Alireza AkbariKhaje Nasir Toosi University of Technology | KNTU · Faculty of Civil Engineering
research assistant of geotechnical engineering at khaje nasir toosi university of technology
I'm solving nonlinear second order equation by using finite difference method . finally for calculating value at any desired node, knowing three preceding nodes is required however by knowing boundary condition just one of these nodes becomes obvious and still knowing two other values is necessary. it must be noted there are plenty of guesses for values of these nodes which lead to compatible response.
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.
Im modeling interaction of soil and reinforcement in abaqus. As you know there are two obtaining parameters for soil-reinforcement interface from direct shear test of soil and reinforcement:
1. Friction coefficient between these surfaces
2. Apparent cohesion (adhesion)
for simulating mentioned interaction in abaqus I used surface to surface contact algorithm.
Friction coefficient can be defined in Tangential behavior >> Penalty method, However I can not find any way to insert apparent cohesion of interface.
It should be mentioned that Intrinsic cohesion of soil inserted as a plastic property of soil in mohr - coulomb plasticity. But apparent cohesion between these two surfaces cannot be defined in mentioned part, because this property is related in both surfaces.(its not the plastic property of one material).
Im wondering to hear any suggestion.
Thanks for your attention beforehand.
I wanna model interaction between two different material(soil and reinforcement)in abaqus.
As I know when there is no penetration between these two parts, hard contact must be defined in normal behavior however in my simulation reinforcement penetrates in soil due to loading in normal direction so I think soft contact is required in normal behavior. right??
for this purpose linear relation must be defined but I don't have stiffness (coefficient between stress and over closure).
It should be noted I tried some different value for stiffness just to see effect of that, however the analysis didn't convergence at all.
I'm willing to hear your suggestions.
I know the procedure of modeling modal analysis to obtain natural frequencies(I mean using Linear perturbation step>>frequency and without defining any other loading....) but the problem is all examples I have seen is just for model made of just one material(most examples for cantilever beam) but my model is consist of two or more material( 2layer soil and layer of polymer between these soil layers), for obtaining natural frequencies in this case, my exact question is: I have to run modal analysis for each material separately or all together?!
I should mention that the polymeric membrane part does not have any type of support and its just in interaction with soil( normal and tangential behaviour), and if I run the modal analysis for this part alone natural frequencies for polymeric membrane is zero. while the soil is fixed at bottom and sides and by running modal analysis once for soil alone and another time soil with polymer,the natural frequencies are the same for both conditions. so i'm willing to know any advise and special point to obtain natural frequencies procedure for model consist of two or more materials in abaqus.
Finding more clear behaviour for interface of soil and reinforcement in different situations.