Accurate Static and Dynamic Analysis Using Unstructured Meshes for Complicated Geometry Problems (Advances in Applied Mathematics and Mechanics, 2025)
The low accuracy using unstructured meshes to solve complicated geometry problems is a significant challenge in practical engineering. It is the key to solve this issue through enhancing the accuracy of tetrahedral element. This work develops a simple strategy to enhance the accuracy of tetrahedral element with the Shepard interpolation function. In which the strain field is reconstructed by introducing the weighted strains of adjacent tetrahedral elements to central tetrahedral element. The stiffness of the discrete system is significantly softened with this simple operation, which leads to a great accuracy improvement. Furthermore, this simple modification makes linear tetrahedral element owns higher accuracy even compared with hexahedral element. The high precision tetrahedral element makes finite element analysis more acceptable for engineers. It provides a novel solution to finite element analysis using unstructured meshes for practical engineering problems with complicated geometry. In order to validate the accuracy and feasibility of present modified tetrahedral element (M-T4) in complicated geometry problems, several engineering examples are performed, including linear static analysis, modal analysis, frequency response analysis, transient response analysis, and response spectrum analysis. The remarkable performance of the M-T4 suggests its wide applicability to practical engineering problems.