Optimizing the placement of nodes in a proposed triangular plate element

Abstract

In this article, the optimization of element node positions using Adam's algorithm is employed to improve the finite element efficiency. While previous research has focused on the effect of changing the mesh on the finite element response, little attention has been given to the impact of node position changes without altering the mesh structure. The article presents a formulation of a triangular element with 15 degrees of freedom using a complete fourth-degree field for deformations. Through numerous numerical tests involving normal and skew geometries, different support conditions, and various loadings, the optimal positions of the nodes are determined. These tests are conducted on both coarse and fine meshes, with and without distortion. The results indicate that in the suggested element, particularly in coarse meshes and situations involving significant distortion, the outcome is greatly influenced by the positions of the nodes. By employing the proposed finite element formulation that incorporates Adam's optimization algorithm, it is possible to achieve accurate results in coarse meshes with distortion. This can be accomplished by using the proposed element without the optimization algorithm and with a uniform distribution of element nodes in fine regular meshes.