Buckling analysis of cracked orthotropic 3D plates and shells via an isogeometric-reproducing kernel particle method

Abstract

This paper aims to develop a three-dimensional isogeometric-reproducing kernel particle method (IGA-RKPM) coupling approach to study the buckling behavior of cracked isotropic and orthotropic plate and shell structures. The IGA and RKPM-based meshfree methods are coupled successfully through a reproducing condition in the physical domain that guarantees the higher-order polynomial continuity of basis functions and overcomes the barrier of global parameterization in the physical domain. The resulting coupling approach not only preserves the geometry exactness and offers a higher-order approximation based on IGA basis functions but also allows local refinement flexibility. Linear eigenvalue buckling analyses for cracked orthotropic plate and shell structures have been carried out within the framework of the proposed coupling approach. The effects of several parameters such as the crack length ratio, thickness-to-length ratio, and orthotropy angle on the critical buckling stress of the structures have been investigated in detail under different boundary and loading conditions. The efficacy and robustness of the proposed coupling approach have been demonstrated by comparing the present results with those available in literature.