Discontinuous zone free element method with variable condensation and applications in thermal-stress analysis of functionally graded material structures with cracks

In this paper, a new solution approach of using Free Element Method (FrEM) is proposed to solve thermal-mechanical problems consisting of composite materials and cracks. In this approach, the computational domain of the problem is discretized into multi-zones and in each zone a set of local nodes are generated. At the local nodes of each zone, the high order free elements are used to collocate the governing differential equations, and at the interface nodes of adjacent zones the balance (conservative) conditions are employed to set up the global system of equations according to the connectivity of each zone's local nodes with respect to the defined global nodes. To improve the ability of the proposed zonal FrEM in solving large-scale problems, the physical variables within each zone are condensed to the boundary variables of the zone through an ingenious equation solving technique. To simulate the discontinuity of the fluxes/tractions at corners and cracks meeting by different zones or on the outer boundaries with jumped fluxes/tractions, a discontinuous zone technique is proposed at these places by defining multiple nodes at the same corner. A number of numerical examples including cracks and functionally graded materials (FGMs) are analyzed to verify the correctness and efficiency of the proposed method. (C) 2020 Elsevier Ltd. All rights reserved.