Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method

Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method

A numerical model for the two-dimensional nonlinear elastic–plastic problem is proposed based on the improved interpolating complex variable element free Galerkin (IICVEFG) method and the incremental tangent stiffness matrix method. The viability of the proposed model is verified through three elast...

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Main Authors: Yajie Deng, Xingkeng Shen, Jixiao Tao, Ying Dai
Format: Article
Language:English
Published: MDPI AG 2021-08-01
Series:Mathematics
Subjects:
elastic–plastic problem
complex variable meshless method
interpolating shape function
singular weight function
complete basis function
Online Access:https://www.mdpi.com/2227-7390/9/16/1967
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spelling doaj-7f87f1bfbb9245779d00c1d659252ea72021-08-26T14:02:26ZengMDPI AGMathematics2227-73902021-08-0191967196710.3390/math9161967Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin MethodYajie Deng0Xingkeng Shen1Jixiao Tao2Ying Dai3School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, ChinaSchool of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, ChinaDepartment of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, ChinaSchool of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, ChinaA numerical model for the two-dimensional nonlinear elastic–plastic problem is proposed based on the improved interpolating complex variable element free Galerkin (IICVEFG) method and the incremental tangent stiffness matrix method. The viability of the proposed model is verified through three elastic–plastic examples. The numerical analyses show that the IICVEFG method has good convergence. The solutions using the IICVEFG method are consistent with the solutions obtained from the finite element method using the ABAQUS program. Moreover, the IICVEFG method shows greater computing precision and efficiency than the non-interpolating meshless methods.https://www.mdpi.com/2227-7390/9/16/1967elastic–plastic problemcomplex variable meshless methodinterpolating shape functionsingular weight functioncomplete basis function
collection DOAJ
language English
format Article
sources DOAJ
author Yajie Deng
Xingkeng Shen
Jixiao Tao
Ying Dai
spellingShingle Yajie Deng
Xingkeng Shen
Jixiao Tao
Ying Dai
Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method
Mathematics
elastic–plastic problem
complex variable meshless method
interpolating shape function
singular weight function
complete basis function
author_facet Yajie Deng
Xingkeng Shen
Jixiao Tao
Ying Dai
author_sort Yajie Deng
title Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method
title_short Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method
title_full Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method
title_fullStr Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method
title_full_unstemmed Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method
title_sort analysis of elastic–plastic problems using the improved interpolating complex variable element free galerkin method
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-08-01
description A numerical model for the two-dimensional nonlinear elastic–plastic problem is proposed based on the improved interpolating complex variable element free Galerkin (IICVEFG) method and the incremental tangent stiffness matrix method. The viability of the proposed model is verified through three elastic–plastic examples. The numerical analyses show that the IICVEFG method has good convergence. The solutions using the IICVEFG method are consistent with the solutions obtained from the finite element method using the ABAQUS program. Moreover, the IICVEFG method shows greater computing precision and efficiency than the non-interpolating meshless methods.
topic elastic–plastic problem
complex variable meshless method
interpolating shape function
singular weight function
complete basis function
url https://www.mdpi.com/2227-7390/9/16/1967
work_keys_str_mv AT yajiedeng analysisofelasticplasticproblemsusingtheimprovedinterpolatingcomplexvariableelementfreegalerkinmethod
AT xingkengshen analysisofelasticplasticproblemsusingtheimprovedinterpolatingcomplexvariableelementfreegalerkinmethod
AT jixiaotao analysisofelasticplasticproblemsusingtheimprovedinterpolatingcomplexvariableelementfreegalerkinmethod
AT yingdai analysisofelasticplasticproblemsusingtheimprovedinterpolatingcomplexvariableelementfreegalerkinmethod
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