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This paper develops a coupling approach which integrates the meshfree method and isogeometric analysis (IGA) for static and free-vibration analyses of cracks in thin-shell structures. In this approach, the domain surrounding the cracks is represented by the meshfree method while the rest domain is meshed by IGA. The present approach is capable of preserving geometry exactness and high continuity of IGA. The local refinement is achieved by adding the nodes along the background cells in the meshfree domain. Moreover, the equivalent domain integral technique for three-dimensional problems is derived from the additional Kirchhoff-Love theory to compute the J-integral for the thin-shell model. The proposed approach is able to address the problems involving through-the-thickness cracks without using additional rotational degrees of freedom, which facilitates the enrichment strategy for crack tips. The crack tip enrichment effects and the stress distribution and displacements around the crack tips are investigated. Free vibrations of cracks in thin shells are also analyzed. Numerical examples are presented to demonstrate the accuracy and computational efficiency of the coupling approach. [ABSTRACT FROM AUTHOR]

We present a rotation free isogeometric analysis formulation based on Kirchhoff-Love theory, which aims to address free vibration and buckling behaviors of functionally graded thin plates with in-plane material inhomogeneity. For Kirchhoff-Love thin plate analysis, construction of C 1 conforming finite element approximation is not straightforward, while isogeometric analysis with high-order continuity splines basis functions is ideally suited for Kirchhoff-Love elements. We first explain the formulations and then provide verification of the present method through numerical examples. Studies on convergence and comparison with reference solutions are demonstrated to show the effectiveness and accuracy of the proposed method. Effects on natural frequencies, critical buckling loads and mode shapes originated from the material inhomogeneity and boundary conditions are numerically investigated. [ABSTRACT FROM AUTHOR]

The paper is to develop stochastic isogeometric analysis for the free vibration of functionally graded plates with spatially varying random material properties. The isogeometric analysis method is employed in the new stochastic analysis scheme which is called Stochastic IsoGeometric Analysis (SIGA). The elastic modulus and mass density are modeled as homogeneous Gaussian random fields along the plane of structure. The governing equation of stochastic isogeometric analysis for free vibration of functionally graded plates is derived in conjunction with perturbation expansions to predict the first and second moments of eigenvalues. In order to verify proposed method, the brute force Monte Carlo simulation is employed. The mean, variance, and COV (Coefficient of Variation) predicted by SIGA and those predicted by Monte Carlo simulation show good agreement. The numerical examples demonstrate that the randomness of material properties affects significantly the structural responses of the functionally graded plates. The correlation between elastic modulus and mass density is also observed to have significant effect on the response COV of eigenvalue. [ABSTRACT FROM AUTHOR]