Pub Date : 2023-07-11DOI: 10.1142/s0219876223500159
L. Peng, S. Y. Chen, W. Chen, X. C. He
This paper adopts the Moving Kriging (MK) interpolation meshless method to analyze the static and dynamic behaviors of stiffened functionally graded material (FGM) plate in thermal environment based on the physical neutral surface. The ribbed FGM plate is regarded as a composite structure of a FGM plate and ribs. The displacement transformation relationship between stiffeners and FGM plates is obtained through the displacement compatible conditions and MK interpolation. The meshfree model for ribbed FGM plate is obtained by superimposing the total energy of the FGM plate and the stiffeners based on the first-order shear deformation theory (FSDT) and physical neutral surface. The nonlinear temperature field along thickness direction is introduced into the meshless model of stiffened FGM plate. The equations governing the bending and free vibration of the ribbed FGM plate in thermal environment are obtained according to the principle of Minimum Potential Energy and Hamilton’s Principle. Thereafter, several ribbed FGM plate examples in different temperatures and with different locations of ribs are calculated. The results are compared with those given by the ABAQUS and literature. The results show that the effectiveness and accuracy of the proposed method in analyzing the ribbed FGM plate in thermal environment.
{"title":"A Moving Kriging Interpolation Meshless for Bending and Free Vibration Analysis of the Stiffened FGM Plates in Thermal Environment","authors":"L. Peng, S. Y. Chen, W. Chen, X. C. He","doi":"10.1142/s0219876223500159","DOIUrl":"https://doi.org/10.1142/s0219876223500159","url":null,"abstract":"This paper adopts the Moving Kriging (MK) interpolation meshless method to analyze the static and dynamic behaviors of stiffened functionally graded material (FGM) plate in thermal environment based on the physical neutral surface. The ribbed FGM plate is regarded as a composite structure of a FGM plate and ribs. The displacement transformation relationship between stiffeners and FGM plates is obtained through the displacement compatible conditions and MK interpolation. The meshfree model for ribbed FGM plate is obtained by superimposing the total energy of the FGM plate and the stiffeners based on the first-order shear deformation theory (FSDT) and physical neutral surface. The nonlinear temperature field along thickness direction is introduced into the meshless model of stiffened FGM plate. The equations governing the bending and free vibration of the ribbed FGM plate in thermal environment are obtained according to the principle of Minimum Potential Energy and Hamilton’s Principle. Thereafter, several ribbed FGM plate examples in different temperatures and with different locations of ribs are calculated. The results are compared with those given by the ABAQUS and literature. The results show that the effectiveness and accuracy of the proposed method in analyzing the ribbed FGM plate in thermal environment.","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45129454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-26DOI: 10.1142/s0219876223500184
Caiqun Wang, Jing An
{"title":"An efficient finite element method and error analysis based on dimension reduction scheme for the fourth order elliptic eigenvalue problems in a circular domain","authors":"Caiqun Wang, Jing An","doi":"10.1142/s0219876223500184","DOIUrl":"https://doi.org/10.1142/s0219876223500184","url":null,"abstract":"","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45211882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-16DOI: 10.1142/s0219876223500172
Monika Choudhary, Aditya Kaushik, M. Sharma
{"title":"A parameter-robust numerical method based on defect-correction technique for parabolic singular perturbation problems with discontinuous convection coefficient and source","authors":"Monika Choudhary, Aditya Kaushik, M. Sharma","doi":"10.1142/s0219876223500172","DOIUrl":"https://doi.org/10.1142/s0219876223500172","url":null,"abstract":"","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43082544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-16DOI: 10.1142/s0219876223500160
A. Hosseinian, P. Assari, M. Dehghan
{"title":"Local Galerkin method based on the moving least squares approximation for solving delay integral equations arisen from an air pollution model","authors":"A. Hosseinian, P. Assari, M. Dehghan","doi":"10.1142/s0219876223500160","DOIUrl":"https://doi.org/10.1142/s0219876223500160","url":null,"abstract":"","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42139393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-08DOI: 10.1142/s0219876223500135
Jinshuai Bai, Hyogu Jeong, C. P. Batuwatta-Gamage, Shusheng Xiao, Qingxia Wang, C. M. Rathnayaka, Laith Alzubaidi, Gui-Rong Liu, Yuantong Gu
Physics-informed neural network (PINN) has recently gained increasing interest in computational mechanics. This work extends the PINN to computational solid mechanics problems. Our focus will be on the investigation of various formulation and programming techniques, when governing equations of solid mechanics are implemented. Two prevailingly used physics-informed loss functions for PINN-based computational solid mechanics are implemented and examined. Numerical examples ranging from 1D to 3D solid problems are presented to show the performance of PINN-based computational solid mechanics. The programs are built via Python with TensorFlow library with step-by-step explanations and can be extended for more challenging applications. This work aims to help the researchers who are interested in the PINN-based solid mechanics solver to have a clear insight into this emerging area. The programs for all the numerical examples presented in this work are available at https://github.com/JinshuaiBai/PINN_Comp_Mech .
{"title":"An Introduction to Programming Physics-Informed Neural Network-Based Computational Solid Mechanics","authors":"Jinshuai Bai, Hyogu Jeong, C. P. Batuwatta-Gamage, Shusheng Xiao, Qingxia Wang, C. M. Rathnayaka, Laith Alzubaidi, Gui-Rong Liu, Yuantong Gu","doi":"10.1142/s0219876223500135","DOIUrl":"https://doi.org/10.1142/s0219876223500135","url":null,"abstract":"Physics-informed neural network (PINN) has recently gained increasing interest in computational mechanics. This work extends the PINN to computational solid mechanics problems. Our focus will be on the investigation of various formulation and programming techniques, when governing equations of solid mechanics are implemented. Two prevailingly used physics-informed loss functions for PINN-based computational solid mechanics are implemented and examined. Numerical examples ranging from 1D to 3D solid problems are presented to show the performance of PINN-based computational solid mechanics. The programs are built via Python with TensorFlow library with step-by-step explanations and can be extended for more challenging applications. This work aims to help the researchers who are interested in the PINN-based solid mechanics solver to have a clear insight into this emerging area. The programs for all the numerical examples presented in this work are available at https://github.com/JinshuaiBai/PINN_Comp_Mech .","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135215638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-26DOI: 10.1142/s0219876222500517
Kalani Rubasinghe, Guangming Yao, Wen Li, G. Tsogtgerel
In this paper, the improved localized method of approximated particular solutions (ILMAPS) using polyharmonic splines (PHS) together with a low-degree of polynomial basis is used to approximate solutions of various nonlinear elliptic Partial Differential Equations (PDEs). The method is completely meshfree, and it uses a radial basis function (RBF) that has no shape parameters. The discretization process is done through a simple collocation technique on a set of points in the local domain of influence. Resulted system of nonlinear algebraic equations is solved by the Picard method. The performance of the proposed method is tested on various nonlinear elliptical problems, including the Poisson-type problems in 2D and 3D with constant or variable coefficients on rectangular or irregular domains and the Poisson–Boltzmann equation with Dirichlet boundary conditions or mixed boundary conditions. The effect of domain shapes in 2D and 3D, types of boundary conditions, and degrees of PHS, and order of polynomial basis are examined. The performance of the method is compared with other bases such as multiquadrics (MQ) basis functions, and with results reported in the literature (method of particular solutions using polynomials). The numerical experiments suggest that ILMAPS with polyharmonic splines yields considerably superior accuracy than other RBFs as well as other approaches reported in the literature for solving nonlinear elliptic PDEs.
{"title":"Solving Nonlinear Elliptic PDEs in 2D and 3D Using Polyharmonic Splines and Low-Degree of Polynomials","authors":"Kalani Rubasinghe, Guangming Yao, Wen Li, G. Tsogtgerel","doi":"10.1142/s0219876222500517","DOIUrl":"https://doi.org/10.1142/s0219876222500517","url":null,"abstract":"In this paper, the improved localized method of approximated particular solutions (ILMAPS) using polyharmonic splines (PHS) together with a low-degree of polynomial basis is used to approximate solutions of various nonlinear elliptic Partial Differential Equations (PDEs). The method is completely meshfree, and it uses a radial basis function (RBF) that has no shape parameters. The discretization process is done through a simple collocation technique on a set of points in the local domain of influence. Resulted system of nonlinear algebraic equations is solved by the Picard method. The performance of the proposed method is tested on various nonlinear elliptical problems, including the Poisson-type problems in 2D and 3D with constant or variable coefficients on rectangular or irregular domains and the Poisson–Boltzmann equation with Dirichlet boundary conditions or mixed boundary conditions. The effect of domain shapes in 2D and 3D, types of boundary conditions, and degrees of PHS, and order of polynomial basis are examined. The performance of the method is compared with other bases such as multiquadrics (MQ) basis functions, and with results reported in the literature (method of particular solutions using polynomials). The numerical experiments suggest that ILMAPS with polyharmonic splines yields considerably superior accuracy than other RBFs as well as other approaches reported in the literature for solving nonlinear elliptic PDEs.","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43574454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-12DOI: 10.1142/s0219876223500147
Yunling Kang, Manxi Liu, Guoqiao You, Guidong Liu
{"title":"An Improved Radial Basis Function Neuron Network Based on the l1 regularization","authors":"Yunling Kang, Manxi Liu, Guoqiao You, Guidong Liu","doi":"10.1142/s0219876223500147","DOIUrl":"https://doi.org/10.1142/s0219876223500147","url":null,"abstract":"","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45855257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-05DOI: 10.1142/s0219876223500111
H. Ramos, L. A. Momoh
{"title":"A tenth-order sixth-derivative block method for directly solving fifth-order initial value problems","authors":"H. Ramos, L. A. Momoh","doi":"10.1142/s0219876223500111","DOIUrl":"https://doi.org/10.1142/s0219876223500111","url":null,"abstract":"","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48963055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-05DOI: 10.1142/s0219876223410086
Hong Yuan, Jun Han, H. Lu, Ziyong Mo, L. Zeng
{"title":"Studies on Interfacial Torsional Behavior of pipe Joints with Hardening and Softening Bond-Slip Law","authors":"Hong Yuan, Jun Han, H. Lu, Ziyong Mo, L. Zeng","doi":"10.1142/s0219876223410086","DOIUrl":"https://doi.org/10.1142/s0219876223410086","url":null,"abstract":"","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42991194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-05-05DOI: 10.1142/s0219876223500123
Poonam Yadav, Aman Singh, V. Singh
{"title":"Stable Computational Techniques for the Advection-Dispersion Variable Order Model","authors":"Poonam Yadav, Aman Singh, V. Singh","doi":"10.1142/s0219876223500123","DOIUrl":"https://doi.org/10.1142/s0219876223500123","url":null,"abstract":"","PeriodicalId":54968,"journal":{"name":"International Journal of Computational Methods","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44537052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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