A nonlocal shell p-element for the nonlinear free vibration of orthotropic doubly curved shallow nanoshells

摘要

A nonlocal shell p-element is developed for the nonlinear free vibration of orthotropic doubly curved shallow nanoshells of rectangular planform. A first-order shear deformation theory based on Donnell's shallow shell theory and von Karman's nonlinear strains is used. The stiffness and mass matrices are derived using the principle of virtual displacements and the harmonic balance method. The governing nonlinear equations are solved by direct iteration. The accuracy of the element is demonstrated through convergence study and comparison with results reported in the literature. It is shown that the hardening spring effect decreases with increasing curvature but remains constant with increasing small length scale.