A novel extended integrated radial basis functions meshfree method for crack analysis in plate problem

Abstract

In this paper, a novel extended meshfree method is presented based on the integrated radial basis functions (iRBF) for crack analysis in bending plate problems. The new method is named XiRBF. The First-order Shear Deformation Theory (FSDT) is adopted to describe the deformation and stresses in cracked plate structures. The advantage of the iRBF approach is that it starts the approximation process with the highest-order derivative of the primary function first and then the lower-order derivatives are obtained by integration. This approximation style can give more accurate results for derivative values that appear a lot in governing equations of boundary value problems. In addition, the iRBF shape function also satisfies the Kronecker delta property, so essential boundary conditions can be applied as simply as the finite element method. In fracture analysis, to model the discontinuous behavior of crack surfaces, the Heaviside function is used, and to capture the singularity at the crack tip, the enriched functions are selected suitably based on the asymptotic analysis from the analytical solution. Various numerical tests are performed in which the stress resultant intensity factors (SRIFs) are calculated and the crack paths are visualized for crack propagation in the plate problems. The accuracy and efficiency of the proposed method are confirmed by comparing the present results with those obtained by other existing methods.