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Erschienen in:
2022 | OriginalPaper | Buchkapitel
Objektorientierte Numerik für Finite Elemente
verfasst von : Udo F. Meißner
Erschienen in: Tensorkalkül mit objektorientierten Matrizen für numerische Methoden in Mechanik und Ingenieurwissenschaften
Verlag: Springer Fachmedien Wiesbaden
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Finally, the application of the object-oriented matrix calculus is presented in two sections about a FEM-parallelogram and a FEM-triangle pannel element on the basis of typical C++ routines, which exemplify in the source code the calculations of the differential geometries, the matrices of the stiffness relationships and of the internal forces for both finite elements as well as the computation of the corresponding numerical results. These elements are a bilinear parallelogram element and a linear triangular element, each with abstracted elasticity parameters, so that the calculated results for deformations and stresses under tension and shear can be verified in the elementary way. The program code, which is kept simple and clear, is primarily intended to demonstrate here how the required matrix objects of the new matrix classes can be created and managed, and how the tensor/matrix arithmetic can be handled intuitively and clearly with the overloaded syntax for matrix operations.