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Published in:
2025 | OriginalPaper | Chapter
Object-oriented Numerics for Finite Elements
Author : Udo F. Meissner
Published in: Tensor Calculus with Object-Oriented Matrices for Numerical Methods in Mechanics and Engineering
Publisher: Springer Nature Switzerland
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Finally, the application of object-oriented matrix calculus is presented in two sections about quadrilateral and triangular plate elements based on typical C++ routines. The numeric functions PARALLELOGRAM and TRIANGLE exemplify, in the source code, the calculations of differential geometries, stiffness matrix relationships, and internal forces for both finite elements. The computation of corresponding numerical results is also demonstrated. The elements discussed are a bilinear parallelogram element and a linear triangular element, each with abstracted elasticity parameters. This allows the verification of calculated results for deformations and stresses under tension and shear in an elementary way. The program code, kept simple and clear, primarily aims to demonstrate how the required matrix objects of the matrix classes can be created and managed. It also illustrates how tensor/matrix arithmetic can be handled intuitively and clearly with the overloaded syntax for matrix operations.