Static, free vibration, and buckling analyses of laminated composite plates via an isogeometric meshfree collocation approach

Abstract

An isogeometric meshfree collocation (IMC) approach is developed for the static, free vibration, and buckling analyses of laminated composite plates. As a promising alternative to the Galerkin method, the collocation method is introduced into the isogeometric analysis framework to reduce the computational cost and improve the convergence rate. An adaptive refinement strategy based on the gradient of strain energy is further implemented to generate more accurate results with higher computational efficiency. By adopting the first-order shear deformation plate theory, only one element is required to be modeled through the thickness of the laminated composite plate with homogenized material properties. The robustness and efficacy of the proposed method are demonstrated through a series of benchmark problems. It is found that the proposed approach can yield more accurate results at a similar convergence rate than its isogeometric analysis collocation counterpart. The effects of changing parameters such as the Young's modulus ratio, thickness-to-span ratio, and orthotropy angle on the structural analysis of composite plates are subsequently investigated in detail under different boundary and loading conditions. The simulation results are in good agreement with reference solutions.