Mixed displacement–rotation–pressure formulations for linear elasticity
Anaya V., de W. Z., Mora D., Ruiz B. R. E`.
Computer Methods in Applied Mechanics and Engineering
Vol.344, P. 71-94
Опубликовано: 2019
Тип ресурса: Статья
DOI:10.1016/j.cma.2018.09.029
Аннотация:
We propose a new locking-free family of mixed finite element and finite volume element methods for the approximation of linear elastostatics, formulated in terms of displacement, rotation vector, and pressure. The unique solvability of the three-field continuous formulation, as well as the well-definiteness and stability of the proposed Galerkin and Petrov–Galerkin methods, is established thanks to the Babuška–Brezzi theory. Optimal a priori error estimates are derived using norms robust with respect to the Lamé constants, turning these numerical methods particularly appealing for nearly incompressible materials. We exemplify the accuracy (in a suitably weighted norm), as well the applicability of the new formulation and the mixed schemes by conducting a number of computational tests in 2D and 3D, also including cases not covered by our theoretical analysis. © 2018 The Author(s)
Ключевые слова:
Elasticity equations; Error analysis; Finite volume element formulation; Mixed finite elements; Rotation vector
Computation theory; Elasticity; Error analysis; Finite volume method; Galerkin methods; Locks (fasteners); Elasticity equations; Finite volume element; Finite volume element method; Linear elastostatics; Mixed finite elements; Nearly incompressible; Optimal a priori error estimates; Rotation vector; Numerical methods
Язык текста: Английский
ISSN: 1879-2138
Anaya V.
de W. Z. Wijn Z.
Mora D.
Ruiz B. R. E`. Bayer Rikardo E`steban 1979-
Анайа В.
де W. З. Wийн З.
Мора Д.
Руиз Б. Р. Э. Байер Рикардо Эстебан 1979-
Mixed displacement–rotation–pressure formulations for linear elasticity
Текст визуальный непосредственный
Computer Methods in Applied Mechanics and Engineering
Elsevier Science Publisher B.V.
Vol.344 P. 71-94
2019
Статья
Elasticity equations Error analysis Finite volume element formulation Mixed finite elements Rotation vector
Computation theory Elasticity Error analysis Finite volume method Galerkin methods Locks (fasteners) Elasticity equations Finite volume element Finite volume element method Linear elastostatics Mixed finite elements Nearly incompressible Optimal a priori error estimates Rotation vector Numerical methods
We propose a new locking-free family of mixed finite element and finite volume element methods for the approximation of linear elastostatics, formulated in terms of displacement, rotation vector, and pressure. The unique solvability of the three-field continuous formulation, as well as the well-definiteness and stability of the proposed Galerkin and Petrov–Galerkin methods, is established thanks to the Babuška–Brezzi theory. Optimal a priori error estimates are derived using norms robust with respect to the Lamé constants, turning these numerical methods particularly appealing for nearly incompressible materials. We exemplify the accuracy (in a suitably weighted norm), as well the applicability of the new formulation and the mixed schemes by conducting a number of computational tests in 2D and 3D, also including cases not covered by our theoretical analysis. © 2018 The Author(s)