Analysis of cracked Reissner-Mindlin plate using an extended meshfree method

Abstract

An extended meshfree method for analyzing cracked plates based on Reissner-Mindlin theory is presented in this paper. Among a variety of meshfree formulations, the radial point interpolation method (RPIM) is chosen in this study due to the satisfaction of the Kronecker delta property. The essential boundary conditions, therefore, are easily imposed in the RPIM. The shape function derived from RPIM is employed to interpolate the field variables. An extended RPIM formulation is used to model the crack segment without explicitly defining it in the discretized domain. The discontinuity due to the crack is defined by extrinsic enriched functions, particularly, the jump in the displacement field on two sides of the crack is modelled by the Heaviside function, and the stress singularity near the crack tip is described by the asymptotic enriched function. In this study, the stress resultant intensity factors (SRIFs) are evaluated through the interaction integral approach. The obtained SRIFs are shown in the paper through many numerical examples for comparison purposes. The trending variation of SRIFs is also observed from the numerical results. It can be remarked that the SRIFs depend on many factors: the number of cracks, crack orientation, load type and boundary conditions. The numerical examples show the accuracy of the present approach. The obtained results are compared with analytical solutions and other numerical methods.