| Texto completo | |
| Autor(es): |
Avancini, Giovane
;
Shauer, Nathan
;
Oliveira, Hugo Luiz
;
Devloo, Philippe R. B.
Número total de Autores: 4
|
| Tipo de documento: | Artigo Científico |
| Fonte: | COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING; v. 446, p. 28-pg., 2025-11-01. |
| Resumo | |
This work presents a novel primal double-hybrid finite element formulation for solving two-or three-dimensional compressible, quasi-incompressible, and incompressible elasticity problems. Hybrid methods are typically derived from an extended variational principle, where interelement continuity requirements are relaxed and weakly enforced via Lagrange multipliers at element interfaces. In this context, we propose using a De Rham-compatible H(div)-L2 pair for displacements and pressure, respectively. The H(div) space ensures normal displacement continuity across elements, while tangential continuity is enforced weakly by introducing a Lagrange multiplier associated with the shear stress on element edges or faces, depending on the problem's dimension. A second hybridization is applied to the shear stress, where the resulting Lagrange multiplier is now associated with a tangent displacement. As a result, the shear stress can be statically condensed to recover a positive-definite matrix that depends on the primal variable components. Although solving a saddle-point system remains necessary in the incompressible limit, numerical results demonstrate that this approach significantly enhances stability compared to the semi-hybrid formulation. Properties such as stability, consistency, and local conservation are discussed in detail. The formulation is tested and verified using 3D benchmarks for which analytical and/or numerical solutions are available. Optimal convergence rates are obtained independent of the Poisson ratio. The proposed methodology is also applied to a complex three-dimensional problem to demonstrate its robustness. (AU) | |
| Processo FAPESP: | 24/06917-8 - Técnicas Avançadas de Elementos Finitos para Simulação de Propagação de Fraturas em Meios Ortotrópicos e Heterogêneos |
| Beneficiário: | Nathan Shauer |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |