Nonlinear Solid Mechanics for Finite Element Analysis: Dynamics

Many universities have started introducing Finite Element Analysis (FEA) at an earlier point in the curriculum. However, there is a wide diversity of university backgrounds, course content and sequence, pedagogical objectives and approaches, etc. This paper describes the development of FEA lab modules in the second course of solid mechanics in our specific context. Students in this course were introduced to FEA earlier in the first course of statics and solid mechanics. They had learned the basic steps in FEA for axially loaded and planar truss structures. In the second course, the FEA was extended to the planar cases. One of the objectives was to make the students aware of the descretization and numerical errors of the FEA. Hence there was a particular focus on element displacement fields and how they influence element behavior in comparison with an actual structure behavior. The lab modules were designed to be complementary to the class room learning. Approximate nature of the FEA was taught via the lab modules on descretization errors and numerical errors. The descretization error was demonstrated in the first part of the lab wherein different types of elements for planar problems were compared. One cantilever beam problem was solved with different types of elements and the results were compared with the theoretical value. Numerical error was studied in the second part of the lab wherein the effect of the element shape quality on the results was studied. A systematic study of the effect of mesh distortion was undertaken. ANSYS Parametric Design Language (APDL) macros were developed to change the mesh distortion quickly in a controlled fashion. A study of convergence of the results followed in the third part of the lab. A reasonable convergence was obtained for a plate with a central hole for which the theoretical results are known. Once the students grasped the need of convergence, a real life problem was attempted in the fourth part of the lab. The actual results are not known in the real life and a reasonable convergence needs to be established for acceptable results and for subsequent analysis and design. Design of a seat belt buckle was undertaken. A Pro/E CAD model was imported into ANSYS. The students used the subset of the CAD model to build their FE model considering only the relevant part, the symmetry and the mid plane. At the end of the semester, the students used the FEA tools for a real life design problem with a firm grasp of the approximate nature of the method.

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A Posteriori Detection of Numerical Locking in hpq-Adaptive Finite Element Analysis

Applied Sciences ◽

10.3390/app10228247 ◽

2020 ◽

Vol 10 (22) ◽

pp. 8247

Author(s):

Łukasz Miazio ◽

Grzegorz Zboiński

Keyword(s):

Finite Element Analysis ◽

Sensitivity Analysis ◽

Finite Element ◽

Solid Mechanics ◽

Problem Solution ◽

Adaptive Finite Element ◽

A Posteriori ◽

Element Analysis ◽

Numerical Locking ◽

Locking Phenomena

The proposed detection algorithms are assigned for the hpq-adaptive finite element analysis of the solid mechanics problems affected by the locking phenomena. The algorithms are combined with the M- and hpq-adaptive finite element method, where M is the element model, h denotes the element size parameter, and p and q stand for the longitudinal and transverse approximation orders within an element. The applied adaptive scheme is extended with the additional step where the locking phenomena are a posteriori detected, assessed and resolved. The detection can be applied to shear, membrane, or shear–membrane locking phenomena. The removal of the undesired influence of the numerical locking on the problem solution is based on p-enrichment of the mesh. The detection algorithm is also enriched with the locking assessment algorithm which is capable of determination of the optimized value of p which is sufficient for the phenomena removal. The detection and assessment algorithms are based on a simple sensitivity analysis performed locally for the finite elements of the thin-walled domain. The sensitivity analysis lies in comparison of the element solutions corresponding to two values of the order p, namely current and potentially eliminating the locking. The local solutions are obtained from the element residual method. The elaborated algorithms are original, relatively simple, extremely reliable, and highly effective.

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Large Scale Finite Element Analysis Via Assembly-Free Deflated Conjugate Gradient

Journal of Computing and Information Science in Engineering ◽

10.1115/1.4028591 ◽

2014 ◽

Vol 14 (4) ◽

Cited By ~ 11

Author(s):

Praveen Yadav ◽

Krishnan Suresh

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Conjugate Gradient ◽

Degrees Of Freedom ◽

Large Scale ◽

Solid Mechanics ◽

Processing Unit ◽

Element Analysis ◽

Central Processing ◽

Computational Bottleneck

Large-scale finite element analysis (FEA) with millions of degrees of freedom (DOF) is becoming commonplace in solid mechanics. The primary computational bottleneck in such problems is the solution of large linear systems of equations. In this paper, we propose an assembly-free version of the deflated conjugate gradient (DCG) for solving such equations, where neither the stiffness matrix nor the deflation matrix is assembled. While assembly-free FEA is a well-known concept, the novelty pursued in this paper is the use of assembly-free deflation. The resulting implementation is particularly well suited for large-scale problems and can be easily ported to multicore central processing unit (CPU) and graphics-programmable unit (GPU) architectures. For demonstration, we show that one can solve a 50 × 106 degree of freedom system on a single GPU card, equipped with 3 GB of memory. The second contribution is an extension of the “rigid-body agglomeration” concept used in DCG to a “curvature-sensitive agglomeration.” The latter exploits classic plate and beam theories for efficient deflation of highly ill-conditioned problems arising from thin structures.

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