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A Novel Multipoint Stress Control Volume Method for Linear Elasticity on Quadrilateral Grids by Fu, Shubin; Zhao, Lina is a scholarly article available to read on EtoBox.

What is A Novel Multipoint Stress Control Volume Method for Linear Elasticity on Quadrilateral Grids about?

In this paper, we develop a novel control volume method that is locally conservative and locking-free for linear elasticity problem on quadrilateral grids. The symmetry of stress is weakly imposed through the introduction of a Lagrange multiplier. As such, the method involves three unknowns: stress, displacement and rotation. To ensure the well-posedness of the scheme, a pair of carefully defined finite element spaces is used for the stress, displacement and rotation such that the inf-sup condition holds. An appealing feature of the method is that piecewise constant functions are used for the approximations of stress, displacement and rotation, which greatly simplifies the implementation. In particular, the stress space is defined delicately such that the stress bilinear form is localized around each vertex, which allows for the local elimination of the stress, resulting in a cell-centered system. By choosing different definitions of the space for rotation, we develop two variants of the method. In particular, the first method uses a constant function for rotation over the interaction region, which allows for further elimination and results in a cell-centered system involving displ

Author

Fu, Shubin; Zhao, Lina

Published

2025

Language

EN