Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element

Abstract

The modulus of elasticity of some materials changes under tensile and compressive states is simulated by constructing a typical material nonlinearity in a numerical analysis in this paper. The meshless Finite Block Method (FBM) has been developed to deal with 3D semi-infinite structures in the bimodular materials in this paper. The Lagrange polynomial interpolation is utilized to construct the meshless shape function with the mapping technique to transform the irregular finite domain or semi-infinite physical solids into a normalized domain. A shear modulus strategy is developed to present the nonlinear characteristics of bimodular material. In order to verify the efficiency and accuracy of FBM, the numerical results are compared with both analytical and numerical solutions provided by Finite Element Method (FEM) in four examples.

Three-Dimensional Fracture Analysis in Functionally Graded Materials Using the Finite Block Method in Strong Form

“…Therefore, it has attracted a great deal of research interest in recent years. Afterwards, the FBM was successfully applied to heat conduction problems [41], contact problems [42], non-linear elasticity [43], and fracture mechanics [44]. Also, many novel numerical methods have been proposed based on the idea of the FBM, such as the finite-and infinite-block Petrov-Galerkin method [45] and the element differential method [46][47][48].…”