scholarly journals A Polygonal Scaled Boundary Finite Element Method for Solving Heat Conduction Problems

2021 ◽  
Author(s):  
Yang Yang ◽  
Zongliang Zhang ◽  
Yelin Feng ◽  
Yuzhen Yu ◽  
Kun Wang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Mass Matrix ◽  
Eigenvalue Decomposition ◽  
Benchmark Problems ◽  
Polygonal Mesh ◽  
Scaled Boundary Finite Element ◽  
Element Method

This paper presents a steady-state and transient heat conduction analysis framework using the polygonal scaled boundary finite element method (PSBFEM) with polygon/quadtree meshes. The PSBFEM is implemented with commercial finite element code Abaqus by the User Element Subroutine (UEL) feature. The detailed implementation of the framework, defining the UEL element, and solving the stiffness/mass matrix by the eigenvalue decomposition are presented. Several benchmark problems from heat conduction are solved to validate the proposed implementation. Results show that the PSBFEM is reliable and accurate for solving heat conduction problems. Not only can the proposed implementation help engineering practitioners analyze the heat conduction problem using polygonal mesh in Abaqus, but it also provides a reference for developing the UEL to solve other problems using the scaled boundary finite element method.

scholarly journals Free and Forced Vibration Analysis in Abaqus Based on the Polygonal Scaled Boundary Finite Element Method

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Nan Ye ◽  
Chao Su ◽  
Yang Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Forced Vibration ◽  
Eigenvalue Decomposition ◽  
Benchmark Problems ◽  
Polygonal Mesh ◽  
Finite Element Software ◽  
Forced Vibration Analysis ◽  
Scaled Boundary Finite Element ◽  
Element Method

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.

scholarly journals PSBFEM-Abaqus: Development of User Element Subroutine (UEL) for Polygonal Scaled Boundary Finite Element Method in Abaqus

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Nan Ye ◽  
Chao Su ◽  
Yang Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Eigenvalue Decomposition ◽  
Benchmark Problems ◽  
Polygonal Mesh ◽  
Finite Element Software ◽  
Linear Elastostatics ◽  
Novel Method ◽  
Scaled Boundary Finite Element ◽  
Element Method

The polygonal scaled boundary finite element method (PSBFEM) is a novel method integrating the standard scaled boundary finite element method (SBFEM) and the polygonal mesh technique. This work discusses developing a PSBFEM framework within the commercial finite element software Abaqus. The PSBFEM is implemented by the User Element Subroutine (UEL) feature of the software. The details on the main procedures to interact with Abaqus, defining the UEL element, and solving the stiffness matrix by the eigenvalue decomposition are present. Moreover, we also develop the preprocessing module and the postprocessing module using the Python script to generate meshes automatically and visualize results. Several benchmark problems from two-dimensional linear elastostatics are solved to validate the proposed implementation. The results show that PSBFEM-UEL has significantly better than FEM convergence and accuracy rate with mesh refinement. The implementation of PSBFEM-UEL can conveniently use arbitrary polygon elements by the polygon/quadtree discretizations in the Abaqus. The developed UEL and the associated input files can be downloaded from https://github.com/hhupde/PSBFEM-Abaqus.

IMPACT SIMULATIONS USING SMOOTHED FINITE ELEMENT METHOD

2013 ◽  
Vol 10 (04) ◽  
pp. 1350012 ◽  
Author(s):  
V. KUMAR ◽  
R. METHA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Impact Analysis ◽  
Mass Matrix ◽  
Time Integration ◽  
Benchmark Problems ◽  
Smoothed Finite Element Method ◽  
Domain Integration ◽  
Impact Simulations ◽  
Element Method

We present impact simulations with the Smoothed Finite Element Method (SFEM). Therefore, we develop the SFEM in the context of explicit dynamic applications based on diagonalized mass matrix. Since SFEM is not based on the isoparametric concept and is based on line integration rather than domain integration, it is very promising for events involving large deformations and severe element distortion as they occur in high dynamic events such as impacts. For some benchmark problems, we show that SFEM is superior to standard FEM for impact events. To our best knowledge, this is the first time SFEM is applied in the context of impact analysis based on explicit time integration.

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