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.

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 Forced Vibration Analysis of Laminated Composite Shells Reinforced with Graphene Nanoplatelets Using Finite Element Method

2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Trung Thanh Tran ◽  
Van Ke Tran ◽  
Pham Binh Le ◽  
Van Minh Phung ◽  
Van Thom Do ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Thermal Environments ◽  
Forced Vibration Analysis ◽  
Laminated Composite Shells ◽  
Element Method

This paper carries out forced vibration analysis of graphene nanoplatelet-reinforced composite laminated shells in thermal environments by employing the finite element method (FEM). Material properties including elastic modulus, specific gravity, and Poisson’s ratio are determined according to the Halpin–Tsai model. The first-order shear deformation theory (FSDT), which is based on the 8-node isoparametric element to establish the oscillation equation of shell structure, is employed in this work. We then code the computing program in the MATLAB application and examine the verification of convergence rate and reliability of the program by comparing the data of present work with those of other exact solutions. The effects of both geometric parameters and mechanical properties of materials on the forced vibration of the structure are investigated.

A Coupled SBFEM-FEM Approach for Evaluating Stress Intensity Factors

2013 ◽  
Vol 353-356 ◽  
pp. 3369-3377 ◽  
Author(s):  
Ming Guang Shi ◽  
Chong Ming Song ◽  
Hong Zhong ◽  
Yan Jie Xu ◽  
Chu Han Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Complex Geometry ◽  
Stress Singularity ◽  
Intensity Factors ◽  
Finite Element Software ◽  
Scaled Boundary Finite Element ◽  
Element Method

A coupled method between the Scaled Boundary Finite Element Method (SBFEM) and Finite Element Method (FEM) for evaluating the Stress Intensity Factors (SIFs) is presented and achieved on the platform of the commercial finite element software ABAQUS by using Python as the programming language. Automatic transformation of the finite elements around a singular point to a scaled boundary finite element subdomain is realized. This method combines the high accuracy of the SBFEM in computing the SIFs with the ability to handle material nonlinearity as well as powerful mesh generation and post processing ability of commercial FEM software. The validity and accuracy of the method is verified by analysis of several benchmark problems. The coupled algorithm shows a good converging performance, and with minimum additional treatment can be able to handle more problems that cannot be solved by either SBFEM or FEM itself. For fracture problems, it proposes an efficient way to represent stress singularity for problems with complex geometry, loading condition or certain nonlinearity.

FREE AND FORCED VIBRATION ANALYSIS USING THE n-SIDED POLYGONAL CELL-BASED SMOOTHED FINITE ELEMENT METHOD (nCS-FEM)

2013 ◽  
Vol 10 (01) ◽  
pp. 1340008 ◽  
Author(s):  
T. NGUYEN-THOI ◽  
P. PHUNG-VAN ◽  
T. RABCZUK ◽  
H. NGUYEN-XUAN ◽  
C. LE-VAN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Forced Vibration ◽  
Solid Mechanics ◽  
Mass Matrix ◽  
Elastic Solid ◽  
Polygonal Cell ◽  
Smoothed Finite Element Method ◽  
Forced Vibration Analysis ◽  
Element Method

A n-sided polygonal cell-based smoothed finite element method (nCS-FEM) was recently proposed to analyze the elastic solid mechanics problems, in which the problem domain can be discretized by a set of polygons with an arbitrary number of sides. In this paper, the nCS-FEM is further extended to the free and forced vibration analyses of two-dimensional (2D) dynamic problems. A simple lump mass matrix is proposed and hence the complicated integrations related to computing the consistent mass matrix can be avoided in the nCS-FEM. Several numerical examples are investigated and the results found of the nCS-FEM agree well with exact solutions and with those of others FEM.

scholarly journals Development of User Element Routine (UEL) for Cell-Based Smoothed Finite Element Method (CSFEM) in Abaqus

2019 ◽  
Vol 17 (02) ◽  
pp. 1850128 ◽  
Author(s):  
Pramod Y. Kumbhar ◽  
A. Francis ◽  
N. Swaminathan ◽  
R. K. Annabattula ◽  
S. Natarajan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Salient Feature ◽  
Three Dimensions ◽  
Benchmark Problems ◽  
Element Analysis ◽  
Finite Element Software ◽  
Linear Elastostatics ◽  
Smoothed Finite Element Method ◽  
Element Method

In this paper, we discuss the implementation of a cell-based smoothed finite element method (CSFEM) within the commercial finite element software Abaqus. The salient feature of the CSFEM is that it does not require an explicit form of the derivative of the shape functions and there is no need for isoparametric mapping. This implementation is accomplished by employing the user element subroutine (UEL) feature in Abaqus. The details on the input data format together with the proposed user element subroutine, which forms the core of the finite element analysis are given. A few benchmark problems from linear elastostatics in both two and three dimensions are solved to validate the proposed implementation. The developed UELs and the associated input files can be downloaded from https://github.com/nsundar/SFEM_in_Abaqus .

An Adaptive Polygonal Scaled Boundary Finite Element Method for Elastodynamics

2016 ◽  
Vol 13 (02) ◽  
pp. 1640015 ◽  
Author(s):  
Z. H. Zhang ◽  
Z. J. Yang ◽  
J. H. Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Responses ◽  
Adaptive Finite Element Method ◽  
Error Estimator ◽  
State Variables ◽  
Time Step ◽  
Polygonal Mesh ◽  
Scaled Boundary Finite Element ◽  
Element Method

An adaptive polygonal scaled boundary finite element method (APSBFEM) is developed for elastodynamics. Flexible polygonal meshes are generated from background Delaunay triangular meshes and used to calculate structure’s dynamic responses. In each time step, a posteriori-type energy error estimator is employed to locate the polygonal subdomains with exceeding spatial discretization error, then edge midpoints of the corresponding triangles are inserted into the background. A new Delaunay triangular mesh and a polygonal mesh are regenerated successively. The state variables, including displacement, velocity and acceleration are mapped from the old polygonal mesh to the new one by a simple algorithm. A benchmark elastodynamic problem is modeled to validate the developed method. The results show that the adaptive meshes are capable of capturing the steep stress regions, and the dynamic responses agree well with those from the adaptive finite element method and the polygonal scaled boundary finite element method without adaptivity using fine meshes.

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