Reference : Trefftz polygonal finite element for linear elasticity: convergence, accuracy, and pr...
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Computational Sciences
Trefftz polygonal finite element for linear elasticity: convergence, accuracy, and properties
Hirshikesh []
Natarajan, Sundararajan []
Ratna Kumar, A. K. []
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Atroshchenko, Elena []
Asia Pacific Journal on Computational Engineering
Yes (verified by ORBilu)
[en] Trefftz finite element ; Polytopes ; T-complete functions ; Boundary integration
[en] In this paper, the accuracy and the convergence properties of Trefftz finite element method over arbitrary polygons are studied. Within this approach, the unknown displacement field within the polygon is represented by the homogeneous solution to the governing differential equations, also called as the T-complete set. While on the boundary of the polygon, a conforming displacement field is independently defined to enforce the continuity of the field variables across the element boundary. An optimal number of T-complete functions are chosen based on the number of nodes of the polygon and the degrees of freedom per node. The stiffness matrix is computed by the hybrid formulation with auxiliary displacement frame. Results from the numerical studies presented for a few benchmark problems in the context of linear elasticity show that the proposed method yields highly accurate results with optimal convergence rates.
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