Computers & Mathematics with Applications最新文献_第3页

Static and vibration analyses of laminated conical shells under various boundary conditions using a modified scaled boundary finite element method 使用改进的比例边界有限元法对各种边界条件下的层叠锥壳进行静态和振动分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-11-26 DOI: 10.1016/j.camwa.2024.11.024

Jun Liu , Chenxi Ji , Wenbin Ye , Lei Gan , Lei Qin , Quansheng Zang , Haibo Wang

{"title":"Static and vibration analyses of laminated conical shells under various boundary conditions using a modified scaled boundary finite element method","authors":"Jun Liu , Chenxi Ji , Wenbin Ye , Lei Gan , Lei Qin , Quansheng Zang , Haibo Wang","doi":"10.1016/j.camwa.2024.11.024","DOIUrl":"10.1016/j.camwa.2024.11.024","url":null,"abstract":"<div><div>In this paper, a modified scaled boundary finite element method (SBFEM) is developed to study static and vibration behaviors of laminated conical shells under the conical coordinate system. In the modified SBFEM, the geometry of the conical shell is defined entirely by scaling the internal surface of the structure. This approach eliminates geometric errors caused by discretization, thereby enhancing modeling accuracy. The three-dimensional problem is simplified to a two-dimensional analysis since discretization is only applied to the boundary of the computational domain. Additionally, the semi-analytic property of the SBFEM allows for the derivation of a linear analytical solution for the laminated conical shell in the radial direction. First, a scaled boundary coordinate system for the scaling surface is established, and a second-order scaled boundary finite element governing equation with variable coefficients is derived for a single layer of the conical shell using the principle of virtual work. Next, the governing equation is transformed into a first-order system by introducing a combined vector of displacement and nodal force, and the stiffness matrices for each layer of the laminated conical shell are obtained using the precise integration method. Finally, an overall analysis of the laminated structure is conducted by assembling each single-layer structure while considering the continuity boundary condition at interfaces. Static and vibration analyses of laminated conical shells are conducted, and the results are compared with those from the literature to demonstrate the adaptability and convergence of the proposed method. Several numerical examples are presented to examine the effects of various geometric parameters, such as thickness, length, semi-vertex angles, layup directions, and stacking sequences, on the responses of the structure.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"177 ","pages":"Pages 147-166"},"PeriodicalIF":2.9,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An energy stable bound-preserving finite volume scheme for the Allen-Cahn equation based on operator splitting method 基于算子分裂法的艾伦-卡恩方程能量稳定保界有限体积方案

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-11-26 DOI: 10.1016/j.camwa.2024.11.014

Gang Peng , Yuan Li

引用次数: 0

The simplified weak Galerkin method with θ scheme and its reduced-order model for the elastodynamic problem on polygonal mesh 多边形网格上弹性力学问题的θ方案简化弱伽勒金方法及其降阶模型

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-11-25 DOI: 10.1016/j.camwa.2024.11.023

Lu Wang , Minfu Feng

{"title":"The simplified weak Galerkin method with θ scheme and its reduced-order model for the elastodynamic problem on polygonal mesh","authors":"Lu Wang , Minfu Feng","doi":"10.1016/j.camwa.2024.11.023","DOIUrl":"10.1016/j.camwa.2024.11.023","url":null,"abstract":"<div><div>This paper presents a simplified weak Galerkin (SWG) method for solving the elastodynamic problem and its reduced-order model (ROM) using the proper orthogonal decomposition (POD) technique. The SWG method allows for the use of polygonal meshes. It only utilizes degrees of freedom associated with the boundary, reducing computational complexity compared to the classical weak Galerkin method. Moreover, we apply the POD technique to develop a POD-SWG-ROM for the problem, further enhancing the computational efficiency. Then, to discretize in time, we utilize a <em>θ</em>-scheme, where the scheme is explicit when <span><math><mn>0</mn><mo>≤</mo><mi>θ</mi><mo><</mo><mn>1</mn><mo>/</mo><mn>4</mn></math></span> and implicit when <span><math><mn>1</mn><mo>/</mo><mn>4</mn><mo>≤</mo><mi>θ</mi><mo>≤</mo><mn>1</mn><mo>/</mo><mn>2</mn></math></span>. We establish the theoretical analysis of the semi-discrete scheme and the fully-discrete <em>θ</em> scheme. The theoretical analysis demonstrates that the method is locking-free, and the convergence rate in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norms is <span><math><mi>O</mi><mo>(</mo><mi>Δ</mi><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>)</mo></math></span> and <span><math><mi>O</mi><mo>(</mo><mi>Δ</mi><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> respectively. Finally, we verify the theoretical analysis through numerical tests and effectively simulate the propagation of elastic waves under polygonal meshes. Moreover, the proposed POD-SWG-ROM can significantly improve computational efficiency.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"178 ","pages":"Pages 19-46"},"PeriodicalIF":2.9,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Numerical analysis and simulation of a quasistatic frictional bilateral contact problem with damage, long-term memory and wear 具有损伤、长期记忆和磨损的准静态摩擦双边接触问题的数值分析与模拟

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-11-23 DOI: 10.1016/j.camwa.2024.11.020

Wensi Wang , Hailing Xuan , Xiaoliang Cheng , Kewei Liang

{"title":"Numerical analysis and simulation of a quasistatic frictional bilateral contact problem with damage, long-term memory and wear","authors":"Wensi Wang , Hailing Xuan , Xiaoliang Cheng , Kewei Liang","doi":"10.1016/j.camwa.2024.11.020","DOIUrl":"10.1016/j.camwa.2024.11.020","url":null,"abstract":"<div><div>We present a mathematical model describing the equilibrium of a viscoelastic body with long-term memory in frictional contact with a sliding foundation. The process is quasistatic, and material damage resulting from excessive stress or strain is captured by a damage function. We assume the material is inhomogeneous, leading to multiple contact boundary conditions. The contact interface is partitioned into two segments: One part takes into account the wear of the contact surface, utilizing Archard's law. Here, contact is modeled with a normal compliance condition with unilateral constraints, coupled with a sliding version of Coulomb's law of dry friction. In the other part, contact is modeled with a nonmonotone condition involving normal compliance and a subdifferential frictional boundary condition. Variational formulation of the model is governed by a coupled system consisting of a variational–hemivariational inequality for the displacement field, a parabolic variational inequality for the damage field and an integral equation for the wear function. We study a fully discrete scheme for numerical approximation with an error estimation of the solution to this problem. Optimal error estimates for the linear finite element method are derived, followed by numerical simulations illustrating the behavior of the model.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"177 ","pages":"Pages 130-146"},"PeriodicalIF":2.9,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A subspace method based on the Neumann series for the solution of parametric linear systems 基于诺依曼数列的子空间法求解参数线性系统

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-11-22 DOI: 10.1016/j.camwa.2024.11.019

Antti Autio, Antti Hannukainen

{"title":"A subspace method based on the Neumann series for the solution of parametric linear systems","authors":"Antti Autio, Antti Hannukainen","doi":"10.1016/j.camwa.2024.11.019","DOIUrl":"10.1016/j.camwa.2024.11.019","url":null,"abstract":"<div><div>In this work, a subspace method is proposed for efficient solution of parametric linear systems with a symmetric and positive definite coefficient matrix of the form <span><math><mi>I</mi><mo>−</mo><mi>A</mi><mo>(</mo><mi>σ</mi><mo>)</mo></math></span>. The motivation is to use the method for solution of linear systems appearing when solving parameter dependent elliptic PDEs using the finite element method (FEM). In the proposed method, one first computes a method subspace and then uses it to approximately solve the linear system for any parameter vector. The method subspace is designed in such a way that it contains the <span><math><mi>j</mi><mo>+</mo><mn>1</mn></math></span>-term truncated Neumann series approximation of the solution to desired accuracy for any admissible parameter vector. This allows us to use the best approximation property of subspace methods to show that the subspace solution is at least as accurate as the truncated Neumann series approximation. The performance of the method is demonstrated by numerical examples with the parametric diffusion equation. In these examples, the method yields much smaller errors than anticipated by the Neumann series based error analysis. We study this phenomenon in some special cases.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"178 ","pages":"Pages 1-18"},"PeriodicalIF":2.9,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142699956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Two-step numerical methods for a coupled parabolic-hyperbolic transmission problem 抛物线-双曲面耦合传输问题的两步数值方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-11-20 DOI: 10.1016/j.camwa.2024.11.015

Ihor Borachok , Roman Chapko , Leonidas Mindrinos

引用次数: 0

Lowest order stabilization free virtual element method for the 2D Poisson equation 二维泊松方程的最低阶稳定自由虚拟元素法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-11-19 DOI: 10.1016/j.camwa.2024.11.017

Stefano Berrone , Andrea Borio , Francesca Marcon

引用次数: 0

A semi-Lagrangian radial basis function partition of unity closest point method for advection-diffusion equations on surfaces 表面平流-扩散方程的半拉格朗日径向基函数统一分割最邻近点法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-11-19 DOI: 10.1016/j.camwa.2024.11.013

Yajun Liu, Yuanyang Qiao, Xinlong Feng

{"title":"A semi-Lagrangian radial basis function partition of unity closest point method for advection-diffusion equations on surfaces","authors":"Yajun Liu, Yuanyang Qiao, Xinlong Feng","doi":"10.1016/j.camwa.2024.11.013","DOIUrl":"10.1016/j.camwa.2024.11.013","url":null,"abstract":"<div><div>A semi-Lagrangian radial basis function partition of unity (RBF-PU) closest point method is designed for solving advection-diffusion equations on surfaces. This new meshfree method combines the semi-Lagrangian method with the RBF-PU closest point method. The semi-Lagrangian RBF-PU closest point method traces the departure point backwards along the velocity field based on patches at each time step. Therefore, it saves the computational cost compared with the semi-Lagrangian radial basis function finite difference (RBF-FD) closest point method. Our proposed RBF-PU closest point method for approximating the Laplace-Beltrami operator has two main advantages over the RBF-FD closest point method. Firstly, the RBF-PU closest point method to construct the local influence domain is not required to identify the size of the computational tube. Therefore, our method is more concise and easier to implement. Secondly, the RBF-PU closest point method not only improves the accuracy but also saves computational costs, and we confirm the advantage by testing differential accuracy. Numerical experiments verify the convergence and effectiveness of the semi-Lagrangian RBF-PU closest point method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"177 ","pages":"Pages 100-114"},"PeriodicalIF":2.9,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142673451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Well-posedness and finite element analysis for the elastic scattering problem with a modified DtN map 修正 DtN 图的弹性散射问题的拟合和有限元分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-11-19 DOI: 10.1016/j.camwa.2024.11.016

Xiaojuan Liu , Maojun Li , Kun Wang , Jiangming Xie

引用次数: 0

Numerical analysis and scientific computation with applications, Part II 数值分析和科学计算及其应用，第二部分

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-11-18 DOI: 10.1016/j.camwa.2024.10.040

Khalide Jbilou , Marilena Mitrouli , Ahmed Ratnani

引用次数: 0