoint (3) non-linear.

For a F.E. method to be used successfully for a specific differential equation, the resulting coefficient matrix in [K]{u}={F} must be positive-definite (This means that [K] can be inverted and the obtained solution {u} will be unique).

The following 3 statements are not opinions but Theorems with proofs:

- When the differential operator is self-adjoint: Galerkin method with weak form and least squares process are the only F.E. methods that guarantee positive-definite coefficient matrix [K].

- When the differential operator is non-self adjoint or non-linear: least square process is the only F.E. method that guarantees a positive-definite coefficient matrix [K].

- When considering an IVP, the differential operator is either non-self adjoint or nonlinear. It is never self-adjoint. Hence, the only F.E. method that can guarantee positive definite coefficient matrices for all IVPs is least squares process.

There is a lot of research done to make the Galerkin method with weak form produce coefficient matrices that are positive-definite. These are known as stabilizing techniques. However, all of these techniques, without exception, end up changing the original IVP.

Many people are under the impression that Galerkin method with weak form is the only F.E. method. This is because ALL commercial F.E. softwares are based on this method. The reason for this being that the differential operators of differential equations describing elastic solid mechanics are always self-adjoint, hence Galerkin method with weak form works great! Least-squares process also works great, however, Least-squares process requires additional resources (in terms of interpolation theory) that didn't exist at the time when commercial F.E. softwares started to appear (1960s). Hence, people didn't consider Least-squares process. Around the late 1990s, those additional resources needed for least-squares were invented, and least-squares started being used in the research area. However, since so many companies were built on Galerkin  method with weak form and they are only marketed towards solid mechanics applications, they still continue to use it.

Other methods to solve differential equations such as: Finite Volume, Finite Difference, Runge-Kutta etc suffer from the same disease than Galerkin method with weak form. Meaning, that they do not guarantee positive-definite coefficient matrices. This does not mean that unique solutions are not possible using these methods, but it means that you will only know it after the [K]{u}={F} is obtained and if [K] is not positive definite, then stabilizing techniques must be used. Runge-Kutta method and Finite Difference methods are very easy and fast to implement. Hence they popularity. However,  when considering complex problems where you might end up having a [K] matrix that is a million-by-million, then they might or might not work and if they don't work, stabilizing techniques might or might not give you the right solution.

So to answer your question, F.E. method can be used to solve IVP. Either using Galerkin method with weak from combined with stabilizing techniques (see works of T. Hughes) or using least-squares process. If you are interested on using F.E. method to solve ODEs in time, then you should real this article:

- K. S. Surana, L. Euler, J. N. Reddy, A. Romkes: Methods of Approximation in hpk Framework for ODEs in Time Resulting from Decoupling of Space and Time in IVPs. American J. Computational Mathematics 1(2): 83-103 (2011)

This article explains into details how to handle IVPs by decoupling space and time and as a result, obtaining a system of ODEs in time. Then it compares F.E. methods and other methods such as Newmark, Wilson method. I hope that gives you a better idea of the subject.

How do you perform modeling in simapro for a LCA analysis of water tanks?
Any related papers to assist me in modeling.
Carlo Ingrao · Università degli studi di Foggia

Modeling should be done starting from considering the life cycle of the tank that includes production, use and disposal. I don't know exactly the system you're studying but a tank can be considered as a big container and therfore no relavent impact is to be attributed to the use phase. Therefore, the latter could be neglected. Production should be implemented by accounting for all the material and energy inputs and outputs and, in this way, it would be great if you could collect data on site. Otherwise, you can access literature as the one suggested by Edward. The end-of-life should be modeled considering scenarios adopted in your country. If the tank could be recycled, the avoided product should be included in the assessment, thereby accounting for the environmental gains coming from this disposal treatment. The avoided product is the steel (for instance) that you obtain from recycle and therefore allows avoiding production of the equivalent vergin and the resulting environmental impacts. Finally, the tank should be represented as 1 p (unit) and associated with the service time so that you can calculate the share associated to the functional unit you have chosen for assessment of your system. For instance, if the tank has a 20 year lifespan and is used for storing 10,000 litre of water per year, the impact due to the tank's life cycle to be associated to 1 litre results from the following calculation: 1 p: 10000 litre/y*20 y=x (p): 1 l --> x= 5E-6 p. This is the share of the life cycle of the tank to be associated to 1 litre of water

I hope my answer has been useful.

I wish you all the best and all the success.

• Amir Kessentini asked a question:
RPD technology in civil engineering applications

How  to improve materials in civil engineering construction, by using RPD technology?

Which software is used to draw streamlines in open channel flow?
I have the experimental data of flow field. Can I use it to draw the streamlines?
Mostafa Eidiani · Khorasan Institute of Higher Education

Hi

I think Tecplot too

Which software would be the best for "dome" design?
I would like to design a mosque with a help of a software, where there are several domes.
Mostafa Eidiani · Khorasan Institute of Higher Education

Hi

• Bharat Bhushan Jindal asked a question:
Can GPC at ambient temperature be able to give higher compressive strength at 28 days ?

Practical observation of ambient temperature cured geopolymer concrete doesn't give satisfatory results.

What advice one can give to someone who is thinking of doing Ph.D?
It is an important decision whether to do Ph.D or not. Getting a good supervisor, identifying the right topic for research, computational / experimental facilities available, 3/4 or even more number of years required if working full time and the uncertain future are some of the important items for consideration.
Muralidhar Lakkanna · National Institute of Technology Karnataka

How Nations Fare in PhDs?

Are Kirsch equations for fractured rocks applicable for a borehole penetrating highly fractured rock?

Analytical solution by Kirsch for stresses around the borehole has been studied in great detail for continuous rocks. However, are they also applicable for a borehole penetrating a highly fractured rock? Would these discontinuities alter the state of stress around the borehole?

Ehtesham Karatela · University of Adelaide

Thank you guys for your comments. I have viewed few publications that use these equations to define the stress state in fractured rock mass which was a bit confusing for me. Thank you for the references, they will surely help me.

Cheers

How to find the natural frequencies of truss?

I want to initiate dynamic analysis of truss structure to optimize its weight. Initial reading explore that it need natural frequencies. But I could not found how to get it. Could you please suggest or if possible share related materials?

Ghanshyam G Tejani · RK University

Dear Gurikini Lalitha ,

Regards

Is there a simple method to prepare artificial pore solution corresponding to the cement based systems?

Please advice on any reliable and preferably a simple technique for the synthesis of solution representing the pore solution of ordinary cement system.

Kaustav Sarkar · Indian Institute of Technology Delhi

Thank you Professor X. Ramón Nóvoa

How to assign seismic load on truss for structural optimization?

Dear all,

I want to initiate investigation on optimization of truss structure which is subjected to seismic load. and I don't know how to assign seismic load to truss.

I have worked in the field of truss topology optimization with static and dynamic constraints, hence I am families with some basics of it.

Can any one help me about this topic? and if possible kindly share papers or materials related to this.

Kindly See attached file

Thank you

Ghanshyam G Tejani · RK University

Thanks prof. Grande Ernesto

Is there a non-destructive technique to evaluate the loss in steel rebar due to corrosion in RC structures?

The technique should give the loss of steel occurred over the years before the technique is applied.

Shahabeddin Torabian · Johns Hopkins University

I have had some experiences using half cell potential method.

& ACI-222-3R-11

Does anyone know about modeling concrete filled steel tube using ANSYS by simply merging the common nodes of elements without using contact elements?

Modeling in ANSYS.

Rameshbabu Chandran · Mepco Sclenk Engg. College

thanks professor

What is the effect of water cement ratio on fresh density of concrete?

Fresh concrete density and water cement ratio

S. Abd.El.Aleem · Fayoum University

Yes, as the w/c increases the density decreases.

Is the Exfoliated Kaolinite-clay stronger, in strength, than the normal clay (if there is an article recommended, it will be highly appreciated)?

Exfoliated Kaolinite-Clay.

I dont really get you; in particular which "strength" you refers to. Talking about strenght of interlayer interactions within the clay, the exfoliated kaolinite is rather weaker in comparison to the non exfoliated sample.  I attached for you a paper which deals with the study of interlayer bonding forces in kaolinite  in case it could be useful to you.

Involvement of Quantity Surveyors in Civil Engineering Projects

Factors Militating against the involvement of Qs in Civil Engineering Projects

Deep mixing method, cement stabilized soil
Hi all, I have to make a literature review about this method, so i need a lot of its documents. So would you like to share it, everyone?. Expecially in its engineering behavior. Thanks alot.
Binh Tang Thanh Nguyen · Ho Chi Minh City University of Technology (HCMUT)

Hi Khanh,

I am also going to make a literature review about deep mixing method from now. I found that you started from 2011. Do you have any result now, could you share it to me?

By the way, about reference for the literature review, I read the book http://www.crcpress.com/product/isbn/9781138000056

Binh.

• Miroslava Hajdúchová asked a question:
Does anyone have some tips for determination of phase equilibria in CaO-Fe2O3-SO3-H2O system at 25°C?

Hello, I need to construct the phase diagram CaO-Fe2O3-SO3-H2O at 25 °C. At first I have to determinate the phase equilibria. I try used some method but I had problem with low solubility of each component, especially with Fe2O3. Does anyone have tips what experimental method I should be use? Thank you very much for your answer.

Can someone suggest a rural water filtration solution?
Fifteen communities at my field site rely on a central water treatment system. The system's intake draws water from a river. The river water has high levels of clayey sediment. We are told that this results in the intake becoming jammed.
Hansa Jeswani · Indian Institute of Technology Bombay

We have tested pervious concrete filter for rural water filtration. It is the best option as there would not be any need to change the sand. Moreover the rates achieved are that for slow sand filtration. The basic treatment train would be intake tower followed by a pervious concrete filter and a disinfection tank after the same.

Can strain measurements from RCC beam be related to damage identification?

Vibration methods are used to approach changes in natural frequencies of the intact/damaged (concrete) structures and damage detection is only possible if the damage is significant. Stress-strain characteristics seem to be more reliable approach. Is it possible to relate strain measurements with the damage detection?

Alessandro Schiavi · INRIM Istituto Nazionale di Ricerca Metrologica

You're welcome.

• What will happen when we partially replace 6mm aggregate with coconut shell pieces in flexible pavement design?

Anyone tried? Or can anyone give me link where I will get a good answer?

Mandar Pandurang Ganbavale · BITS Pilani, Hyderabad

Thanks a lot Kaustubh.

Anyone know how I can model a cracking of concrete to reinforce concrete modelling?

I want to model between reinforcing bar and concrete in ANSYS workbench.

Hussien Abdel Baky · Université de Sherbrooke

if you want to represent the model between reinforcement bars and concrete then you have to use contact element in ANSYS then you can use appropriate bond-slip model. Please check my page as I have several papers discuss the FE of RC members and bond issue

What are the advance methods for earthquake resistant design of buildings?

How can these methods be applied in country like Bhutan?

D.K. Jain · Maulana Azad National Institute of Technology, Bhopal

As far as implementation is concerned you may find a good example on seismic analysis and design of building at the following link;

http://www.iitk.ac.in/nicee/IITK-GSDMA/EQ26.pdf

How much can the estimation of the statistical measures of nodal response processes help a damage investigation procedure?

Dealing with a series of nodal response processes for damage identification purposes, I wonder if the estimation of statistical measures (i.e. RMS) may be useful to detect and localize the damage and/or help to reduce somehow the noise present in the data.

Esmaeel Esmaeeli · University of Minho

Hoping that I understood well enough your question, I would like to refer you to the following papers on damage analysis of concrete members and structures. You might be able to generalize techniques described in these papers to masonry structures, as well. If you can't find these papers, please let me know to send them to you.

Park Y, Ang A, Wen Y. Seismic Damage Analysis of Reinforced Concrete Buildings. Journal of Structural Engineering, 111(4) (1985)

Mechanistic seismic damage model for reinforced concrete. Journal of Structural Engineering, 111(4) (1985)

Park YJ, Ang AHS, Wen YK. Damage‐Limiting Aseismic Design of Buildings. Earthq Spectr, 3(1) (1987)

What is the suitability of water content for soft clay model test?
High amount of water ensure ease and uniformity in the mixing process
Shenbaga R. Kaniraj · University Malaysia Sarawak

The shear strength of the clay-water mix should be less than 25 kPa.

Could you name durability tests of FRP-masonry bond done by the laboratories?

Durability and bonding of FRP system on masonry is crucial, especially for possible application in historical context.

Sreejith V. Nanukuttan · Queen's University Belfast

If you are using FRP fibres in repair mortar - Try a pull out test or pull off test. You can core the cover concrete to the level of your FRP (not sure if you are using a fibres, rebar or mesh) and do a pull off test. This will give you an indication of the bond strength between the repair layer and masonry.

Durability test is not necessary unless the masonry has elements that can attack Fibres. If moisture is an issue modify the repair material accordingly or let the masonry surface dry out before application of repair mortar. If either is not possible study the de-bonding in moist condition and if you are satisfied with the results proceed.

Can anybody help me in providing a right procedure for thermo-gravimetric analysis of cement paste samples?
Some perform TGA under nitrogen environment and some under air. Also, some dry their samples before performing TGA and some do the TGA without drying the powdered hardened paste samples. If we dry at elevated temperature before performing TGA, wouldn't it increase hydration?
Rajeev Roychand · RMIT University

Thanks Mateusz

How can we find the natural frequencies of truss? Which theories are generally used by published results?

Dear all,

I want to initiate dynamic analysis of truss structure to optimize its weight. Kindly get problem definition as attachment.

I considered 10 bar trust of size optimization problem to check & compare results of my program with dynamic constraint.

Considered Area=[35.944 15.530 35.285 15.385 0.648 4.583 23.610 23.599 13.135 12.357];% in cm2 % % Democratic PSO 2014, A. Kaveh & A. Zolghadr

E=6.89e10 N/m2
ρ=2770 kg/m3
Added mass at each node = 454 Kg
Constraints w1≥7 w2≥15 w3≥20

I have coded this problem in MATLAB by using all three theories of dynamic constraint, yet I am not getting exact natural frequencies but getting nearer answer. kindly note all other answers are same except natural frequencies.

For more detail kindly see attachment

Angus Ramsay · Ramsay Maunder Associates Limited

Hi Ghanshyam,  really pleased to hear you have sorted you problem and many thanks for letting us know. Angus.

How do i optimize hydro-dam operating parameters using Laplace transform?

This a new project am working on really don't know how to go about it. Require step by step guidance since the system is dependent on head, flow rate and turbine efficiency.

Hello

Here there is a link of a good book that can help you, look at the chapter 4.

You must define what you want to optimize in the operation, usually minimize costs, then define the restrictions, for example Head min or max, and so on.

http://hydrologie.org/BIB/Publ_UNESCO/SR_999_E_2005.pdf

How to bring innovations into UG course students projects?

UG civil engineering course students are required to undertake a project work which involves field work, survey, industrial interaction, design, use of smart materials, solid waste management etc

Narayan Chandak · Galgotias College of Engineering and Technology (GCET)

Give the topics from our side to the group of students and ask them to collect the related material from industry, research organisations, research papers etc.

What I am observing from my students is they are very much enthusiastic and excited to do the given task and bringing quality work.