A new hybrid-Trefftz triangular and quadrilateral plate elements

作者：Choo Yeon Seok^*; Choi Noori; Lee Byung Chai

来源：Applied Mathematical Modelling, 2010, 34(1): 14-23.

DOI：10.1016/j.apm.2009.03.022

• Hybrid-Trefftz
• Thick plate
• Transverse shear locking
• Finite element

We develop 9 DOF triangular and 12 DOF quadrilateral plate bending elements based on the hybrid-Trefftz method. Among the two independent displacement fields, i.e. the internal and the boundary displacements, we use the Mindlin-Reissner's thick plate solution with a particular solution under pressure load as the internal displacement field. For the boundary displacement field, we approximate transverse displacement (w) over tilde and rotations (beta) over tilde (x) and (beta) over tilde (y) cubic and quadratic hierarchical shape functions, respectively. We derive the transverse shear strains from constitutive equations and equilibrium equations, respectively, and then, remove additional degrees of freedom of hierarchical shape functions using the relations between these two shear strains. Results of numerical tests reveal that the new triangular (T32 - 7) and quadrilateral (Q32 - 11) elements are robust, accurate and free of shear locking in the thin limit.

• 出版日期2010-1