Static and dynamic analysis of the composite laminated stiffened plates via the MLS meshless method

A meshfree method combined the first-order shear deformation (FSDT) theory to moving least-squares (MLS) approximation for static and dynamic investigations of composite laminated stiffened plates is presented. The novelty is that the resultant meshfree model presented in this paper considers the coupling effects in laminated plates and torsional effects and out-of-plane deformations for laminated ribs. The composite laminated stiffened plate is viewed as a composite structure of a laminated plate and ribs. MLS and FSDT are employed to establish the displacement fields, and the transformation equation of the nodal parameters between laminated rib and laminated plate is proposed. After superposing the potential and kinetic energy of the plate and stiffeners and introducing the displacement compatibility condition, the equations governing the bending and free vibration of the stiffened plates are obtained according to the principle of Minimum Potential Energy and Hamilton's Prin-ciple, respectively. Thereafter, several stiffened plate examples with different numbers and heights of ribs, different laminated arrangements and boundary conditions are calculated. The comparison of the present results with those given by ABAQUS and the literature. The results show the effectiveness and accuracy of the present method in analyzing the bending and free vibration properties of composite laminated stiffened plates.