Abstract: A stress model of the hybrid-mixed formulation is implemented on a compact radial basis and applied to the solution of elliptic problems. The formulation is based on a two-field domain approximation coupled with an independent boundary approximation. It is strictly meshless, as its implementation does not require the decomposition of the domain to define the approximation bases or to support the numerical integration of the coefficients of the solving system. The performance of the formulation is illustrated on a two-dimensional linear elastostatic problem. The meshless formulation used here has been originally developed in the context of the finite element method and applied to the solution of solid mechanics problems. A review of the alternative hybrid-mixed, hybrid and hybrid-Trefftz formulations and their complementary stress and displacement models that have been studied in the context of the finite element method applied to the solution of solid mechanics problems can be found in (1). The paper reports on the implementation of the stress model of the hybrid mixed formulation in a mesh free context (2). The formulation used here is termed mixed because two fields are approximated independently in the domain under analysis (the stress and displacement fields). It is termed hybrid because a boundary field is also approximated independently (the boundary displacements in the stress model used here). This formulation endures two major disadvantages when compared with formulations based on single-field approximations, namely a substantially higher number of degrees- of-freedom and a higher susceptibility to spurious solutions. The advantages it offers are a better modelling of gradient fields, as they are approximated independently, and the possibility of using virtually any approximation bases, as no constraints are placed a priori in terms of the fundamental equations of the problems.
Publication Year: 2003
Publication Date: 2003-01-01
Language: en
Type: article
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