On the use of exponential basis functions in the analysis of shear deformable laminated plates

In this report, we introduce a meshfree approach for static analysis of isotropic/orthotropic crossply laminated plates with symmetric/non-symmetric layers. Classical, first and third order shear deformation plate theories are employed to perform the analyses. In this method, the solution is first split into homogenous and particular parts and then the homogenous part is approximated by the summation of an appropriately selected set of exponential basis functions (EBFs) with unknown coefficients. In the homogenous solution the EBFs are restricted to satisfy the governing differential equation. The particular solution is derived using a similar approach and another series of EBFs. The imposition of the boundary conditions and determination of the
unknown coefficients are performed by a collocation method through a discrete transformation technique. The solution method allows us to obtain semi-analytical solution of plate problems with various shapes and boundary conditions. The solutions of several benchmark plate problems with various geometries are presented to validate the results.