Buckling and post-buckling of variable stiffness plates with cutouts by a single-domain Ritz method

Structural components with variable stiffness can provide better performances with respect to classical ones and offer an enlarged design space for their optimization. They are attractive candidates for advanced lightweight structural applications whose functionalities often impose the presence of cutouts that requires accurate and effective analysis for their design. In the present work, a single-domain Ritz formulation is proposed, implemented and validated for the analysis of buckling and post-buckling behaviour of variable stiffness plates with cutouts. The plate model is based on the first-order shear deformation theory with nonlinear von Karman strain–displacement relationships. The plate generalized displacements are approximated with trial functions built as products of one-dimensional Legendre orthogonal polynomials. The non linear governing equations system is then deduced from the stationarity of the energy functional; the involved matrices are numerically computed by a special integration algorithm based on the implicit description of the cutout via suitable level-set functions. The formulation has been implemented in a computer code which has been used to validate the method through comparison with literature solutions for variable angle tow laminates with circular cutouts. Several investigations on buckling and post-buckling behaviour of variable angle tow composite plates with cutouts having different shapes and dimensions are then presented to illustrate the approach capabilities, provide benchmark results and point out features and design opportunities of the variable stiffness concept for the buckling and post-buckling design of advanced lightweight structures.