A new nine DOF triangular element for analysis of thick and thin plates

Abstract

A simple triangular 9 DOF plate bending element for analysis of thick and thin plate is presented in this paper. This element is constructed by the following procedure:(i) the variation functions of the rotation and shear strain along each side of the element are determined using Timoshenko's beam theory; and (ii) the rotation, curvature and shear strain ®elds in the domain of the element are then determined using the technique of improved interpolation.The proposed element, denoted by ARS-T9, is robust and free of shear locking and, thus, it can be employed to analyze very thin plate. Numerical examples show that the proposed element is a high performance element for thick and thin plates.

Application of the quadrilateral area co‐ordinate method: a new element for Mindlin–Reissner plate

“…The consistent nodal forces for M ns = 1 are given in Figure 8 for an arbitrary thickness t. Table Ishows that the results of M xy obtained using the proposed element are exactly the same as those of the exact solution, except the case of thick plate in which the discrepancy between the two solutions is less than 4%. These errors arise from the fact that the rotation fields obtained by Equation (46) are not exactly compatible with Equation (20b) in a distorted mesh, especially for thick plates. Since they are in an acceptable range, the element AC-MQ4 is still considered to pass this patch test.…”

“…and [E] and [P ] are given in Appendix A. Secondly, the normal slope n by rotation field can be obtained from Equation (46). Then substitute it into Equation (48), we have…”

A Refined Higher-Order Hybrid Stress Quadrilateral Element for Free Vibration and Buckling Analyses of Reissner-Mindlin Plates

“…Substituting the stress equation (11), boundary force equation (12), and displacement approximations equation (13) into the functional (10),…”

“…Bathe et al [12] introduced the MITC element and proposed strain energy patch test function to evaluate the convergence. Based on Timoshenko beam function, Soh et al [13] proposed a triangular 9-DOF plate bending element which can be employed to analyze very thin plate (the thickness/span ratio of the plate is about 10 −11 ). Soon, Soh et al [14] introduced a quadrilateral 12-DOF plate bending element.…”

Purely electrical damping of vibrations in arbitrary PEM plates: a mixed non-conforming FEM-Runge-Kutta time evolution analysis

“…There is a huge literature about triangular FE suitable for our requirements. The most part of the triangular elements used in structural mechanics are based upon the Reissner-Mindlin plate theory, see [2], [8][9][10], [12], [13] and for this reason have not been considered for the problem proposed in this paper.…”