Displacement-pseudostress formulation for the linear elasticity spectral problem

2021/01/24 by Daniel Inzunza, Felipe Lepe, Inzunza, Daniel +3 · 3 citations
Engineering · #Composite Structure Analysis and Optimization #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA) #Structural Health Monitoring Techniques

paper · pdf · doi:10.48550/arxiv.2101.09828

openalex publication_date 2021/01/24 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28

Abstract

In this paper we analyze a mixed displacement-pseudostress formulation for the elasticity eigenvalue problem. We propose a finite element method to approximate the pseudostress tensor with Raviart-Thomas elements and the displacement with piecewise polynomials. With the aid of the classic theory for compact operators, we prove that our method is convergent and does not introduce spurious modes. Also, we obtain error estimates for the proposed method. Finally, we report some numerical tests supporting the theoretical results.

Cited by

• A locking-free mixed virtual element discretization for the two dimensional elasticity eigenvalue problem
• The two-grid weak Galerkin method and enriched Crouzeix-Raviart element method for linear elastic eigenvalue problems
• The Weak Galerkin and Crouzeix-Raviart element method for elastic eigenvalue problems

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