Meshless finite block method with infinite elements for axisymmetric cracked solid made of functionally graded materials

Axisymmetric cracked solid structures in functionally graded materials (FGMs) under static and dynamic loading are analysed by using the Finite Block Method (FBM). Based on the axisymmetric elasticity theory, the equilibrium equations inside the rotating section of FGMs in the cylinder coordinate system are formulated in strong form. The shape functions in the FBM are constructed by Lagrange polynomial interpolation with mapping techniques for the irregular finite or semi-infinite physical domains. A special approximation technique is proposed to avoid singularities in the traction boundary conditions on the axis of symmetry. The stress intensity factor is obtained by the crack opening displacement. The time-dependent problems are addressed using the Laplace transform and Durbin's inverse approach. Several numerical examples are investigated in order to illustrate the accuracy and convergence of the proposed method, and the numerical solutions are compared with analytical solutions, the finite element method and other methods. •Algorithm for layered 3D structure in semi-infinite space.•Infinite element in the finite block method.•Static/Dynamic load for fracture problems.•Functionally graded material.