Evaluation of fracture parameters in cracked plates using an extended meshfree method

Abstract

In this paper, an extended meshfree method approach is developed for numerical analysis of cracked plates using the First order Shear Deformation Theory — FSDT. Extrinsic enriched functions are employed to capture the jump in deflection and rotation fields, as well as the stress singularity in the vicinity of crack tip. Meshfree approximation of field variables is done by the Radial Point Interpolation Method, which possesses the desirable Kronecker-delta property, unlike many other meshfree methods. Numerical integration is conducted by the Cartesian Transformation Method (CTM), which turns a domain integration into a 1D integration and a boundary integration. As alternative to conventional Gaussian Quadrature (GQ), CTM is advantageous in the context of meshfree analysis, such that background cells are no longer required, forming a truly meshfree formulation. Furthermore, crack surfaces are viewed as part of the domain boundaries and thus, it is guaranteed that no discontinuities exist within the integration domain. The accuracy of the present approach is demonstrated by various numerical examples, in which Stress Resultant Intensity Factors (SRIFs) are evaluated. Obtained numerical results are compared with reference solutions derived from analytical, experimental and other existing numerical methods. It is also exhibited that CTM is more suitable to the meshfree context than GQ.