A Trefftz meshfree framework for stability and dynamic analysis of laminated composite plates based on various higher order shear deformation theories

This paper develops a novel meshfree method based on Trefftz formulation for buckling and free vibration analysis of laminated composite plates, considering various higher order shear deformation theories, using exponential bases. Domain discretization is performed by an arbitrary nodal grid including the degrees of freedom, whose formation needs considerably less effort than that of the element grid in mesh-based methods, with the solution quality insensitive to the grid irregularities. Sufficient number of nearby nodes are correlated in a local subdomain named “cloud”, whose overlap with its adjacent clouds integrates the solution over the entire domain. In this framework, we propose a novel technique to solve the corresponding eigenvalue problem without needing the common iterative approach in Trefftz methods, yet enforcing the bases almost exactly satisfy the equation. To this end, the part of the equation with the unknown eigenvalue is moved to the right side of the equality as external loading. The resulted nonhomogeneous problem is then solved to give an eigenvalue matrix equation, from which the critical buckling loads or free vibration frequencies are extracted. Numerical experiments covering a wide range of geometries, materials, boundary conditions and interior point supports, reveal the methods’ accuracy and efficiency.