Static and dynamic analysis of shallow shells with functionally graded and orthotropic material properties

The first-order shear deformation theory is used for description of shear deformable shallow shells with orthotropic material properties and continuously varying material properties through the shell thickness. Static and dynamic loads are considered here. For transient elastodynamic cases the Laplace-transform is used to eliminate the time dependence of the field variables. The first-order shear deformation theory reduces the original three-dimensional (3-D) problem into a two-dimensional (2-D) one. A meshless local Petrov-Galerkin (MLPG) formulation is applied to solve the 2-D problem. A weak formulation with a unit test function transforms the set of governing equations into local integral equations on local subdomains in the basic plane of the shell. Nodal points are randomly spread in that domain and each node is surrounded by a circular subdomain to which local integral equations are applied. The meshless approximation based on the Moving Least-Squares (MLS) method is employed for the implementation. The unknown Laplace-transformed quantities are computed from the local boundary-domain integral equations. The time-dependent values are obtained by the Stehfest's inversion technique.