SUMMARYA novel approach based on a combination of isogeometric analysis (IGA) and extended FEM is presented for fracture analysis of structures. The extended isogeometric analysis is capable of an efficient analysis of general crack problems using nonuniform rational B-splines as basis functions for both the solution field approximation and the geometric description, and it can reproduce crack tip singular fields and discontinuity across a crack. IGA has attracted a lot of interest for solving different types of engineering problems and is now further extended for the analysis of crack stability and propagation in two-dimensional isotropic media. Concepts of the extended FEM are used in IGA to avoid the necessity of remeshing in crack propagation problems and to increase the solution accuracy around the crack tip. Crack discontinuity is represented by the Heaviside function and isotropic analytical displacement fields near a crack tip are reproduced by means of the crack tip enrichment functions. Also, the Lagrange multiplier method is used to impose essential boundary conditions. Moreover, the subtriangles technique is utilized for improving the accuracy of integration by the Gauss quadrature rule. Several two-dimensional static and quasi-static crack propagation problems are solved to demonstrate the efficiency of the proposed method and the results of mixed-mode stress intensity factors are compared with analytical and extended FEM results.

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In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using the rule of mixtures or by Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation plate theory (FSDT). The shear correction factors are evaluated employing the energy equivalence principle and a simple modification to the shear correction factor is presented to alleviate shear locking. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates.

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Buckling, free and forced vibration analyses of orthotropic plates are studied numerically using Isogeometric analysis. The present formulation is based on the classical plate theory (CPT) while the NURBS basis function is employed for both the parametrization of the geometry and the approximation of plate deflection. An efficient and easy-to-implement technique is used for imposing the essential boundary conditions. Numerical examples for free and forced vibration and buckling of orthotropic plates with different boundary conditions and configurations are considered. The numerical results are compared with other existing solutions to show the efficiency and accuracy of the proposed approach for such problems.