Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity

Chen, Alvin; Bishop, Joseph E.; Sukumar, N.

doi:10.1016/j.cma.2024.116971

Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity

Journal Article · Tue Apr 09 00:00:00 EDT 2024 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2024.116971· OSTI ID:2372955

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Univ. of California, Davis, CA (United States)
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

In this paper, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. Here, we adopt the Hellinger–Reissner variational principle to construct a weak equilibrium condition and a stress based projection operator. In each element, the stress projection operator is expressed in terms of the nodal displacements, which leads to a displacement based formulation. This stress-hybrid approach assumes a globally continuous displacement field while the stress field is discontinuous across each element. The stress field is initially represented by divergence-free tensor polynomials based on Airy stress functions, but we also present a formulation that uses a penalty term to enforce the element equilibrium conditions, referred to as the Penalty Stress-Hybrid Virtual Element Method (PSH-VEM). Numerical results are presented for PSH-VEM and SH-VEM, and we compare their convergence to the composite triangle FEM and B-bar VEM on benchmark problems in linear elasticity. The SH-VEM converges optimally in the L 2 norm of the displacement, energy seminorm, and the L 2 norm of hydrostatic stress. Furthermore, the results reveal that PSH-VEM converges in most cases at a faster rate than the expected optimal rate, but it requires the selection of a suitably chosen penalty parameter.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)

Grant/Contract Number:: NA0003525

OSTI ID:: 2372955

Alternate ID(s):: OSTI ID: 2369921

Report Number(s):: SAND--2024-07294J

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 426; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Hellinger–Reissner variational principle
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Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity

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