Analysis of cracked functionally graded material plates using XIGA based on generalized higher-order shear deformation theory

Abstract

A generalized higher-order shear deformation theory (GHSDT) along with extended isogeometric analysis (XIGA) is presented for the analysis of cracked functionally graded material (FGM) plates. The material properties of the FGM vary exponentially along the thickness of the plate. The GHSDT ensures a traction-free boundary conditions at the surfaces of the plate without a need of shear correction factor (SCF). To model a crack, the isogeometric analysis (IGA) approximation is enriched with partition of unity (PU) enrichment functions. The C1 continuity requirement of the GHSDT is easily achieved in IGA through Non-uniform rational B-splines (NURBS). The stress intensity factor (SIF) at any location along the thickness of the plate is computed using domain based interaction integral approach. In the interaction integral, 2-D asymptotic crack-tip fields obtained from the LEFM provide a straightforward and simple solution scheme for SIF along the thickness of the FGM plate. The accuracy of the proposed approach is demonstrated by solving various problems. The effect of various parameters such as loading, boundary conditions, crack length and plate thickness is investigated on the SIF. The solutions of several cracked FGM plate problems obtained by GHSDT based XIGA (GHSDT-XIGA) are compared with FSDT based XIGA (FSDT-XIGA) and reference solutions.