Pub Date : 2025-02-01DOI: 10.1016/j.enganabound.2024.106109
Arezoo Hajesfandiari
A boundary element formulation is developed based on consistent couple stress flexoelectricity. The formulation is used here to study the flexoelectric response of a two-dimensional isotropic bimaterial consisting of a flexoelectric dielectric thin film on a non-flexoelectric dielectric material. Flexoelectric phenomenon is a coupled problem of mechanical and electrostatic effects, each specified by only one parameter in the formulation: couple-stress parameter , and flexoelectric coefficient , respectively. The primary variables in the boundary element analysis are displacement, rotation, and electric potential, while the secondary variables are force- and couple-tractions and normal electric displacement. In order to investigate the flexoelectric response in such bimaterials and validate the formulation and the numerical technique, a long rectangular bimaterial strip is considered as an initial case study. Then, the flexoelectric responses in a bimaterial semi-circular strip and a bimaterial solid cylinder are explored using the same implementation.
{"title":"Flexoelectricity in bimaterials via boundary element analysis","authors":"Arezoo Hajesfandiari","doi":"10.1016/j.enganabound.2024.106109","DOIUrl":"10.1016/j.enganabound.2024.106109","url":null,"abstract":"<div><div>A boundary element formulation is developed based on consistent couple stress flexoelectricity. The formulation is used here to study the flexoelectric response of a two-dimensional isotropic bimaterial consisting of a flexoelectric dielectric thin film on a non-flexoelectric dielectric material. Flexoelectric phenomenon is a coupled problem of mechanical and electrostatic effects, each specified by only one parameter in the formulation: couple-stress parameter <span><math><mi>η</mi></math></span>, and flexoelectric coefficient <span><math><mi>f</mi></math></span>, respectively. The primary variables in the boundary element analysis are displacement, rotation, and electric potential, while the secondary variables are force- and couple-tractions and normal electric displacement. In order to investigate the flexoelectric response in such bimaterials and validate the formulation and the numerical technique, a long rectangular bimaterial strip is considered as an initial case study. Then, the flexoelectric responses in a bimaterial semi-circular strip and a bimaterial solid cylinder are explored using the same implementation.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"171 ","pages":"Article 106109"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143049720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Free, fixed (clamped), and simply supported boundary conditions are standard edge boundary conditions that are normally considered in the modeling and analysis of plates. In many cases, the edge support of the plate is elastic, which cannot be modeled using the standard edge boundary conditions. To model the elastic edge of a plate, some parameters need to be determined. The aim of this study is to determine the elastic edge parameters of Reissner thick plates using inverse analysis. For the direct problem of a plate with an elastic edge, the method of fundamental solutions (MFS) formulated with the first-order shear deformation theory is used. An inverse method for determining the elastic edge parameters using measured displacements is presented. A gradient-based method is used for the optimization process in the inverse analysis. For the sensitivity analysis of elastic parameters, an analytical method based on the differentiation of governing equations is proposed. Two numerical examples for identifying elastic edge parameters in plates are presented and the effects of important parameters on the results are also investigated. Based on the results obtained, it is found that the proposed inverse method is very effective in identifying the elastic edge parameters.
{"title":"Identification of elastic edge parameters of plates using the method of fundamental solutions","authors":"Ehsan Samandizade , Mohammad-Rahim Hematiyan , Yui-Chuin Shiah","doi":"10.1016/j.enganabound.2024.106093","DOIUrl":"10.1016/j.enganabound.2024.106093","url":null,"abstract":"<div><div>Free, fixed (clamped), and simply supported boundary conditions are standard edge boundary conditions that are normally considered in the modeling and analysis of plates. In many cases, the edge support of the plate is elastic, which cannot be modeled using the standard edge boundary conditions. To model the elastic edge of a plate, some parameters need to be determined. The aim of this study is to determine the elastic edge parameters of Reissner thick plates using inverse analysis. For the direct problem of a plate with an elastic edge, the method of fundamental solutions (MFS) formulated with the first-order shear deformation theory is used. An inverse method for determining the elastic edge parameters using measured displacements is presented. A gradient-based method is used for the optimization process in the inverse analysis. For the sensitivity analysis of elastic parameters, an analytical method based on the differentiation of governing equations is proposed. Two numerical examples for identifying elastic edge parameters in plates are presented and the effects of important parameters on the results are also investigated. Based on the results obtained, it is found that the proposed inverse method is very effective in identifying the elastic edge parameters.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"171 ","pages":"Article 106093"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142901663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-02-01DOI: 10.1016/j.enganabound.2024.106058
Ali Habibirad , Yadollah Ordokhani , Omid Baghani , Hadis Azin
This research has been conducted to investigate a numerical solution for the Allen–Cahn equation featuring the generalized fractional time derivative. The finite difference method is employed to discretize the equation in the time variable. Subsequently, an error estimate is derived for the proposed method in space. Furthermore, a meshless technique based on radial point interpolation is used to discretize the problem in spatial variables. Through these procedures, the equation is transformed into a system of linear equations at each time step. The method’s effectiveness for solving this equation is demonstrated by three examples on both regular and irregular domains. These examples illustrate that the current method has a high level of accuracy and efficiency for solving the given problem.
{"title":"A local meshless numerical scheme based on the radial point interpolation for the generalized time-fractional Allen–Cahn equation","authors":"Ali Habibirad , Yadollah Ordokhani , Omid Baghani , Hadis Azin","doi":"10.1016/j.enganabound.2024.106058","DOIUrl":"10.1016/j.enganabound.2024.106058","url":null,"abstract":"<div><div>This research has been conducted to investigate a numerical solution for the Allen–Cahn equation featuring the generalized fractional time derivative. The finite difference method is employed to discretize the equation in the time variable. Subsequently, an error estimate is derived for the proposed method in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>q</mi></mrow></msub></math></span> space. Furthermore, a meshless technique based on radial point interpolation is used to discretize the problem in spatial variables. Through these procedures, the equation is transformed into a system of linear equations at each time step. The method’s effectiveness for solving this equation is demonstrated by three examples on both regular and irregular domains. These examples illustrate that the current method has a high level of accuracy and efficiency for solving the given problem.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"171 ","pages":"Article 106058"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The characterization and understanding of cracking propagation behaviors in non-uniform geological structures are crucial for predicting the mechanical response of rock-like materials under varying loading conditions. In this study, an improved Peridynamics (PD) model with degree of heterogeneity characterized by random pre-breaking "bond" ratio is introduced to capture the intricacies of crack initiation, and propagation in Brazilian disk (BD) specimens with different pre-cracks was explored. The crack propagation paths and the whole process of breakage of specimens with single pre-crack or pre-crack system were obtained. Next, the splitting mechanism and bearing capacity of the BD specimens with different inclinations of pre-crack were investigated through the improved PD model. Finally, the results of the PD simulations based on non-local actions were compared with the experimental ones in terms of crack propagation and breakage patterns. The simulation results are in good agreement with the experimental results, which can help explain the observed behaviors of cracking propagation and growth behaviors. The simulation results show that the improved PD model can accurately describe the whole process of micro-cracks initiation, aggregation, macro-crack generation, propagation and breakage process. This study provides valuable insights for improving simulations and contributing to the field of geomechanics.
{"title":"Numerical simulation of fracture and breakage behaviors in rock disks containing pre-defects with an improved non-local model","authors":"Shijun Zhao , Liang Kong , Qing Zhang , Xinbo Zhao , Wei Xu","doi":"10.1016/j.enganabound.2024.106061","DOIUrl":"10.1016/j.enganabound.2024.106061","url":null,"abstract":"<div><div>The characterization and understanding of cracking propagation behaviors in non-uniform geological structures are crucial for predicting the mechanical response of rock-like materials under varying loading conditions. In this study, an improved Peridynamics (PD) model with degree of heterogeneity characterized by random pre-breaking \"bond\" ratio is introduced to capture the intricacies of crack initiation, and propagation in Brazilian disk (BD) specimens with different pre-cracks was explored. The crack propagation paths and the whole process of breakage of specimens with single pre-crack or pre-crack system were obtained. Next, the splitting mechanism and bearing capacity of the BD specimens with different inclinations of pre-crack were investigated through the improved PD model. Finally, the results of the PD simulations based on non-local actions were compared with the experimental ones in terms of crack propagation and breakage patterns. The simulation results are in good agreement with the experimental results, which can help explain the observed behaviors of cracking propagation and growth behaviors. The simulation results show that the improved PD model can accurately describe the whole process of micro-cracks initiation, aggregation, macro-crack generation, propagation and breakage process. This study provides valuable insights for improving simulations and contributing to the field of geomechanics.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"171 ","pages":"Article 106061"},"PeriodicalIF":4.2,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142825136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-01-30DOI: 10.1016/j.enganabound.2025.106136
Y.F. Wang , Y. Lu , L. Chen , M.J. Peng , Y.M. Cheng
Because of the nonlinearity, three-dimensional (3D) elastoplastic problems are very important for any numerical method. In this study, the improved interpolating element-free Galerkin (IIEFG) method based on nonsingular weight functions for elastoplastic problems is presented. An improved interpolating moving least-squares (IIMLS) method with nonsingular weight functions is applied to construct the shape function. The elastoplastic control equations are formulated using the incremental Galerkin weak form with considering the nonlinear stress-strain relationship. Then the equations of IIEFG are presented. A key advantage of IIEFG is its ability to directly apply boundary conditions to improve computational efficiency because of the interpolating property of IIMLS. And using nonsingular weight functions can overcome the disadvantage of singular weight functions, and the computational accuracy is improved. Five numerical examples are presented to evaluate the impact of parameters such as node arrangement, the number of loading steps, and scaling parameters of the influence domain impact the calculation results of this method. Comparisons with other numerical methods demonstrate the superior computational efficiency and accuracy of IIEFG for solving 3D elastoplastic problems.
{"title":"The improved interpolating element-free Galerkin method based on nonsingular weight functions for three-dimensional elastoplastic problems","authors":"Y.F. Wang , Y. Lu , L. Chen , M.J. Peng , Y.M. Cheng","doi":"10.1016/j.enganabound.2025.106136","DOIUrl":"10.1016/j.enganabound.2025.106136","url":null,"abstract":"<div><div>Because of the nonlinearity, three-dimensional (3D) elastoplastic problems are very important for any numerical method. In this study, the improved interpolating element-free Galerkin (IIEFG) method based on nonsingular weight functions for elastoplastic problems is presented. An improved interpolating moving least-squares (IIMLS) method with nonsingular weight functions is applied to construct the shape function. The elastoplastic control equations are formulated using the incremental Galerkin weak form with considering the nonlinear stress-strain relationship. Then the equations of IIEFG are presented. A key advantage of IIEFG is its ability to directly apply boundary conditions to improve computational efficiency because of the interpolating property of IIMLS. And using nonsingular weight functions can overcome the disadvantage of singular weight functions, and the computational accuracy is improved. Five numerical examples are presented to evaluate the impact of parameters such as node arrangement, the number of loading steps, and scaling parameters of the influence domain impact the calculation results of this method. Comparisons with other numerical methods demonstrate the superior computational efficiency and accuracy of IIEFG for solving 3D elastoplastic problems.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106136"},"PeriodicalIF":4.2,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper develops a stable numerical method based on RBFs to solve two-dimensional time-fractional partial integro-differential equations with singular kernels. The spatial discretization uses an RBF-generated Hermite finite difference approach, which applies a geometric greedy sparse approximation technique for node selection, ensuring accuracy and controlling consistency errors. The temporal direction is discretized using a nonuniform formulation to achieve faster and more accurate temporal convergence compared to the uniform formulation. The method includes a detailed analysis of convergence and stability. Its accuracy and efficiency are tested with numerical examples, including cases with nonsmooth initial conditions, and compared to other existing methods, showing its superior performance.
{"title":"A stable numerical investigation based on geometric greedy points for 2D time-fractional partial integro-differential equations with singular kernels","authors":"Mojtaba Fardi, Banafsheh Raeisi, Mohammadreza Ahmadi Darani","doi":"10.1016/j.enganabound.2025.106129","DOIUrl":"10.1016/j.enganabound.2025.106129","url":null,"abstract":"<div><div>This paper develops a stable numerical method based on RBFs to solve two-dimensional time-fractional partial integro-differential equations with singular kernels. The spatial discretization uses an RBF-generated Hermite finite difference approach, which applies a geometric greedy sparse approximation technique for node selection, ensuring accuracy and controlling consistency errors. The temporal direction is discretized using a nonuniform formulation to achieve faster and more accurate temporal convergence compared to the uniform formulation. The method includes a detailed analysis of convergence and stability. Its accuracy and efficiency are tested with numerical examples, including cases with nonsmooth initial conditions, and compared to other existing methods, showing its superior performance.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106129"},"PeriodicalIF":4.2,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-01-29DOI: 10.1016/j.enganabound.2025.106133
Yang Yang , Zixin Su , Yijun Liu
Peridynamic is an effective method for addressing fracture problems. However, the non-local theory makes it time-consuming. Although some techniques have been developed to improve computational efficiency, the acceleration effect remains relatively limited. This paper introduces a parallel algorithm for bond-based peridynamic using the GPU parallel CUDA programming technology. The calculation process is divided into functions with material points and bonds as the smallest calculation units. The loop of material points and bonds is changed to the index to achieve parallelism. A general horizon generation module is established to optimize storage. Additionally, a general register technique is proposed for high-speed access register memory to reduce global memory access. This technique not only eliminates the restriction on the number of horizon points, also suitable for nonuniform distribution of material points. Compared to serial and OpenMP parallel programs, the present algorithm can achieve up to 800-fold and 100-fold acceleration, respectively. In a typical simulation of one million particles, executing 4000 iterations can be completed in 5 minutes for single precision and 20 minutes for double precision on a low-end GPU PC.
{"title":"A fast bond-based peridynamic program based on GPU parallel computing","authors":"Yang Yang , Zixin Su , Yijun Liu","doi":"10.1016/j.enganabound.2025.106133","DOIUrl":"10.1016/j.enganabound.2025.106133","url":null,"abstract":"<div><div>Peridynamic is an effective method for addressing fracture problems. However, the non-local theory makes it time-consuming. Although some techniques have been developed to improve computational efficiency, the acceleration effect remains relatively limited. This paper introduces a parallel algorithm for bond-based peridynamic using the GPU parallel CUDA programming technology. The calculation process is divided into functions with material points and bonds as the smallest calculation units. The loop of material points and bonds is changed to the index to achieve parallelism. A general horizon generation module is established to optimize storage. Additionally, a general register technique is proposed for high-speed access register memory to reduce global memory access. This technique not only eliminates the restriction on the number of horizon points, also suitable for nonuniform distribution of material points. Compared to serial and OpenMP parallel programs, the present algorithm can achieve up to 800-fold and 100-fold acceleration, respectively. In a typical simulation of one million particles, executing 4000 iterations can be completed in 5 minutes for single precision and 20 minutes for double precision on a low-end GPU PC.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106133"},"PeriodicalIF":4.2,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-01-28DOI: 10.1016/j.enganabound.2025.106130
Zulfiqar Ali , Weiyin Ma
This paper presents some results on steady-state thermal analysis with variable thermal conductivity under general boundary conditions and other internal constraints using isogeometric methods. Non-Uniform Rational B-splines (NURBS) serve as basis functions for representing both the geometry of the physical domains and the solution. While both isogeometric collocation method and Galarkin formulation are discussed for facilitating comparisons, the main emphasis of the presented work is on isogeometric collocation method (IGA-C) for thermal analysis. To obtain the final solution, the respective partial differential equation (PDE) is discretized in its strong form at a number of collocation sites in IGA-C, as opposed to Galerkin formulations that involve a costly process of numerical integration in building up the system equations. The proposed method on IGA-C for thermal analysis can be easily implemented due to the simplicity of IGA-C in setting up the system equations. In addition to general boundary conditions of the respective PDE, other arbitrary constraints can also be easily incorporated into the final system of equations for producing desired solutions. Numerical examples with different kinds of spatially varying thermal conductivity along with other additional constraints and heat sources are provided to demonstrate the effectiveness of the proposed methods. The results show that the proposed methods are capable of conveniently handling arbitrary boundary and other additional constraints when solving thermal PDEs and can produce stable and accurate solutions with expected convergence.
{"title":"Isogeometric methods for thermal analysis with spatially varying thermal conductivity under general boundary and other constraints","authors":"Zulfiqar Ali , Weiyin Ma","doi":"10.1016/j.enganabound.2025.106130","DOIUrl":"10.1016/j.enganabound.2025.106130","url":null,"abstract":"<div><div>This paper presents some results on steady-state thermal analysis with variable thermal conductivity under general boundary conditions and other internal constraints using isogeometric methods. Non-Uniform Rational B-splines (NURBS) serve as basis functions for representing both the geometry of the physical domains and the solution. While both isogeometric collocation method and Galarkin formulation are discussed for facilitating comparisons, the main emphasis of the presented work is on isogeometric collocation method (IGA-C) for thermal analysis. To obtain the final solution, the respective partial differential equation (PDE) is discretized in its strong form at a number of collocation sites in IGA-C, as opposed to Galerkin formulations that involve a costly process of numerical integration in building up the system equations. The proposed method on IGA-C for thermal analysis can be easily implemented due to the simplicity of IGA-C in setting up the system equations. In addition to general boundary conditions of the respective PDE, other arbitrary constraints can also be easily incorporated into the final system of equations for producing desired solutions. Numerical examples with different kinds of spatially varying thermal conductivity along with other additional constraints and heat sources are provided to demonstrate the effectiveness of the proposed methods. The results show that the proposed methods are capable of conveniently handling arbitrary boundary and other additional constraints when solving thermal PDEs and can produce stable and accurate solutions with expected convergence.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106130"},"PeriodicalIF":4.2,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-24DOI: 10.1016/j.enganabound.2025.106126
Leilei Chen , Chengmiao Liu , Haojie Lian , Wenxiang Gu
This study proposes a sensitivity analysis framework for Transverse Magnetic polarized electromagnetic scattering problems, with a focus on Perfectly Electric Conductors (PEC). To enable seamless integration of Computer-Aided Design and Computer-Aided Engineering, the isogeometric boundary element method based on the Galerkin scheme is employed. This method utilizes Non-Uniform Rational B-splines to represent geometries and unknown physical fields. A direct differentiation formulation is derived to evaluate the sensitivity of the Radar Cross Section (RCS) with respect to shape design variables and incident wave angles. The accuracy and effectiveness of the algorithm are validated through numerical examples.
{"title":"Electromagnetic scattering sensitivity analysis for perfectly conducting objects in TM polarization with isogeometric BEM","authors":"Leilei Chen , Chengmiao Liu , Haojie Lian , Wenxiang Gu","doi":"10.1016/j.enganabound.2025.106126","DOIUrl":"10.1016/j.enganabound.2025.106126","url":null,"abstract":"<div><div>This study proposes a sensitivity analysis framework for Transverse Magnetic polarized electromagnetic scattering problems, with a focus on Perfectly Electric Conductors (PEC). To enable seamless integration of Computer-Aided Design and Computer-Aided Engineering, the isogeometric boundary element method based on the Galerkin scheme is employed. This method utilizes Non-Uniform Rational B-splines to represent geometries and unknown physical fields. A direct differentiation formulation is derived to evaluate the sensitivity of the Radar Cross Section (RCS) with respect to shape design variables and incident wave angles. The accuracy and effectiveness of the algorithm are validated through numerical examples.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106126"},"PeriodicalIF":4.2,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143049713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-01-24DOI: 10.1016/j.enganabound.2025.106123
Shenshen Chen , Hao Dong , Xing Wei , Fengtao Liu
This paper proposes a novel numerical method based on the cell-based smoothed radial point interpolation method (CS-RPIM) combined with second-order cone programming to perform lower bound limit analysis of elastic-perfectly-plastic thin plates, using only deflection as nodal variable. The problem domain is initially discretized using a simple triangular background mesh, where each triangular cell is subsequently subdivided into multiple smoothing domains. Shape functions are formulated using the radial point interpolation method, allowing direct imposition of essential boundary conditions for deflection. Rotational constraints are conveniently handled through the construction of smoothed curvatures. By utilizing a generalized gradient smoothing technique, complex domain integrals are simplified into boundary integrals over the smoothing domains, thus eliminating the need to compute second-order derivatives of the shape functions. The virtual work principle is employed to enforce the equilibrium conditions for the self-equilibrated residual moment field in a weak sense. The von Mises yield conditions are expressed as conic constraints and the resulting optimization problems are solved using highly efficient primal-dual interior point solvers. Numerical examples demonstrate that it is feasible and effective to conduct lower bound limit analysis of thin plates using the proposed CS-RPIM and second-order cone programming.
{"title":"A cell-based smoothed radial point interpolation method applied to lower bound limit analysis of thin plates","authors":"Shenshen Chen , Hao Dong , Xing Wei , Fengtao Liu","doi":"10.1016/j.enganabound.2025.106123","DOIUrl":"10.1016/j.enganabound.2025.106123","url":null,"abstract":"<div><div>This paper proposes a novel numerical method based on the cell-based smoothed radial point interpolation method (CS-RPIM) combined with second-order cone programming to perform lower bound limit analysis of elastic-perfectly-plastic thin plates, using only deflection as nodal variable. The problem domain is initially discretized using a simple triangular background mesh, where each triangular cell is subsequently subdivided into multiple smoothing domains. Shape functions are formulated using the radial point interpolation method, allowing direct imposition of essential boundary conditions for deflection. Rotational constraints are conveniently handled through the construction of smoothed curvatures. By utilizing a generalized gradient smoothing technique, complex domain integrals are simplified into boundary integrals over the smoothing domains, thus eliminating the need to compute second-order derivatives of the shape functions. The virtual work principle is employed to enforce the equilibrium conditions for the self-equilibrated residual moment field in a weak sense. The von Mises yield conditions are expressed as conic constraints and the resulting optimization problems are solved using highly efficient primal-dual interior point solvers. Numerical examples demonstrate that it is feasible and effective to conduct lower bound limit analysis of thin plates using the proposed CS-RPIM and second-order cone programming.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"172 ","pages":"Article 106123"},"PeriodicalIF":4.2,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143049714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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