Triangular plate-bending elements by combined node with improved non-conforming modes and substitute shear strain fields

Abstract

A new triangular element for the finite element analysis of plate-bending problems is presented. For the purpose of sharing the program code of 4 node plate-bending element, two nodes of the 4 node element are combined to form a triangular element. Thus, the presented element would bring about great deal of efficiency of the computer program. To improve the behavior of the element, 3 non-conforming modes are added to the original rotations. In this study, Mindlin Plate theory is adapted to take into account shear deformation and the substitute shear strain fields are used to circumvent the shear locking phenomena. Furthermore, an efficient direct modification method for strains due to the various non-conforming modes are also applied. (Choi. and Lee., 2002). The direct modification method not only satisfies the requirement for passing patch test in the case of general non-conforming modes, but also requires relatively low computational cost. And also the selective integration scheme is available. The proposed element passes the patch tests and does not possess spurious zero-energy modes. Moreover, it does not show shear locking phenomena and has a good solution even in the distorted mesh. It is shown that the results using the new element give reliable solutions for several benchmark problems.