Simulation of Stress Concentration Problems in Laminated Plates by Quasi-Trefftz Finite Element Models

Abstract

Hybrid quasi-Trefftz finite elements have been applied with success to the analysis of laminated plates. Two independent fields are approximated by linearly independent, hierarchical polynomials: the stress basis in the domain, adapted from PapkovitchNeuber solution of Navier equations, and the displacement basis, defined on element surface. The stress field that satisfies the Trefftz constraint a priori for isotropic material is adapted for orthotropic materials, which leads to the term "quasi". In this work, the hexahedral hybrid quasi-Trefftz stress element is applied to the modeling of nonsymmetric laminates and laminated composite plates with geometric discontinuities. The hierarchical prefinement is exploited.

On the sparsity of linear systems of equations for a new stress basis applied to three-dimensional Hybrid-Trefftz stress finite elements

“…In the subject of crack analysis, stress concentration and singular fields, the hybrid-Trefftz elements were applied by Bussamra et al (2014Bussamra et al ( , 2016 in a generalized framework with associated Legendre and Chebyshev polynomials, and by Kaczmarczyk and Pearce (2009) in a nodal framework with Airy functions. To verify the accuracy of the stress predictions of the proposed finite element, a structure with high level of stress gradient is analyzed.…”

“…Hybrid-Trefftz elements with both nodal and generalized variables framework have shown good performance in linear elastic (Freitas and Bussamra, 2000) and elastoplastic (Bussamra et al, 2001) analysis of solids with LC functions. In crack analysis, singular stress fields and stress concentration problems were analyzed using LC and Airy functions (Bussamra et al, 2014) and Kaczmarczyk and Pearce (2009), respectively. In multisite cracked solids, Chebyshev functions were applied in a nodal framework (Argôlo and Proença, 2016).…”

Hybrid Fundamental Solution Based Finite Element Method: Theory and Applications

“…A novel hybrid finite element formulation, called the hybrid fundamental solution based FEM (HFS-FEM), was recently developed based on the framework of hybrid Trefftz finite element method (HT-FEM) and the idea of the method of fundamental solution (MFS) [1][2][3][4][5]. In this method, two independent assumed fields (intraelement filed and auxiliary frame field) are employed and the domain integrals in the variational functional can be directly converted to boundary integrals without any appreciable increase in computational effort as in HT-FEM [6][7][8]. It should be mentioned that the intraelement field of HFS-FEM is approximated by the linear combination of fundamental solutions analytically satisfying the related governing equation, instead of -complete functions as in HT-FEM.…”

Método da partição e formulação híbrido-Trefftz na análise de sólidos bidimensionais contendo múltiplas fissuras

“…Por fim, a formulação híbrido-Trefftz (JIROUSEK, 1978, JIROUSEK, LEON, 1977, JIROUSEK, TEODORESCU, 1982, JIROUSEK, VENKATESH, 1992, JIROUSEK, WRÓBLEWSKI, 1996, FREITAS, 1998, FREITAS, ALMEIDA, PEREIRA, 1999, FREITAS, BUSSAMRA, 2000, BUSSAMRA, NETO, PONCIANO, 2014, BUSSAMRA, NETO, RODRIGUES, 2016 também é um caso particular da híbrido-mista ao impor que as funções de aproximação das tensões no domínio do elemento atendam a equação governativa: a equação de Navier. Apesar da forte restrição na escolha de funções para a aproximação, essa formulação proporciona soluções mais precisas (mesmo com malhas grosseiras) dentre as três formulações híbridas aqui apresentadas, particularmente nos problemas da elasticidade linear.…”