Bending analysis of laminated composite plates using isogeometric collocation method

Analytical Bending Solutions of Orthotropic Rectangular Thin Plates with Two Adjacent Edges Free and the Others Clamped or Simply Supported Using Finite Integral Transform Method

“…us, the research on the mechanical behavior of orthotropic plate aroused the interest of scientists and engineers for more than a century. Literature surveys reveal that numerical methods such as finite difference method [1], spline element method [2], boundary element method [3], meshless method [4], finite element method (FEM) [5], boundary particle method [6], isogeometric collocation method [7], discrete singular convolution method [8][9][10][11], and differential quadrature method [12,13] are competent to analyze the bending of plates with different edge conditions, loading patterns, and material properties. However, the aforementioned numerical methods satisfy the engineering requirements with acceptable error, but approximate solution is obtained, which is the main disadvantage of the numerical methods.…”

Fast and accurate elastic analysis of laminated composite plates via isogeometric collocation and an equilibrium-based stress recovery approach

“…IGA-Galerkin methods have already been used to solve composite laminate problems, especially relying on high-order theories for enhanced plate and shell theories [27,42,66,69,72]. Recently an isogeometric collocation numerical formulation has been proposed [61] to study Reissner-Mindlin composite plates. Other Galerkin methods [32,33,66] compute instead a full 3D stress state using isogeometric analysis, applying a layerwise technique.…”

Two-dimensional generalized finite integral transform method for new analytic bending solutions of orthotropic rectangular thin foundation plates

“…Many previous studies have dealt with plate problems with different combinations of boundary conditions, load patterns and material properties by using various approximate or numerical methods. Besides the classical methods such as the finite difference method [1], finite element method (FEM) [2] and boundary element method [3], which are still popular in handling plate problems, some recently developed effective approaches have shown important progresses in the field, including the meshless method [4], isogeometric collocation method [5], boundary particle method [6], finite volume method [7], virtual element method [8], discrete singular convolution method [9], simple hp cloud method [10], finite-layer method [11], etc. In comparison with the numerical methods, analytic methods are sparse, which is attributed to the difficulty in seeking analytic solutions to the complex boundary value problems (BVPs) of higher-order partial differential equations (PDEs) that describe the plate problems.…”