Finite Element Method - Science method

Hello!

It is a bit hard to answer your question without more context. Nonetheless, if the strain on the metal surface doesn't match the experimental values, then I would assume that either your contact definition or the friction coefficient between the two surfaces is not correct. However without more information it is difficult to provide more assistance.

I am curious, how did you measure the strain on the surface experimentally? And did you measure the fiction coefficient between those two surfaces experimentally?

https://gmsh.info/

You can use Gmsh for generating mesh for any FEA solver

Check Point In Surface within Gmsh

Hi, you may be helped by one of my recent publications,

"A p-refinement Method Based on a Library of Transition Elements for 3D Finite Element Applications". Link:

Here, the heat can be implemented at the center of a fourth-order element that transitions from order 4 to 1. I have implemented the refinement procedure to a Matlab app you can use readily. Please reach me if you have any questions.

App link: https://github.com/AdnanShahriar64/P-refinery

YouTube tutorial video link: https://www.youtube.com/watch?v=81O3n6KFZmg

Sir @Tomáš Létal, I also tested the contact statut using the CNCHECK,Auto command and it gives these results about contact statut analysis. Maybe this can give more complet information about the contact definition.

Dear sir @Ajibike Joan Farounbi really thank you so much for your important answer thank you. Definitely, when I got results it seems that in step 1 the program detect contact between wheel and the rail while in step 2 program don't detect any contact and the wheel continue traveling in vertical direction as there is no rail. Please sir @Ajibike Joan Farounbi if you can show me how can I apply your solution in Apdl?

Hi Mr. Azar,

in contrast to the gradient for compliance in TopOpt that only has negative entries (assuming the standard case of a linear model and positive material stiffness...), the sensitivities for stress can have both signs. For compliance this simply means that adding material anywhere always will reduce the overall compliance of the part so the performance is always increased. For stress however, adding material can either reduce the stresses in some areas (negative gradient sign) but sometimes also increase the stresses (positive gradient sign), so more material is not always better in a stress-based TopOpt especially around sharp corners. Now for the magnitudes: Using p-norm will introduce a weighting of the stress values and also their sensitivities to derive a single global stress measure from a large number of local stress values. The currently highest stress value will get the highest weight and all other values will quickly get very low weights the further away their stress values are compared to the current maximum stress value. This is the “trick” used to replace the maximum stress by a differentiable expression using the p-norm. A very low sensitivity magnitude means that a certain design variable has negligible effect on the change of stresses the currently highest stressed regions. Locally it may still have a significant effect on local stresses in other regions but not on the highest stress values that make up the largest contribution to the global stress measure.

So yes, you have to expect everything (negative and positive values and high and very low magnitudes of sensitivities) in a stress-based TopOpt using p-norm.

Best regards,

Olaf

Masoud Ahmadi You might be interested in http://www.geuz.org/gl2ps/

Danish Fayaz

Many thanks for your response.

I do not think it is that easy, as for Kirchhoff plate there are three unknowns at every node ( transverse disp., and two rotations). The two rotations are the differentiation of the transverse displacement itself.

Based on my experience with various simulation experiments, such as tensile and compression tests, I highly recommend using ABAQUS. Not only can you obtain more accurate results, but there are also excellent learning resources available for it. I personally learned how to use ABAQUS with the USFLD subroutine from the website mentioned below. I hope it can help you as well.

Joshua Depiver Hello , can you please help me with this concern ?

i use USDFLD to compute phase fractions (3 phases) , law kinetics are written in SDVs , everything seems working good except the fact that i have negative values in the middle of my axsymmetric model , negative values are displayed also in the legend of SDVs which is not reasonable at all ?

Dear Michele Ciavarella ,

in order to insert the friction please change the contact171 element to contact 172 in the code I sent. The friction properties can be assigned using the command TB. Please refer to the ansys help for more details or use the following link

Rida Bensailaa, here is how you can do it: https://youtu.be/_H5B5XdEIgM

At a boundary surface you can either specify the temperature or heat flux, not both, as the one determines the other. So if you have nodes on the the boundary line which separates these two regions, then, I think you can specify one of these two conditions alternately on every consecutive node.

Regards

Dr Kumar Eswaran

Professor

Sadikbasha Shaik Yes, and much more. Here are the coordinates, areas, labels, and surfaces files for the Python outputs. You can use Python code in a similar domain to generate the resulting files for your project.

Dear Abdulhameed Qahtan Abbood Al-Tai ,

The modified weak Galerkin method does not require the penalty parameter by comparing with traditional DG methods.

Regards,

Shafagat

Dear Abdulhameed Qahtan Abbood Al-Tai ,

The modified weak Galerkin method does not require the penalty parameter by comparing with traditional DG methods.

Regards,

Shafagat

Go under "Property" tab. In the two columns of functions, you will find "Assign beam orientation" (on the right, 4 down).

Now select the problematic beam and click "Done". Now it will ask you for a direction of a vector n1. If you look under "Profile manager" (right, 5 down)-> select the created profile and you will see vectors 1 and 2. Vector 1 points to the right.

So when you assign beam orientation you tell the program where that vector roughly points (blue arrow, when you hit enter after typing in the direction). Hope that helps.

Yes, please check the method in this article :

Hi Konrad,

The Kocks-Mecking parameter (kf) quantifies how strain rate influences strain hardening during plastic deformation. Sample geometry, such as diameter, potentially impact kf. Smaller diameters can lead to strain localization, different stress distributions, and variations in dislocation densities in comparison to larger diameters.

Initial mechanical properties of samples also influence the material's overall strain hardening behaviour and its sensitivity to changes in strain rate, which in turn affects the kf parameter. Higher initial yield strength can lead to greater potential for strain hardening and increased sensitivity to strain rate changes, potentially resulting in a higher kf value. The initial stiffness of a material can influence how it responds to stress. Materials with faster work hardening rates tend to exhibit higher strain hardening responses. Ductile materials deform more uniformly, while less ductile materials may experience localized deformation. The initial microstructure, including grain size and distribution, can also impact dislocation mobility, deformation mechanisms, and consequently kf.

If you look in Materials Science and Engineering Textbooks, such as "Materials Science and Engineering" by William D. Callister and David G. Rethwisch; These text books often cover topics related to plastic deformation, strain hardening, and strain rate sensitivity. Look for chapters on mechanical behaviour of materials.

Hope this helps,

Kind regards

This is a frequently asked question. The only method to influence the identification of citations by ResearchGate's algorithm, developed by Andrejs Krauklis, is decribed here:

And here is an incomplete list of related questions and answers:

As you have mentioned displacement 2 that means total displacement is two, here, i am unable to figure out how the rate of displacement has been defined in your solution. please let me know.

In my opinion, Python is a brilliant choice for scientific computing and numerical analysis. Also, I think C++ would work, but it’s a complicated and difficult to master it.

Please also make sure that the beam behaves linearly before buckling. Otherwise, I suggest applying preload that is close to the critical load and then performing the BUCKLE analysis.

Dear Mustafa Shqair I didn't see your reply before sir, I will review it and see if with this information I can solve the problem.

Thank you !

I can still offer some suggestions to help you address the issue you're facing with the Indentation Size Effect (ISE) in your ABAQUS simulations.

Here are a few potential reasons why you might not be observing the expected trend of decreasing hardness with increasing indentation depth:

It is worth noting that the Indentation Size Effect (ISE) can be influenced by various factors, including material properties, strain gradient effects, and surface roughness. It is possible that other mechanisms or phenomena are counteracting the expected trend in your specific simulation. Additional considerations may be necessary to capture these effects accurately.

Victória Geovana Hollanda do Amaral ,

What material model did you use?

Change the bars to solid and use the LaRC05 material model for FRPs.

Good luck

When you are writing an ABAQUS UMAT or USDFLD subroutine, you have access to certain information from the current and previous increments.

If you need access to a history of SDVs, you must implement that functionality yourself. For example, you could use an array of SDVs and, at each increment, "shift" the array, discarding the oldest value and adding the newest one.

This method could be implemented as follows:

Remember that these modifications must be thoroughly tested to ensure they work as expected.

As always, when working with complex subroutines like these, it is a good idea to refer to the ABAQUS documentation and consider contacting ABAQUS support or an experienced ABAQUS user for guidance.

Please download the code from iVABS from wenbinyugroup.github.io which include codes for cross-sectional analysis, and general-purpose linear/nonlinear analysis of beams made of arbitrary cross-section and arbitrary material.

thanks for your reply Victor.

I'm still searching for ways to do it by Abaqus subroutines since subroutines provide you with great capabilities.

I have had very good success with FRAC3D-VS which was developed at Waterloo. Lots of models with a variety of configurations and properties.

1. Chen, Y., Xiao, H., & Zhang, S. (2018). A doublet lattice method–finite element method hybrid approach to compressible flows in two-dimensional steady and unsteady cavities. International Journal for Numerical Methods in Fluids, 85(7), 441-474.

2. Geng, S., Chen, J., & Yue, D. (2006). A doublet lattice method–finite element method hybrid approach for viscous, incompressible flows. International Journal for Numerical Methods in Fluids, 51(8), 877-894.

3. Jiang, M., & Li, T. (2008). Doublet lattice method-finite element method hybrid approach for thermal-fluid problems. International Journal of Heat and Mass Transfer, 51(17-18), 4270-4284.

4. Hsu, C., & Dai, C. (2012). A doublet lattice–finite element hybrid solution for compressible flows and applications to nozzle design. Computers & Fluids, 51, 107-116.

5. Kane, U. K., & Jiang, W. (2016). A hybrid doublet lattice–finite element coupling approach for multi-thermal fluids with linear divergence free constraint. Computers & Fluids, 127, 44-58.

you need to ensure that the mode shapes being compared are in the same format. Here's a suggested approach:

Once you have both mode shapes in the same format (real-valued), you can calculate the MAC using the standard formula. The MAC formula involves comparing corresponding displacement values at each node between the two mode shapes.

Remember to normalize the mode shapes before applying the MAC formula. Normalization helps in removing any scaling effects and ensures a fair comparison between the mode shapes.

I hope this explanation helps you resolve the issue and accurately calculate the MAC between your experimental and FEM mode shapes. If you have any further questions or need additional assistance, please feel free to ask.

As you said，expanding the dynamic stiffness matrix in powers of frequency-squared is curcial. Perhaps， the difference between Timoshenko and Eular lies in the ease of calculation.

And why sparse matrix has computational benefits than diagonal matrix for large sizes ?

here is the equation with the Neumann condition. that Diriclet is zero on all borders.

F(x,y) est une fonction polynôme

In PLAXIS 3D, you can actually simulate the railway loading using moving loads option

Hi Muhammad,

It is important to understand why this is happening first. Finite element analyses are usually not coded for large deformation problems. At the stress concentration area like singular points at the edge of the foundations, the elements tend to have large differential settlements and the soil becomes highly plastic.

Having said that we have some tools to deal with this:

1. Increasing the tolerance of analyses slightly. One should bear in mind that this option will decrease the accuracy of analyses but might be a good tool to show you the failure mechanism development.

2. Introducing a small value for tensile strength in soil.

3. Increasing cohesion in the soil.

Usually one of these measures will solve the problem.

If you are starting with FEA, I would suggest trying some simple elements that have exact analytic solution, like straight springs (you can use these in 1D, 2D and 3D) or beams (in 2D or 3D). You can derive basis functions for these from analytic solutions, but of course you can also try different basis functions and compare the results.

Hi Neda,

The technique that worked for me was to output the coordinates of the surfaces in contact before any load was applied. After that, I developed a formula in excel to find the closest point between these surfaces and locate their nodes by indexing the position in the excel database. By this point the nodes that are closest from the formula, I considered them as matched.

After the load was applied, I looked again at the final coordinates of the nodes of the surfaces in contact, and substracted their final position from their initial position.

That enabled me obtain the relative motion in the three directions. The overall magnitude of relative motions was obtained as the square root of the sum of squares of the relative motions in the three directions.

I hope this helps.

Just take quadratic form which gives the best approximation in the sense you chose to the nodal data you have.

Aung Nyein Soe , your code is not correct and it is likely that your fortran compiler is not able to compile it. Indeed, according to Fortran 77 standards, all Fortran statements must be written in columns 7 to 72, which is not the case in your code (e.g. lines 20, 21 and 28).

Also, lines 56 to 61 do not make sense as you are trying to assign a value to an array, which is not possible for Fortran 77 (and also probably not what you want to do). The indexes of S11, S22... arrays are likely missing.

Before running an abaqus simulation, you should first try compiling your code to make sure no obvious programming mistake is present.

Charles

Dear Mr. Delmonte,

By neglecting the influence of the shear forces the induced errors in the strain amplitude and the Smix figure are small. For IPC/COX/ASTM devices in which the effective length L of the beam is 355-356 mm and the height of the beam is 50 mm, the error is around 5% that is to say the Smix figure is underestimated by 5% and the strain amplitude is overestimated by 5%.

In other devices with bigger L figures (see 4PB platform) the error is less and dropped to around 3%. Thank you for your interest.

Best Regards

Ad Pronk

what you need to do if you are using finite elements is to first produce an analysis that follows the steady state conditions produced by your boundary and find for each element the total strain. From this subtract the plastic strain components which leaves the elastic strain components. Take this strain tensor and multiple by the elastic constitutive relations this will give you the residual stress in the model. This is a simple version for the effect to be more precise you are dealing with eigenstrain when you carry this removal of the plastic strain tensor at each coordinate in a given element.

You haven't received many responses because your question is vague. Do you hope to use the finite element method to solve an inverse problem? If that is the case, you must first define some field of interest and then identify which partial differential equation governs the process contained in your selected problem. If you hope to infer the shape of an object from the flow field (which would be an inverse problem), that would be quite a task and likely have no unique solution. If you hope to infer the thermal properties of an object from the temperature field associated with heat transfer, that is a tractable problem and has been successfully solved. In any event, you would need a finite element model of the process you have in mind. I have developed many such models and would be glad to make suggestions if you provide more details on what you hope to accomplish. Of course, I would never suggest anyone ever use MATLAB for anything.

There is simple solution to this - you need to use cell centered discrete action for temperature, Then Boundary conditions will be defined at the center of boundary faces. There is no unknowns or know temperatures at the nodes.

Hello dear

You must read the article published by Adnan Kefal, Tesler and oterkus

Yes , you can use that

Nice

i finally did it in comsol using pde modules and i've used paper of selvadurai for the equations, and the convergence issue was tackled using changing the discretisation order and through hit and trial.

during porohyperelastic make sure u are defining correct value of the stress tensor matrix

There is probably cleaner way to do this, but you could also try varying temperature of the strand to "fake" prestress. This would of course complicate things if you need to also consider temperatures in the analysis.

The issue of "verification, validation, and uncertainty quantification" is fundamental to the real-world application of numerical methods to critical applications. ASME has published has published standards for solid mechanics (VVUQ 10) as well as fluid mechanics and heat transfer (VVUQ 20). There are additional VVUQ standards that build upon these for specific needs, such as Nuclear Power (VVUQ 30) and Medical Devices (VVUQ 40). There is one under development for Machine Learning (VVUQ 70) that has nothing directly to do with 10 or 20.

The point is, there is lot that goes into engineering tools before they are accepted for engineering applications. Once it's in the "engineering" world (as opposed to "in development"), it must be good enough to be widely used without the dev team or algorithm designer providing any feedback or guidance. This is part of the issue -- as other have already answered, there are issues of quality control with respect to the use of the software tools.

And no, absolutely no, meshing is not 80% of the time in using FEM. That was vaguely true back when one did manual meshing back in the early 90s for more complex models, but it's not true now. Your question is based on an incorrect premise ... and that is why there is not a market-based drive to make the change to an IGA-pure method you hypothesize.

Novelty has it's place in peer-reviewed work. It's a starting point. You seem to be citing just a single set of authors instead of spending a few minutes looking beyond that using RG or Google Scholar. The thing is, IGA is essentially FEM, just taking it from a different angle (no pun intended). ( )

"The goal of integrating computer aided design (CAD) and finite element analysis (FEA) has led to a new computational method called Isogeometric Analysis (IGA). Its main idea is to use the same mathematical description for the geometry in the design (CAD) and the analysis (FEA). Much of the recent research on isogeometric analysis uses Non-Uniform Rational B-Splines (NURBS) as basis functions, as this geometrical representation is the most widely used in engineering design systems. It has been shown that NURBS-based finite elements are very well suited for computational analysis leading to qualitatively more accurate results in comparison with standard finite elements based on Lagrange polynomials. Due to these motivating results, NURBS-based finite elements are currently implemented into LS-DYNA."

Overall ... IGA techniques are growing in popularity and are being folded into existing computational platforms, just a BEM (boundary element method) techniques have. It's not a question of "one size fits all".

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Dear Fazel Ghiasvand ,

When you speak about convergence do you receive an error message from the software? In that case, I would begin with letting HFSS solve more adaptive passes, or in CST, reduce the convergence criteria and see if it converges in both software.

Best regards,

Patrick

Set interactions your cheek

If you are working with modal bases, it is more straightforward to change the order of an element. This means that the existing basis functions do not change. Some people enjoy this because it is easier to work with. Some antialiasing techniques require modal bases to be filtered directly, but this is not a performance bottleneck. Modal commands can also highlight sparsity within an element for special operators. This means that the savings are small for the modest order typically used in 3D. Nodal bases simplify the definition of element continuity and simplify the implementation of boundary conditions, contact, and the like. They are also easier to plot, leading to better ḥh-ellipticity in discretized operators. This, in turn, allows the use of less expensive smoothers/preconditioners. This means that people who create ways of solving problems can more easily use terms like "rigid body modes" and "multigrid methods," and they do not have to change how they think about things when they are using these methods. Discretization is a way to turn an ongoing problem into a discrete one that a computer can solve. An embedded discretization is one where the discretization is done in a way that makes it easy to access and use later on.

The check of mesh quality has to do with the numerical integration of stiffness matrix [k] by Gauss quadrature in isoparametric formulation. In “full integration”, matrix [k] is computed exactly if the element has a perfect shape, i.e. cube for hexahedral elements, square for plane quadrilateral elements, etc. Any deviation from this ideal shape will introduce approximations in the numerical computation of [k]. If distortion is excessive, numerical integration may even become impossible (à problem with Jacobian). Of course, if distortion is limited to few elements far apart the critical location of interest, the mesh could be considered acceptable. However, no general conclusions can be drawn without seeing the mesh.

Without using COMSOL, you can solve fourth-order or higher-order equations in Matlab easily using the explicit method (forward in time and central in space) or the implicit method and vice versa with the crank-Nicolson method or other numerical methods finite difference method with consistency and stability with Dirichlet boundary conditions.

In our example, we used planar finite elements with two displacements per node (x and y) and therefore considered only the first 7 bending modes in the xy plane. For the expansion process, the numerical mode shapes were further reduced to 29 displacement DOFs in the y-direction.

From your description, I assume you are trying to use spatial linear finite elements. In this case, bending modes in the xz-plane (and possibly torsional modes) are also present in the numerical solution.

In our experimental model, the excitation was only performed in the y-direction, and the response was also measured in the y-direction using uniaxial accelerometers. Thus, only xy-plane bending was excited and observed.

Due to the lack of observability and controllability for the xz bending and torsional modes, an expansion to a spatial FEM model is unlikely to be successful.

If you are interested in a comparison of different expansion methods (SEREP, SEMM, and M-SEMM), open-source code and an example can be found in the Python library pyFBS (https://gitlab.com/pyFBS/pyFBS/-/blob/master/examples/21_expansion_methods.ipynb).

For calculating the through-thickness profiles, the DC adopts the two conventions used by DISPERSE, as described in the DC (v2.2) manual, p. 11. The first is phase normalization. Since displacement, stress, and strain are complex, the phase of the second point (because the value at the first can be zero sometimes) from the top surface is taken, and the rest of the points is plotted with this phase, but only the real part. This is done for each component u1, u2, u3, sigma11, etc. Energy density and power flow density are integral quantities, so there is no phase to consider. The second convention is power normalization. All components are calculated for guided waves carrying a power of one Watt in the propagation direction x1, with the assumption that the waveguide is one meter wide. Then, when calculating the components at the same number of through-thickness points (samples x3, samples per layer) as DISPERSE, which uses 50 by default, you find very good agreement of the result from DISPERSE and from the DC.

But in Ansys, I found that achieving solution convergence was difficult. Abaqus, I found that the solution convergence happening nicely and I could complete my work

I think Praveen meant stable solutions and not steady. To get unstable solutions you can integrate backward in time or use continuation methods to trace steady-state stable and unstable solutions including bifurcations.

dear thank you for your answer,

all these tricks are done for simplifying the model and to keep the number of surface contacts as low as possible (there are plenty in my case), also the exact E-Modules of the roller of the machine is not available.

As you said, applying the symmetry conditions to the side edge and the load to the top node may work.

your answer helped...

I will be following other ideas on this issue

God bless

Hello, Tilmann Allzeit

When you impose in your model scale factor, what you are analysing is "almost" an unrealistic motion. The scale factor is based on the node displacement, so if the nodes are connected, for instance using "tie" constraint Abaqus can predict quite well the deformation. On other hand, when you have contacts, the nodes are unconnected, when you introduce the scale factor visually you may observe some penetrations, which is quite normal and this does not mean that you model is wrong. In order to verify if the contact is behaving as you want, I suggest you to analyse the CPRESS or the COPEN, as Raffael Bogenfeld mentioned.

Ok what is the meaning of that?

You can try the tips given in this thread:

If anyone ever encounters this question, the best way to circumvent this issue is just writing a newLAMMPS potential that has an elastic spring response (not the harmonic bond potential which is directionally limited).