An Arbitrary Polygonal Stress Hybrid Element for Structural Dynamic Response Analysis

This paper constructs a new two-dimensional arbitrary polygonal stress hybrid dynamic (APSHD) element for structural dynamic response analysis. Firstly, the energy function is established based on Hamilton’s principle. Then, the finite element time–space discrete format is constructed using the generalized variational principle and the direct integration method. Finally, an explicit polynomial form of the combined stress solution is give, and its derivation process is shown in detail. After completing the theoretical construction, the numerical calculation program of the APSHD element is written in Fortran, and samples are verified. Models show that the APSHD element performs well in accuracy and convergence. Furthermore, it is insensitive to mesh distortion and has low dependence on selecting time steps.