A Simple High-Order Shear Deformation Triangular Plate Element with Incompatible Polynomial Approximation

Abstract

Featured Application: Due to the mathematical complexity raised by a high continuity requirement, developing simple/efficient standard finite elements with general polynomial approximations applicable for arbitrary HSDTs seems to be a difficult task at the present theoretical level. In this article, a series of High-order Shear Deformation Triangular Plate Elements (HSDTPEs) are developed using polynomial approximation for the analysis of isotropic thick-thin plates, through-thickness functionally graded plates, and cracked plates. The HSDTPEs have the advantage of simplicity in formulation, are free from shear locking, avoid using a shear correction factor and reduced integration, and provide stable solutions for thick and thin plates. The work can be further applied to plates and shells analysis with arbitrary shapes of elements, as well as more general problems related to the shear deformable effect, such as fracture and functionally graded plates. Abstract:The High-order Shear Deformation Theories (HSDTs) which can avoid the use of a shear correction factor and better predict the shear behavior of plates have gained extensive recognition and made quite great progress in recent years, but the general requirement of C 1 continuity in approximation fields in HSDTs brings difficulties for the numerical implementation of the standard finite element method which is similar to that of the classic Kirchhoff-Love plate theory. As a strong complement to HSDTs, in this work, a series of simple High-order Shear Deformation Triangular Plate Elements (HSDTPEs) using incompatible polynomial approximation are developed for the analysis of isotropic thick-thin plates, cracked plates, and through-thickness functionally graded plates. The elements employ incompatible polynomials to define the element approximation functions u/v/w, and a fictitious thin layer to enforce the displacement continuity among the adjacent plate elements. The HSDTPEs are free from shear-locking, avoid the use of a shear correction factor, and provide stable solutions for thick and thin plates. A variety of numerical examples are solved to demonstrate the convergence, accuracy, and robustness of the present HSDTPEs.

Finite Elements for the One Variable Version of Mindlin-Reissner Plate

“…The only variable in CPT is the lateral deflection of the plate middle plane. Because of neglecting the effect of shear deformation, the (CPT) applies mainly to thin plates [1,2].…”