Nonlinear Dynamic Bending Analysis of Plates Using a Higher-Order Shear Deformation Theory

Abstract

The transient dynamic elastoplastic bending analysis of plates is investigated. Higher-order shear deformation theory is employed for the purpose, so as to have more realistic transverse shear representation. The formulation requires C 0 continuity for nodal variables. Isoparametric parabolic finite element discretization is adopted. The yield criteria incorporated are von Mises and Tresca along with associated flow rules. The isotropic hardening is also included. Equations of motion are satisfied at discrete time intervals using direct integration method and central difference scheme. A special mass lumping scheme is adopted. As critical time step is very important in explicit integration scheme, precaution has been taken so as to have the time step smaller than the critical one. Numerical examples are solved and compared with solutions from literature. The formulation is shown to be superior in comparison to previous formulations, being more generic in all respects.

Nonlinear transient dynamic response of damped plates using a higher order shear deformation theory

“…The constitutive relations in terms of stress-resultants and other details are available elsewhere [27].…”

Linear Transient Dynamic Analysis of Plates With and Without Cutout

“…The practical implications here are of importance, as the failure of the structure is most likely to occur when subjected to extremely high transient load. Explosions, impacts, or catastrophic earth tremors can cause such loads, and even though the exact knowledge of the loads may not be available, the responsibility of the engineer for public safety makes it imperative for him to give the matter serious consideration [3][4][5][6]. This paper attempts to investigate the present dynamic behavior of the moderately thick plate in a linear domain.…”