An efficient three-node triangular Mindlin–Reissner flat shell element

Abstract

Shell elements are extensively used by engineers for modeling the behavior of shell structures. Among common shell elements, triangular shell elements are not influenced by element warping. This paper proposes a new three-node triangular flat shell element with six degrees of freedom per each node, named TMRFS. The element is formed by assemblage of new bending and membrane elements. The bending element is formulated based on the hybrid displacement function element method and Mindlin–Reissner plate theory. In this element, an assumed displacement function is employed as the trial function. The membrane component is an unsymmetric triangular membrane element with drilling vertex rotations. The membrane element employs two different types of displacement fields as the test and trial functions. The test function is a displacement field which is the same as one used in well-known Allman triangular element. Meanwhile, instead of displacement field, the analytical stress field is considered as the trial function. Numerical tests show that the accuracy of the proposed flat shell element is reasonable in comparison with some popular triangular elements and its performance is insensitive to geometry, load and boundary conditions. Moreover, the proposed element preserves the advantages of its formulation including free of membrane locking, shear locking and stiffness matrix singularity problems.