Geometrically nonlinear analysis of variable-stiffness plates using the R-functions combined with the Ritz method

This paper illustrates an advanced Ritz-based strategy for the geometrically nonlinear analysis of variable-stiffness (VS) laminates with complex planar shapes and arbitrary boundary conditions. The approach relies on the combined use of the R-functions theory to represent the plate geometry and first-order shear deformation theory (FSDT) to approximate the kinematics. The asymptotic-numerical method (ANM) is used as an effective means for solving the nonlinear equilibrium equations. The proposed tool offers the advantage of allowing a wide class of configurations to be analyzed in a meshfree framework with reduced modeling time. The procedure based on the ANM provides robustness and few parameters to be defined to set up the solution process. Four exemplary test cases are presented to clarify the potential offered by the proposed semi-analytical tool. The accuracy of the prediction is established by comparison against finite element simulations. The ease in defining relatively complex laminate configurations suggests the use of this tool as an effective means for performing preliminary nonlinear computations with minimal modeling effort.