An asymptotic variational formulation for dynamic analysis of multilayered anisotropic plates Original Research Article

A multilevel variational formulation for dynamic analysis of multilayered anisotropic plates is developed within the framework of three-dimensional elasticity. By means of asymptotic expansions the Hellinger-Reissner functional for the elastodynamic problem is decomposed into a series of functionals with which a computational model can be constructed. In the formulation multiple time scales are introduced so that the secular terms can be eliminated systematically in obtaining a uniform expansion leading to valid asymptotic solution. Modifications to the approximation of various orders are determined by considering the solvability conditions of the higher-order equations. The model is adaptive, when combined with the finite element method, it has many appealing features, including that the displacements and transverse stresses may be interpolated independently, that the nodal degree-of-freedom (DOF) at each level is less than that of Kirchhoff plates, and that the mass and stiffness matrices generated at the leading-order level are always used at subsequent levels. Above all, the solution is three-dimensional in effect yet requires only two-dimensional interpolation. The through-thickness variations of the field variables are determined analytically with no need of interpolating in the thickness direction.