Hybrid meshless/displacement discontinuity method for FGM Reissner's plate with cracks

• Published in: Applied Mathematical Modelling Vol. 90; pp. 1226 - 1244
• Main Authors: Zheng, H., Sladek, J., Sladek, V., Wang, S.K., Wen, P.H.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.02.2021; Elsevier BV
• Subjects: Boundary element method; Chebyshev approximation; Collocation methods; Cracks; Discontinuity; Displacement discontinuity method; Finite element method; Functionally graded materials; Functionally gradient materials; Interpolation; Kirchhoff and Reissner plate theories; Meshless local Petrov-Galerkin method; Meshless methods; Polynomials; Software; Stress intensity factors; Kirchhoff and Reissner plate theories; Stress intensity factors; Displacement discontinuity method; Functionally graded materials; Meshless local Petrov-Galerkin method; Boundary element method
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2020.10.023

•Advantages of the boundary element method and meshless approaches are inherited in the hybrid MDDM to deal with crack problems.•Cracked Reissner's plate with non homogenous media is investigated by MDDM first time.•High accurate/convergent solutions using Chebyshev polynomials can be obtained by the hybrid method. Growing applications of non-homogenous media in engineering structures require the application of powerful computational tools. A novel hybrid Meshless Displacement Discontinuity Method (MDDM) for cracked Reissner's plate in Functionally Graded Materials (FGMs) is presented in this paper. The fundamental solutions of slope and deflection discontinuity for an isotropic homogenous media are chosen as a part of general solutions to create the gaps between the crack surfaces. The governing equation is satisfied by using the meshless methods such as the Meshless Local Petrov-Galerkin (MLPG) and the Point Collocation Method (PCM) with Lagrange series interpolation and mapping technique. The Stress Intensity Factors (SIFs) are evaluated analytically with the Chebyshev polynomials. The accuracy is verified by comparison of numerical and analytical results.