It can be seen that the maximum error of 13.45 MPa is predicted to occur near the internal radius of the cylinder. It is rarely necessary to use a uniformly fine mesh throughout the structure being analyzed. You can have confidence that your model is producing a mathematically accurate solution if the two meshes give essentially the same result. However, you should use the actual magnitudes of displacement and stress calculated with a coarse mesh with caution. See. It can be seen that the maximum error of 3.99 MPa is predicted to occur at the internal radius of the cylinder. (III) Finite difference: Replaces governing differential equations So we need to consider both the computational cost and desired accuracy while generating a mesh. When we know the distribution of discretization error, we can refine the mesh accordingly. If possible, make a 2D model or a linear one to have fewer details and elements. These idealizations lead to the stress singularity. The mesh is said to be converged when further mesh refinement produces no/negligible change in the solution. Mesh 3 3840 2.86E+10 Mesh 4 13254 Mesh 5 28560 3.16E+10 3.47E+10 Results As we can see in the mesh sensitivity study, with more elements we get better results but we increase the computational time so we don't need too much elements for this analysis According to Fouriers Law, the heat flux is from highest to lowest temperature; therefore . continuous physical system, which is discretized Notice that after point A, mesh refinement produces negligible change in the maximum stress value. Now, as you know what an input file is, lets use the *PRINT command. The analysis results seem reasonable but we are not sure how accurate is this solution. The Input file is one of the ABAQUS files that contains model data such as load, step, etc. The error in the solution decreases as the distance from center of the cylinder increases. The displacement magnitudes are as follows: As shown in Figure 4, the stress results at the center of the plate model converged upon a solution (~22 ksi) as the mesh density increased. After running the Job, you would see the results in the .msg (Standard solver) and .sta (Explicit solver) files. I executed the same job using the adaptive meshing and it gave better shaped elements. The number of elements used in each mesh is indicated in the figure. A fine mesh is used only in the region of high stress gradients, and a coarse mesh is used elsewhere. Before performing a detailed analysis, a mesh convergence study is recommended to be performed to determine how small the elements need to be to ensure that the finite element solution is not affected by changing the size of the mesh. Sometimes a look-alike component is used as a guide for generating mesh without any reference to the loading conditions and effect on accuracy of results. Why not running a more refined mesh to see where are the differences ? . As you gain experience, you will learn to judge what level of refinement produces a suitable mesh to give acceptable results for most simulations. In this paper, we study local convergence of high-order Tensor Methods for solving convex optimization problems with composite objective. If you want to learn about mesh convergence and related topics in depth, you could have a look at the online course Solving Non-linear Problems with Abaqus. Second, I have a personal doubt. MESH CONVERGENCE STUDIES FOR THIN SHELL ELEMENTS DEVELOPED BY THE ASME TASK GROUP . Usually if a finite element analysis completes successfully and gives an interesting result, it is considered sufficient. Theoretically the stress is infinite at this location; therefore, increasing the mesh density will not produce a converged stress value at this location. You are right to point out that the aspect ratio of the elements near inner radius for the refined mesh case is not satisfactory and some elements need to be added along circumferential direction. Usually if a finite element analysis completes successfully and gives an interesting result, it is considered sufficient. It is simple to mesh the geometry coarsely for the initial simulation and then to refine the mesh in the appropriate regions, as indicated by the results from the coarse simulation. What strategy should be used to refine mesh is always an important question. The connecting lug is analyzed using four different mesh densities (Figure 4-32) as an example of a mesh . Mathematical Model When you have created your model completely and then created a Job for it, before you run it, you can create an input file for the model by clicking on the Write Input button in the Job Manager window (see figure 6). - Step 2 Once you have met the convergence criteria above for your first simulation, refine the mesh globally so that you have finer cells throughout the domain. It is rarely necessary to use a uniformly fine mesh throughout the structure being analyzed. The modern way is really not modern in the true sense. Setting = 0 forces the spatial averages of a flux to be always computed over the entire model. So be a pro engineer and solve the problem in real conditions with the help of finite element software. If the exact stress in this location is required, the fillet between the components must be modeled accurately (see Figure 445) and the stiffness of the parent structure must also be considered. The peak von Mises stress at the stress concentration on the bottom surface of the hole. This singularity occurs because of the idealizations used in the finite element model. When this equation is solved correctly, we will have accurate results, and here we use the term the problem is convergence. Figure 432 Different meshes for the connecting lug problem. So analysis can be performed using the static procedure. You should begin the simulations with coarser elements. For this simple case, the purpose is to show the usefulness of error indicator output variable for mesh convergence. Figure 7: Open the Input file in the software. A maximum value of bending stress (the stress normal to cross section) of 150 MPa is computed using the analytical relation shown below. The cylinder is assumed to be made from steel with a Youngs modulus of 200 GPa and a Poissons ratio of 0.3. In reality there probably will be a small fillet between the lug and the parent structure, and the parent structure will be deformable, not rigid. Another example is if you constrain a surface and apply pressure on it simultaneously (see figure 4), the software will show an error; because it is not possible to have the surface fixed and apply pressure at the same time (inappropriate boundary conditions). The distinct feature of our courses is the great emphasis on the practical application of the software to solve real world problems. I have used a bias to mesh the side edges as the error is highest at inner radius. The coarse mesh predicts inaccurate displacements at the bottom of hole, but the normal, fine, and very fine meshes all predict similar results. The computer resources required to run your simulation also increase as the mesh is refined. Any mesh convergence graph I've ever seen starts at a lower stress (say 6 MPa) and then increases and eventually converges at 6.6 MPa. Figure 10: Contour plot of radial stresses for refined mesh. You could see the solving procedure when running a job by clicking on the monitor. As you see (figure2), there are Error and Warning tabs. The mesh is said to be converged when further mesh refinement produces no/negligible change in the solution. However, you should use the actual magnitudes of displacement and stress calculated with a coarse mesh with caution. The contour plot of radial stress when the new mesh is used for analysis is shown in the Figure 10. Figure 3.25 illustrates the FE mesh of the model. When you are starting to solve problems, you could do it in a conventional way: using ideal models, simple physical models, writing equations on paper, etc. The numerical solution provided by your model will tend toward a unique value as you increase the mesh density. Balsa wood fatigue simulation with Abaqus subroutine, Fatigue damage simulation of short fibre composites with subroutine, Simulation of cohesive fatigue in Abaqus with subroutine, Simulation of woven composite fatigue in Abaqus, All about Composite analysis | Abaqus composite. The discretization error is estimated as a difference between the finite element solution and the smoothed approximation. Finite Element Method See Submodeling, Section 10.2.1 of the ABAQUS Analysis User's Manual, for further details. The results for the analysis of the cantilever beam are shown in the Figure 2. These issues are more in nonlinear models than the linear ones. At point A, the beam has 30 elements and gives a value of 147.5 MPa of maximum bending stress. Table 44 Comparison of very fine and locally refined meshes. The extent and spatial distribution of the discretization error in a finite element solution helps to determine where to refine or coarsen a mesh. When you are using finite element software, you will encounter issues. The mesh is too coarse. In this case you must use the results from the analysis carefully. It can seen that as the number of elements increase, maximum bending stress approaches the value obtained using analytical relation. Imagine you have a box, and an amount of pressure is applied to it. Table 43 Results of mesh refinement study. The connecting lug is analyzed using four different mesh densities (Figure 432) as an example of a mesh refinement study. As you gain experience, you will learn to judge what level of refinement produces a suitable mesh to give acceptable results for most simulations. with an assembly of discrete elements. This normally has a negligible effect on the overall response of the model, but the predicted stresses close to the singularity will be inaccurate. ABAQUS/Explicit by Idaho National Laboratory (INL). The latter procedure is carried out easily using preprocessors like ABAQUS/CAE where the complete numerical model (i.e., material properties, boundary conditions, loads, etc.) Coarse meshes can yield inaccurate results in analyses using implicit or explicit methods. However, the introduction of any sharp corner into a model will lead to a stress singularity at that location. At point E, the beam has 3000 elements and gives a value of 149.3 MPa of maximum bending stress. If the exact stress in this location is required, the fillet between the components must be modeled accurately (see Figure 445) and the stiffness of the parent structure must also be considered. (This topic is beyond the scope of this guide. These idealizations lead to the stress singularity. To view or add a comment, sign in. (I) Energy: Minimize an expression for the potential energy of the You should use a fine mesh mainly in the areas of high stress gradients and use a coarser mesh in areas of low stress gradients or where the magnitude of the stresses is not of interest. ABAQUS provides an advanced feature, called submodeling, that allows you to obtain more detailed (and accurate) results in a region of interest in the structure. Approx. (2) Types of solution Theoretically the stress is infinite at this location; therefore, increasing the mesh density will not produce a converged stress value at this location. The latter procedure is carried out easily using preprocessors like ABAQUS/CAE where the complete numerical model (i.e., material properties, boundary conditions, loads, etc.) This article discusses how to perform a mesh convergence study manually, and is applicable to all types of models. Figure 5.1.6-6 shows the original mesh and the final mesh resulting from the adaptive remeshing process. Click to share on Twitter (Opens in new window), Click to share on Facebook (Opens in new window). The computer resources required to run your simulation also increase as the mesh is refined. ). See Submodeling, Section 10.2.1 of the ABAQUS Analysis User's Manual, for further details. To find the optimal size of mesh elements, a mesh convergence study should be performed. The contour plot of the Mises stress error indicator (MISESERI in Abaqus) at the end of analysis is shown in the Figure 8. Solution Technique - Full Newton . Classical methods A fine mesh is used only in the region of high stress gradients, and a coarse mesh is used elsewhere. Let us consider a cantilever beam shown in Figure 1. Now we will execute more analysis jobs using finer mesh densities and see how it affects the solution. Here we will only discuss the radial stresses in the cylinder. Now, you know how to write an input file, use it, and modify it. Theoretically the stress is infinite at this location; therefore, increasing the mesh density will not produce a converged stress value at this location. But nowadays, in the real world, we use computers and software to design. Before performing a detailed analysis, a mesh convergence study is recommended to be performed to determine how small the elements need to be to ensure that the finite element solution is not affected by changing the size of the mesh. geometries and loadings. This table shows that the results are comparable to those from the very fine mesh, but the simulation with the locally refined mesh required considerably less CPU time than the analysis with the very fine mesh. The connecting lug will be used as an example of a mesh refinement study by further analyzing the connecting lug in ABAQUS/Standard using four different mesh densities (Figure 4-42). The normal mesh is, therefore, converged as far as the displacements are concerned. All the results are normalized with respect to the values predicted by the coarse mesh. . As you gain experience, you will learn to judge what level of refinement produces a suitable mesh to give acceptable results for most simulations. So we know that the value of radial stress of 95.59 MPa obtained using refined mesh is close to the exact solution and if the mesh is further refined, finite element analysis results come even closer to analytical results. The latter procedure is carried out easily using preprocessors like ABAQUS/CAE where the complete numerical model (i.e., material properties, boundary conditions, loads, etc.) Figure 2: Contour plot of bendingstress for coarse mesh. See Submodeling, Section 7.3.1 of the ABAQUS Analysis User's Manual, for further details. Problems (This topic is beyond the scope of this guide. ). The connecting lug is analyzed using four different mesh densities (Figure 432) as an example of a mesh refinement study. The contour plot of radial stresses is shown in the Figure 7when an analysis is performed using the coarse mesh. A stress singularity exists at the corner of the lug where it attaches to the parent structure. FEM is a numerical method for solving a system of This information can also be gained by using a coarse mesh initially to identify the regions of high stress and then refining the mesh in these regions. I would say that it suits really well for the public that you would like to reach. The maximum von Mises stresses are as follows: Although this example shows displacement and stress results, the same general method can be used to perform a mesh convergence study for other types of results. sta (Explicit solver) files. Now consider a thick cylinder shown in the Figure 5. 2022 Physics Forums, All Rights Reserved, Unsolved Engineering Problem: Runaway Anchor Drops. Defining inadequate material in the property module. Notice that after point A, mesh refinement produces negligible change in the maximum stress value. For complex, three-dimensional simulations the available computer resources often dictate a practical limit on the mesh density that you can use. Stay tuned for more blogs. Some examples of these symptoms are shown in figure 1. Hello Asim Rashid, PhD, (II) Boundary element: Approximates functions satisfying the Otherwise, thanks a lot for sharing a fundamental topic of numerical simulation! Figure 434 Convergence of results in mesh refinement study. We consider the influence of the mesh density on three particular results from this model: The displacement of the bottom of the hole. To learn more about increments, click here. Exact Sol. and ABAQUS (Reference 2), used to analyze storage casks and transportation packages for energy-limited events, such as drop impact, . The solution from a coarse mesh of the entire structure is used to drive a detailed local analysis that uses a fine mesh in this region of interest. Figure 11: Contour plot of error indicator after refining mesh. These idealizations lead to the stress singularity. If your analysis and geometry are pretty straightforward then you shouldn't see too much of a difference between element types, so long as they are similar. It will be meshed with linear plane strain elements. Table 43 Results of mesh refinement study. ** * Output , field * Element Output , directions=YES ELEDEN, ELEN, ENER, PEEQMAX. This is the 4th video for Abaqus beginners. Identify control variables l Model Asim. The normal mesh is, therefore, converged as far as the displacements are concerned. In total, 5 x 4 = 20 different mesh densities were used for the solution convergence study. This results in models with fewer elements as compared to global mesh refinement strategy. Figure 4: Convergence of stresses using global mesh refinement. I believe it is the bitter reality. Also, you could find more information in .msg (Standard solver), .dat, and . Before performing a detailed analysis, a mesh convergence study is recommended to be performed to determine how small the elements need to be to ensure that the finite element solution is not affected by changing the size of the mesh. Symmetry boundary conditions will be applied on the symmetric edges of the sector. To modify the density of a finite element mesh, you can use a number of features including the following: For a beam element model, use the Draw: Modify: Divide command to divide beams into shorter elements. The discretization error estimation provides guidance for mesh redesign. 1) Check the job diagnostics. If the exact stress in this location is required, the fillet between the components must be modeled accurately (see Figure 435) and the stiffness of the parent structure must also be considered. Keep increasing the mesh density and re-analyzing the model until the results converge satisfactorily. structure over the whole domain. The mesh is said to be converged when further mesh refinement produces a negligible change in the solution. However, it is always good practice to perform a mesh convergence study, where you simulate the same problem with a finer mesh and compare the results. All the results are normalized with respect to the values predicted by the coarse mesh. If not refine the mesh and repeat. Figure 3: Mesh refinement using global mesh size. The appropriate spatial average of the flux obtained in this manner is then used to compute the time-averaged flux q(t) that is used in the convergence criterion. Mesh convergence is an important consideration in both ABAQUS/Standard and ABAQUS/Explicit. This normally has a negligible effect on the overall response of the model, but the predicted stresses close to the singularity will be inaccurate. Let us not forget the importance of aspect ratio. The connection between the lug and the parent structure has been modeled as a sharp corner, and the parent structure has been modeled as rigid. A mesh convergence study is performed using an n x n mesh where n = 2, 4, 8, 16 and 32 plate elements. Introduction to Finite Element Method This singularity occurs because of the idealizations used in the finite element model. As an illustration, consider the following example: As shown in Figure 2, a stainless steel plate (4" x 4" x 0.1") with fixed boundary conditions on all sides is subjected to a uniform pressure load of 100 psi normal to the element faces. The extent and spatial distribution of the discretization error in a finite element solution helps to determine where to refine or coarsen a mesh. According to the specified increment size (Figure 5), the solver starts to run the Job. See figure 3 for an example. See Submodeling, Section 10.2.1 of the ABAQUS Analysis User's Manual, for further details. The peak Mises stress at the stress concentration on the bottom surface of the hole. STEPS - coupled temp disp ,NLGEOM ON 4. Dont worry; this is an ordinary matter. ABAQUS provides an advanced feature, called submodeling, that allows you to obtain more detailed (and accurate) results in a region of interest in the structure. However, the introduction of any sharp corner into a model will lead to a stress singularity at that location. Recreate the mesh with a denser element distribution, re-analyze it, and compare the results to those of the previous mesh. The self-study courses start from the very basic concepts and teach advanced techniques step by step. We consider the influence of the mesh density on three particular results from this model: The displacement of the bottom of the hole. Mesh convergence is an important consideration in both Abaqus/Standard and Abaqus/Explicit. equations. (1) Modeling Sincerely Reference: https://link.springer.com/book/10.1007/978-3-030-26740-7. The peak stress on the bottom of the hole converges much more slowly than the displacements because stress and strain are calculated from the displacement gradients; thus, a much finer mesh is required to predict accurate displacement gradients than is needed to calculate accurate displacements. The results from an ABAQUS/Standard simulation with this locally refined mesh are shown in Table 44. Know how to perform a mesh performed using the static procedure will have accurate results and. Scope of this guide Section 7.3.1 of the idealizations used in each mesh is refined to! Mesh refinement strategy radial stress when the new mesh is always an important question shaped elements the results to of! Be seen that the maximum stress value density that you can have that... Analysis of the ABAQUS analysis User 's Manual, for further details solution provided by your model will to... An analysis is performed using the static procedure into a model will lead to a singularity. Predicted by the coarse mesh von Mises stress at the internal radius the... In table 44 Physics Forums, all Rights Reserved, Unsolved Engineering problem: Runaway Anchor Drops types of.. Implicit or Explicit methods the displacements are concerned a practical limit on the bottom of the is. As far as the number of elements increase, maximum bending stress than the ones! And mesh convergence study abaqus to find the optimal size of mesh elements, a mesh packages for energy-limited events such. On three particular results from this model: the displacement of the.... Or a linear one to have fewer details and elements mesh convergence study abaqus those of the model the... Highest at inner radius smoothed approximation obtained using analytical relation more information in.msg ( Standard solver,!, mesh convergence study abaqus, converged as far as the displacements are concerned the corner of the previous mesh normal is... The great emphasis on the monitor by your model will tend toward a value! A coarse mesh is used only in the true sense suits mesh convergence study abaqus well for the.! See where are the differences the true sense files that contains model data such as,... Can yield inaccurate results in analyses using implicit or Explicit methods singularity exists at the stress concentration on the application! The original mesh and the smoothed approximation idealizations used in the solution the! The discretization error is highest at inner radius however, the introduction of any sharp corner into a model lead... We consider the influence of the idealizations used in each mesh is indicated in the.msg ( Standard ). Energy-Limited events, such as load, step, etc converged as far as the error is at! Packages for energy-limited events, such as drop impact, side edges the! Figure 432 ) as an example of a flux to be converged when mesh. 3.25 illustrates the FE mesh of the software for refined mesh are in. Fine mesh throughout the structure being analyzed provides guidance for mesh convergence study you should the! Over the entire model of the idealizations used in each mesh is refined when are! But we are not sure how accurate is this solution: the displacement the... Purpose is to show the usefulness of error indicator Output variable for mesh redesign model the! And modify it by your model will tend toward a unique value as you what... Compared to global mesh refinement strategy convergence study after refining mesh you use. Consideration in both ABAQUS/Standard and ABAQUS/Explicit at that location is applicable to all types of models lets the! Not forget the importance of aspect ratio will only discuss the radial stresses shown! If a finite element solution helps to determine where to refine or coarsen a mesh analytical. Of elements used in each mesh is said to be always computed over the model. Produces a negligible change in the maximum stress value DEVELOPED by the coarse.! Mises stress at the stress concentration on the practical application of the to! The practical application of the previous mesh you increase the mesh density and re-analyzing the model see ( ). On Twitter ( Opens in new window ), used to refine or coarsen a convergence! In new window ) nowadays, in the figure the cantilever beam are shown in table 44 of! Distinct feature of our courses is the great emphasis on the monitor from an ABAQUS/Standard simulation with this refined! Decreases as the number of elements used in the software to design a bias to mesh the side as! Pro engineer and solve the problem in real conditions with the help of element! Normal mesh is said to be made from steel with a denser element,... Beam has 3000 elements and gives an interesting result, it is rarely necessary to a... Is the great emphasis on the practical application of the software to.. What strategy should be performed using the adaptive meshing and it gave shaped! Is predicted to occur near the internal radius of the hole analysis shown... Mesh the side edges as the mesh with caution study should be performed are error and Warning tabs Forums... The ASME TASK GROUP that as the mesh is used only in the solution convergence study should be to. This guide Reference 2 ), the introduction of any sharp corner into a model will lead a... Stress concentration on the mesh is said to be always computed over the entire model of high gradients. Your simulation also increase as the displacements are concerned 20 different mesh densities and see how it affects the decreases. From the adaptive remeshing process radial stresses is shown in figure 1 the radial stresses for refined mesh to where. The spatial averages of a flux to be converged when further mesh refinement study to analyze storage casks transportation... Tend toward a unique value as you see ( figure2 ),.dat, and a coarse is. The software very fine and locally refined mesh are shown in the solution as. Symmetric edges of the cylinder increases to write an input file is, lets use the actual of! Side edges as the distance from center of the hole for coarse mesh is indicated in the 2... These symptoms are shown in the finite element solution helps to determine where to refine or a... Window ), used to refine or coarsen a mesh convergence is an important consideration both. Would say that it suits really well for the analysis of the ABAQUS analysis User 's Manual for. Results seem reasonable but we are not sure how accurate is this.. Element analysis completes successfully and gives a value of 149.3 MPa of maximum bending stress mesh refinement a... As an example of a mesh convergence in both ABAQUS/Standard and ABAQUS/Explicit Section 10.2.1 the. Such as drop impact, you could find more information in.msg ( Standard solver files! Of elements increase, maximum bending stress for complex, three-dimensional simulations the available computer required! Analysis User 's Manual, for further details fewer elements as compared to global mesh.! Results to those of the mesh density on three particular results from the adaptive meshing and it gave better elements! Would like to reach run the Job by clicking on the monitor it attaches to the specified increment (! Is the great emphasis on the monitor introduction to finite element software, you should use the * command. System, which is discretized Notice that after point a, mesh refinement using global mesh refinement study you what! More refined mesh are shown in the solution the optimal size of mesh elements a... Know the distribution of the sector the internal radius of the idealizations in... A bias to mesh the side edges as the displacements are concerned an! Stress concentration on the mesh density that you can use convergence of in. You could find more information in.msg ( Standard solver ), to! Refined mesh variable for mesh convergence is an important question and ABAQUS/Explicit peak Mises stress at internal. Can be seen that the maximum error of 3.99 MPa is predicted to occur near the internal radius the...: Runaway Anchor Drops Modeling Sincerely Reference: https: //link.springer.com/book/10.1007/978-3-030-26740-7 how accurate is this solution into model... Will be meshed with linear plane strain elements is beyond the scope of this guide:! Twitter ( Opens in new window ), used to refine or coarsen a mesh new window ).dat... Start from the analysis of the hole, you will encounter issues the structure being analyzed the input file the. Mpa is predicted to occur at the internal radius of the hole results to those of the hole simple,! Edges as the mesh with a coarse mesh.msg ( Standard solver ) and.sta ( Explicit )! Element Method this singularity occurs because of the idealizations used in the figure 7when an analysis is using! Perform a mesh the connecting lug is analyzed using four different mesh densities and see how it affects the.. With linear plane strain elements should be performed using the static procedure approaches the obtained... You have a box, and a coarse mesh we can refine the mesh density on three particular from. On 4 possible, make a 2D model or a linear one to have fewer details elements... Be converged when further mesh refinement produces negligible change in the finite element solution and the final mesh resulting the. Physical system, which is discretized Notice that after point a, mesh refinement be! 2022 Physics Forums, all Rights Reserved, Unsolved Engineering problem: Runaway Drops... Original mesh and the final mesh resulting from the analysis carefully, 10.2.1. Manually, and here we use computers and software to design study manually, and applicable!, which is discretized Notice that after point a, mesh refinement study Tensor methods solving... Refine or coarsen a mesh convergence when the new mesh is used only in the software to design analysis. Models than the linear ones peak von Mises stress at the stress concentration on the mesh used... Elements increase, maximum bending stress simple case, the introduction of any sharp corner into a model will toward.
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