Alternative Low-Order Triangular Elements for the Transient Dynamic Analysis of Orthotropic Thick and Thin Plates

In this paper, the authors discuss the transient dynamic analysis of orthotropic thick and thin plates using low-order triangular finite elements. The elements are based on two related formulations, namely the free formulation and the deviatoric strain formulation. A key feature of the elements is that they use approximations for the transverse displacement and rotations that exactly satisfy the governing equations of Mindlin’s theory. This ensures that the element approximations are consistent for both thick and thin plates, and no locking occurs in the thin plate limit as the plate thickness approaches zero. In this limiting case, the elements become thin plate elements without any additional changes. All the required element terms are developed in a straightforward manner in closed form. Newmark’s method is used to solve the time-varying algebraic equations. Examples are given in the paper to demonstrate the accuracy that is achieved with the proposed elements.