Abstract
The polygonal scaled boundary finite element method (PSBFEM) is a novel approach integrating the standard scaled boundary finite element method and the polygonal mesh technique. In this work, a user-defined element (UEL) for dynamic analysis based on the PSBFEM is developed in the general finite element software ABAQUS. We present the main procedures of interacting with Abaqus, updating AMATRX and RHS, defining the UEL element, and solving the stiffness and mass matrices through eigenvalue decomposition. Several benchmark problems of free and forced vibration are solved to validate the proposed implementation. The results show that the PSBFEM is more accurate than the FEM with mesh refinement. Moreover, the PSBFEM avoids the occurrence of hanging nodes by constructing a polygonal mesh. Thus, the PSBFEM can choose an appropriate mesh resolution for different structures ensuring accuracy and reducing calculation costs.
Highlights
Structural dynamic analysis, especially the analysis of the response of a structure to an earthquake, is an important problem in engineering design
E scaled boundary finite element method (SBFEM) was presented in the 1990s by Song and Wolf [3]. e SBFEM is a semianalytical method that attempts to fuse the advantages and characteristics of the FEM and boundary element method (BEM) into one approach. e SBFEM only discretizes at the boundary
We show a simple polygon mesh of the polygonal scaled boundary finite element method (PSBFEM) to demonstrate the defining of elements in the user-defined element (UEL), as shown in Figure 3(a). e mesh comprises three types of element: triangular elements (U3), quadrilateral elements (U4), and pentagon elements (U5). e pentagon element (U5) is defined as follows: (a) e keywords of basic information are shown as follows: (1) ∗User element, nodes 5, type U5, properties 2, coordinates 2 (2) 1,2 (3) ∗Element, type U5, elset E5 (4) 3,2,3,4,8,7 (5) ∗Uel property, elest E5 (6) 2e5,0.3,2000,0,0
Summary
Structural dynamic analysis, especially the analysis of the response of a structure to an earthquake, is an important problem in engineering design. E finite element method (FEM) has become the most powerful and routine method of numerically analyzing the timedependent responses of structures in free and forced vibration problems. Ya et al [31] implemented an open-source polyhedral SBFEM element for three-dimensional and nonlinear problems through the Abaqus UEL. Ye et al [32] implemented a polygon SBFEM for two-dimensional linear elastostatic problems using the UEL subroutine. Andersen and Jones [37] compared a two-dimensional model and a threedimensional model for vibration analysis of two railway tunnel structures using the combined finite element method and boundary element method. Is work aims to develop a UEL of the PSBFEM for free and forced vibration analyses by relying on the user subroutine interface of general finite element software Abaqus.
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