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.
Chen, Alvin, et al. "Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity." Computer Methods in Applied Mechanics and Engineering, vol. 426, Apr. 2024. https://doi.org/10.1016/j.cma.2024.116971
Chen, Alvin, Bishop, Joseph E., & Sukumar, N. (2024). Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity. Computer Methods in Applied Mechanics and Engineering, 426. https://doi.org/10.1016/j.cma.2024.116971
Chen, Alvin, Bishop, Joseph E., and Sukumar, N., "Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity," Computer Methods in Applied Mechanics and Engineering 426 (2024), https://doi.org/10.1016/j.cma.2024.116971
@article{osti_2372955,
author = {Chen, Alvin and Bishop, Joseph E. and Sukumar, N.},
title = {Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity},
annote = {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.},
doi = {10.1016/j.cma.2024.116971},
url = {https://www.osti.gov/biblio/2372955},
journal = {Computer Methods in Applied Mechanics and Engineering},
issn = {ISSN 0045-7825},
volume = {426},
place = {United States},
publisher = {Elsevier},
year = {2024},
month = {04}}