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AComparison of All-Hexahedral and All-Tetrahedral Finite Element Meshes for Elastic and Elasto-Plastic Analysis

Benzley, Steven E., Ernest Perry, Karl Merkley, Brett Clark and Greg Sjaardema

Proceedings, 4th International Meshing Roundtable, Sandia National Laboratories, pp.179-191, October 1995


This paper compares the accuracy of elastic and elasto-plastic solid continuum finite element analysis modeled with either all hexahedral or all tetrahedral meshes. Eigenvalues of element stiffness matrices, linear static displacements and stresses, dynamic modal frequencies, and plastic flow values are computed and compared. Elements with both linear and quadratic displacement functions are evaluated. Linear incompressibility conditions are also investigated. A simple bar with a rectangular cross-section, fixed at one end is modeled and results compared to known analytical solutions wherever possible. The evaluation substantiates a strong preference for linear displacement hexahedral finite elements when compared solely to linear tetrahedral finite elements. The use of quadratic displacement formulated finite elements significantly improve the performance of the tetrahedral as well as the hexahedral elements. The non-linear elasto-plastic comparison indicates that linear hexahedral elements may be superior to even quadratic tetrahedrons when shear stress is dominant. Results of this work may serve as guide in selecting appropriate finite element types to be used in three-dimensional elastic and elastic/plastic analysis.

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