WSEAS Transactions on Applied and Theoretical Mechanics
Print ISSN: 1991-8747, E-ISSN: 2224-3429
Volume 15, 2020
Natural Spring Cell Substitutes of Simplex Finite Elements
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Abstract: Spring cell models are presented which derive from the natural description of simplex finite elements, that is in conformity with the geometry of the triangle in the plane and of the tetrahedron in space. Thereby, the spring cells are interpreted as part of the finite elements. The deduction of two spring cells as defective substitutes is demonstrated for the triangular element. One approximates the flexibility matrix of the element, the other approximates the stiffness matrix. The performance with respect to the finite element is analyzed, the issue of elastic anisotropy is discussed. In space, the spring cell substitute of the tetrahedral element is derived from the flexibility matrix, an inherent difference to the plane case is pointed out. Remarks on the implication of plasticity are added. The account gives a brief summary of recent work on the subject.
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Keywords: Simplex finite elements, natural formalism, spring cells, elasticity, anisotropy, plasticity.
Pages: 38-45
DOI: 10.37394/232011.2020.15.6