Pub Date : 2024-11-06DOI: 10.1016/j.enganabound.2024.106014
Yongfeng Zheng, Rongna Cai, Jiawei He, Zihao Chen
Porous structures are extensively used in engineering, and current designs of porous structures are constructed based on linear assumptions. In engineering, deformation cannot be ignored, so it is necessary to consider the effect of geometric nonlinearity in structural design. For the first time, this paper performs the geometrically nonlinear topology optimization of porous structures. This paper presents the theory of geometric nonlinear analysis, the bi-directional evolutionary method is used to search for the topological configurations of porous structures, the number of structural holes is determined by the number of periodicities. Furthermore, the optimization equation, sensitivity analysis, and optimization process are provided in detail. Lastly, four numerical examples are investigated to discuss the influence of geometric nonlinearity on the design of porous structures, such as comparisons between geometric nonlinear and linear design, the ability of geometric nonlinear design to resist cracks, changes in load amplitude and position and 3D porous designs. The conclusions drawn can provide strong reference for the design of high-performance porous structures.
{"title":"Geometrically nonlinear topology optimization of porous structures","authors":"Yongfeng Zheng, Rongna Cai, Jiawei He, Zihao Chen","doi":"10.1016/j.enganabound.2024.106014","DOIUrl":"10.1016/j.enganabound.2024.106014","url":null,"abstract":"<div><div>Porous structures are extensively used in engineering, and current designs of porous structures are constructed based on linear assumptions. In engineering, deformation cannot be ignored, so it is necessary to consider the effect of geometric nonlinearity in structural design. For the first time, this paper performs the geometrically nonlinear topology optimization of porous structures. This paper presents the theory of geometric nonlinear analysis, the bi-directional evolutionary method is used to search for the topological configurations of porous structures, the number of structural holes is determined by the number of periodicities. Furthermore, the optimization equation, sensitivity analysis, and optimization process are provided in detail. Lastly, four numerical examples are investigated to discuss the influence of geometric nonlinearity on the design of porous structures, such as comparisons between geometric nonlinear and linear design, the ability of geometric nonlinear design to resist cracks, changes in load amplitude and position and 3D porous designs. The conclusions drawn can provide strong reference for the design of high-performance porous structures.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"169 ","pages":"Article 106014"},"PeriodicalIF":4.2,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592833","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 : 2024-11-06DOI: 10.1016/j.enganabound.2024.106024
Aman Garg , Li Li , Weiguang Zheng , Mohamed-Ouejdi Belarbi , Roshan Raman
The present work aims to study the free vibration behaviour of bio-inspired helicoidal laminated composite spherical, toroid, and conical shell panels using a single-output Support Vector Machine (SVM) algorithm trained in the chassis of parabolic shear deformation theory under thermal conditions. Different helicoidal lamination schemes are adopted, such as Fibonacci, semi-circular, exponential, recursive, and linear helicoidal schemes. Temperature-dependent material properties are adopted. The effect of the geometry of the shell, temperature, and lamination scheme on the free vibration behaviour of spherical, toroid, and conical shell panels is studied. Also, the mode shapes are obtained using different multi-output SVM surrogate in which the displacements are obtained at different locations and are predicted to obtain the fundamental mode shape. The trained surrogate model can predict the values of fundamental frequency and mode shapes much faster than the parabolic shear deformation theory.
{"title":"Free vibration behaviour of bio-inspired helicoidal laminated composite panels of revolution under thermal conditions: Multi-output machine learning approach","authors":"Aman Garg , Li Li , Weiguang Zheng , Mohamed-Ouejdi Belarbi , Roshan Raman","doi":"10.1016/j.enganabound.2024.106024","DOIUrl":"10.1016/j.enganabound.2024.106024","url":null,"abstract":"<div><div>The present work aims to study the free vibration behaviour of bio-inspired helicoidal laminated composite spherical, toroid, and conical shell panels using a single-output Support Vector Machine (SVM) algorithm trained in the chassis of parabolic shear deformation theory under thermal conditions. Different helicoidal lamination schemes are adopted, such as Fibonacci, semi-circular, exponential, recursive, and linear helicoidal schemes. Temperature-dependent material properties are adopted. The effect of the geometry of the shell, temperature, and lamination scheme on the free vibration behaviour of spherical, toroid, and conical shell panels is studied. Also, the mode shapes are obtained using different multi-output SVM surrogate in which the displacements are obtained at different locations and are predicted to obtain the fundamental mode shape. The trained surrogate model can predict the values of fundamental frequency and mode shapes much faster than the parabolic shear deformation theory.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"169 ","pages":"Article 106024"},"PeriodicalIF":4.2,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592834","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 : 2024-11-06DOI: 10.1016/j.enganabound.2024.106021
Bin Li , Huayu Liu , Jian Liu , Miao Cui , Xiaowei Gao , Jun Lv
In this paper, a novel weak-form meshless method, Galerkin Free Element Collocation Method (GFECM), is proposed for the mechanical analysis of thin plates. This method assimilates the benefits of establishing spatial partial derivatives by isoparametric elements and forming coefficient matrices node by node, which makes the calculation more convenient and stable. The pivotal aspect of GFECM is that the surrounding nodes can be freely chosen as collocation elements, which can adapt to irregular node distribution and suitable for complex models. Meanwhile, each collocation element is used as a Lagrange isoparametric element individually, which can easily construct high-order elements and improve the calculation accuracy, especially for high-order partial differential equations such as the Kirchhoff plate bending problem. In order to obtain the weak-form of the governing equation, the Galerkin form of the governing equation is constructed based on the virtual work principle and variational method. In addition, due to the Lagrange polynomials possessing the Kronecker delta property as shape functions, it can accurately impose boundary conditions compared with traditional meshless methods that use rational functions. Several numerical examples are proposed to verify the correctness and effectiveness of the proposed method in thin plate bending problems.
{"title":"A novel weak-form meshless method based on Lagrange interpolation for mechanical analysis of complex thin plates","authors":"Bin Li , Huayu Liu , Jian Liu , Miao Cui , Xiaowei Gao , Jun Lv","doi":"10.1016/j.enganabound.2024.106021","DOIUrl":"10.1016/j.enganabound.2024.106021","url":null,"abstract":"<div><div>In this paper, a novel weak-form meshless method, Galerkin Free Element Collocation Method (GFECM), is proposed for the mechanical analysis of thin plates. This method assimilates the benefits of establishing spatial partial derivatives by isoparametric elements and forming coefficient matrices node by node, which makes the calculation more convenient and stable. The pivotal aspect of GFECM is that the surrounding nodes can be freely chosen as collocation elements, which can adapt to irregular node distribution and suitable for complex models. Meanwhile, each collocation element is used as a Lagrange isoparametric element individually, which can easily construct high-order elements and improve the calculation accuracy, especially for high-order partial differential equations such as the Kirchhoff plate bending problem. In order to obtain the weak-form of the governing equation, the Galerkin form of the governing equation is constructed based on the virtual work principle and variational method. In addition, due to the Lagrange polynomials possessing the Kronecker delta property as shape functions, it can accurately impose boundary conditions compared with traditional meshless methods that use rational functions. Several numerical examples are proposed to verify the correctness and effectiveness of the proposed method in thin plate bending problems.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"169 ","pages":"Article 106021"},"PeriodicalIF":4.2,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592835","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 study aims to find a solution for crack propagation in 2D brittle elastic material using the local radial basis function collocation method. The staggered solution of the fourth-order phase field and mechanical model is structured with polyharmonic spline shape functions augmented with polynomials. Two benchmark tests are carried out to assess the performance of the method. First, a non-cracked square plate problem is solved under tensile loading to validate the implementation by comparing the numerical and analytical solutions. The analysis shows that the iterative process converges even with a large loading step, whereas the non-iterative process requires smaller steps for convergence to the analytical solution. In the second case, a single-edge cracked square plate subjected to tensile loading is solved, and the results show a good agreement with the reference solution. The effects of the incremental loading, length scale parameter, and mesh convergence for regular and scattered nodes are demonstrated. This study presents a pioneering attempt to solve the phase field crack propagation using a strong-form meshless method. The results underline the essential role of the represented method for an accurate and efficient solution to crack propagation. It also provides valuable insights for future research towards more sophisticated material models.
{"title":"Fourth-order phase field modelling of brittle fracture with strong form meshless method","authors":"Izaz Ali , Gašper Vuga , Boštjan Mavrič , Umut Hanoglu , Božidar Šarler","doi":"10.1016/j.enganabound.2024.106025","DOIUrl":"10.1016/j.enganabound.2024.106025","url":null,"abstract":"<div><div>This study aims to find a solution for crack propagation in 2D brittle elastic material using the local radial basis function collocation method. The staggered solution of the fourth-order phase field and mechanical model is structured with polyharmonic spline shape functions augmented with polynomials. Two benchmark tests are carried out to assess the performance of the method. First, a non-cracked square plate problem is solved under tensile loading to validate the implementation by comparing the numerical and analytical solutions. The analysis shows that the iterative process converges even with a large loading step, whereas the non-iterative process requires smaller steps for convergence to the analytical solution. In the second case, a single-edge cracked square plate subjected to tensile loading is solved, and the results show a good agreement with the reference solution. The effects of the incremental loading, length scale parameter, and mesh convergence for regular and scattered nodes are demonstrated. This study presents a pioneering attempt to solve the phase field crack propagation using a strong-form meshless method. The results underline the essential role of the represented method for an accurate and efficient solution to crack propagation. It also provides valuable insights for future research towards more sophisticated material models.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"169 ","pages":"Article 106025"},"PeriodicalIF":4.2,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592655","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 : 2024-11-04DOI: 10.1016/j.enganabound.2024.106012
J.D. Phan , A.-V. Phan
This paper presents a novel and efficient approach for the computation of energy eigenvalues in quantum semiconductor heterostructures. Accurate determination of the electronic states in these heterostructures is crucial for understanding their optical and electronic properties, making it a key challenge in semiconductor physics. The proposed method is based on utilizing series expansions of zero-order Bessel functions to numerically solve the Schrödinger equation using boundary integral method for bound electron states in a computationally efficient manner. To validate the proposed technique, the approach was applied to address issues previously explored by other research groups. The results clearly demonstrate the computational efficiency and high precision of the approach. Notably, the proposed technique significantly reduces the computational time compared to the conventional method for searching the energy eigenvalues in quantum structures.
{"title":"Accelerated boundary integral analysis of energy eigenvalues for confined electron states in quantum semiconductor heterostructures","authors":"J.D. Phan , A.-V. Phan","doi":"10.1016/j.enganabound.2024.106012","DOIUrl":"10.1016/j.enganabound.2024.106012","url":null,"abstract":"<div><div>This paper presents a novel and efficient approach for the computation of energy eigenvalues in quantum semiconductor heterostructures. Accurate determination of the electronic states in these heterostructures is crucial for understanding their optical and electronic properties, making it a key challenge in semiconductor physics. The proposed method is based on utilizing series expansions of zero-order Bessel functions to numerically solve the Schrödinger equation using boundary integral method for bound electron states in a computationally efficient manner. To validate the proposed technique, the approach was applied to address issues previously explored by other research groups. The results clearly demonstrate the computational efficiency and high precision of the approach. Notably, the proposed technique significantly reduces the computational time compared to the conventional method for searching the energy eigenvalues in quantum structures.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"169 ","pages":"Article 106012"},"PeriodicalIF":4.2,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578666","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 : 2024-11-02DOI: 10.1016/j.enganabound.2024.106007
Yun Chen , Guirong Liu , Junzhi Cui , Qiaofu Zhang , Ziqiang Wang
Numerous simulations have shown that Smoothed Finite Element Method (S-FEM) performs better than the standard FEM. However, there is lack of rigorous mathematical proof on such a claim. This task is challenging since there are so many variants of S-FEM and the standard FEM theory in Sobolev space does not work for S-FEM because of the Smoothed Gradient. Another long-standing open problem is to establish the theory of FEM parameter. The FEM could be the most flexible and fastest S-FEM variant. Its energy is even exact if the parameter is fine-tuned. So this problem is practical and interesting. By the help of nonlinear essential boundary (geometry), Weyl inequalities (algebra) and matrix differentiation (analysis), this parameter problem leads us to estimate the eigenvalue-gap and energy-gap between S-FEM and FEM. Consequently, we provide a definite answer to the long-standing S-FEM superiority problem in a unified framework. The essential boundary, eigenvalue and energy are linked together by four new necessary and sufficient conditions which are simple, practical and beyond our expectations. The standard S-FEM source code can be reused so it is convenient to numerically implement. Finally, the cantilever and infinite plate with a circular hole are simulated to verify the proof.
{"title":"A theoretical proof of superiority of Smoothed Finite Element Method over the conventional FEM","authors":"Yun Chen , Guirong Liu , Junzhi Cui , Qiaofu Zhang , Ziqiang Wang","doi":"10.1016/j.enganabound.2024.106007","DOIUrl":"10.1016/j.enganabound.2024.106007","url":null,"abstract":"<div><div>Numerous simulations have shown that Smoothed Finite Element Method (S-FEM) performs better than the standard FEM. However, there is lack of rigorous mathematical proof on such a claim. This task is challenging since there are so many variants of S-FEM and the standard FEM theory in Sobolev space does not work for S-FEM because of the Smoothed Gradient. Another long-standing open problem is to establish the theory of <span><math><mi>α</mi></math></span>FEM parameter. The <span><math><mi>α</mi></math></span>FEM could be the most flexible and fastest S-FEM variant. Its energy is even exact if the parameter is fine-tuned. So this problem is practical and interesting. By the help of nonlinear essential boundary (geometry), Weyl inequalities (algebra) and matrix differentiation (analysis), this parameter problem leads us to estimate the eigenvalue-gap and energy-gap between S-FEM and FEM. Consequently, we provide a definite answer to the long-standing S-FEM superiority problem in a unified framework. The essential boundary, eigenvalue and energy are linked together by four new necessary and sufficient conditions which are simple, practical and beyond our expectations. The standard S-FEM source code can be reused so it is convenient to numerically implement. Finally, the cantilever and infinite plate with a circular hole are simulated to verify the proof.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"169 ","pages":"Article 106007"},"PeriodicalIF":4.2,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572339","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 : 2024-11-01DOI: 10.1016/j.enganabound.2024.106018
Tailang Dong, Shanju Wang, Yuhong Cui
Thermoelastic problems are prevalent in various practical structures, wherein thermal stresses are of considerable concern for product design and analysis. Solving these thermal and thermoelastic problems for intricate geometries and boundary conditions often requires numerical computations. This study develops a node's residual descent method (NRDM) for solving steady-state thermal and thermoelastic problems. The method decouples the thermoelastic problem into a steady-state thermal problem and an elastic boundary value problem with temperature loading. Numerical validation indicates that the NRDM exhibits excellent performance in terms of precision, iterative convergence, and numerical convergence. The NRDM can readily couple steady-state thermal analysis with linear elastic analysis to enable thermoelastic analysis, which verifies its capability of solving multiphysics field problems. Moreover, the NRDM achieves second-order numerical accuracy using a first-order generalized finite difference algorithm, reducing the star's connectivity requirements while enhancing the convergence rate of the traditional generalized finite difference method (GFDM). Furthermore, the NRDM addresses the numerical challenges of material nonlinearity by simply updating the node thermal conductivities during iterations, without requiring frequent incremental linearization as in the GFDM, thus achieving improved computational efficiency.
{"title":"Node's residual descent method for steady-state thermal and thermoelastic analysis","authors":"Tailang Dong, Shanju Wang, Yuhong Cui","doi":"10.1016/j.enganabound.2024.106018","DOIUrl":"10.1016/j.enganabound.2024.106018","url":null,"abstract":"<div><div>Thermoelastic problems are prevalent in various practical structures, wherein thermal stresses are of considerable concern for product design and analysis. Solving these thermal and thermoelastic problems for intricate geometries and boundary conditions often requires numerical computations. This study develops a node's residual descent method (NRDM) for solving steady-state thermal and thermoelastic problems. The method decouples the thermoelastic problem into a steady-state thermal problem and an elastic boundary value problem with temperature loading. Numerical validation indicates that the NRDM exhibits excellent performance in terms of precision, iterative convergence, and numerical convergence. The NRDM can readily couple steady-state thermal analysis with linear elastic analysis to enable thermoelastic analysis, which verifies its capability of solving multiphysics field problems. Moreover, the NRDM achieves second-order numerical accuracy using a first-order generalized finite difference algorithm, reducing the star's connectivity requirements while enhancing the convergence rate of the traditional generalized finite difference method (GFDM). Furthermore, the NRDM addresses the numerical challenges of material nonlinearity by simply updating the node thermal conductivities during iterations, without requiring frequent incremental linearization as in the GFDM, thus achieving improved computational efficiency.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"169 ","pages":"Article 106018"},"PeriodicalIF":4.2,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572337","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 : 2024-11-01DOI: 10.1016/j.enganabound.2024.106008
I.D. Horvat, J. Iljaž
In this paper, a quadratic time interpolation for temperature and a linear time interpolation for fluxes are implemented for the parabolic (time-dependent) fundamental solution-based scheme for solving transient heat transfer problems with sources using the subdomain BEM (boundary element method), which is the main innovation of this paper. The approach described in this work to incorporate the quadratic time variation does not require doubling the number of equations, which is otherwise required in the BEM literature, for the discretized problem to be well-conditioned. Moreover, the numerical accuracy, compared over an unprecedented range of the Fourier number (Fo) and source strength values, can help in selecting the appropriate scheme for a given application, depending on the rate of the heat transfer process and the included source term. The newly implemented scheme based on the parabolic fundamental solution is compared with the well-established elliptic (Laplace) scheme, where the time derivative of the temperature is approximated with the second-order finite difference scheme, on two examples.
本文采用子域 BEM（边界元法）的抛物线（随时间变化）基本解法，对温度进行二次时间插值，对流量进行线性时间插值，用于求解有源的瞬态传热问题，这是本文的主要创新之处。本文所描述的纳入二次时间变化的方法不需要像 BEM 文献中所要求的那样将方程数量增加一倍，就能对离散化问题进行良好调节。此外，在前所未有的傅立叶数（Fo）和源强度值范围内比较数值精度，有助于根据传热过程的速率和所包含的源项，为特定应用选择合适的方案。在两个示例中，将基于抛物线基本解的新实施方案与成熟的椭圆（拉普拉斯）方案进行了比较，后者使用二阶有限差分方案对温度的时间导数进行近似。
{"title":"Quadratic time elements for time-dependent fundamental solution in the BEM for heat transfer modeling","authors":"I.D. Horvat, J. Iljaž","doi":"10.1016/j.enganabound.2024.106008","DOIUrl":"10.1016/j.enganabound.2024.106008","url":null,"abstract":"<div><div>In this paper, a quadratic time interpolation for temperature and a linear time interpolation for fluxes are implemented for the parabolic (time-dependent) fundamental solution-based scheme for solving transient heat transfer problems with sources using the subdomain BEM (boundary element method), which is the main innovation of this paper. The approach described in this work to incorporate the quadratic time variation does not require doubling the number of equations, which is otherwise required in the BEM literature, for the discretized problem to be well-conditioned. Moreover, the numerical accuracy, compared over an unprecedented range of the Fourier number (Fo) and source strength values, can help in selecting the appropriate scheme for a given application, depending on the rate of the heat transfer process and the included source term. The newly implemented scheme based on the parabolic fundamental solution is compared with the well-established elliptic (Laplace) scheme, where the time derivative of the temperature is approximated with the second-order finite difference scheme, on two examples.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"169 ","pages":"Article 106008"},"PeriodicalIF":4.2,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572336","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 : 2024-11-01DOI: 10.1016/j.enganabound.2024.106003
A.L.N. Pramod
In this work, the scaled boundary finite element method (SBFEM) is used to predict the frequency response of an acoustic cavity with a porous layer based on Biot–Allard theory. For the porous material, both the solid and the fluid displacements are considered as the primary variables. Scaled boundary shape functions are used to interpolate the acoustic pressure within the acoustic cavity, and the solid and fluid displacements in the porous material. The material matrices of the porous material are decomposed in such a way that the elemental matrices are real and frequency independent. This allows the elemental matrices to be computed and stored for a given mesh and is used for each frequency increment thus reducing the number of computations. Numerical examples are presented to show the computational efficiency of the SBFEM in predicting the frequency response of a porous material excited with acoustic cavity.
{"title":"Scaled boundary finite element method for an acoustic cavity with porous layer","authors":"A.L.N. Pramod","doi":"10.1016/j.enganabound.2024.106003","DOIUrl":"10.1016/j.enganabound.2024.106003","url":null,"abstract":"<div><div>In this work, the scaled boundary finite element method (SBFEM) is used to predict the frequency response of an acoustic cavity with a porous layer based on Biot–Allard theory. For the porous material, both the solid and the fluid displacements are considered as the primary variables. Scaled boundary shape functions are used to interpolate the acoustic pressure within the acoustic cavity, and the solid and fluid displacements in the porous material. The material matrices of the porous material are decomposed in such a way that the elemental matrices are real and frequency independent. This allows the elemental matrices to be computed and stored for a given mesh and is used for each frequency increment thus reducing the number of computations. Numerical examples are presented to show the computational efficiency of the SBFEM in predicting the frequency response of a porous material excited with acoustic cavity.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"169 ","pages":"Article 106003"},"PeriodicalIF":4.2,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572338","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 : 2024-10-30DOI: 10.1016/j.enganabound.2024.106010
S.M.H. Jani , Y. Kiani
The present study investigates the thermoelastic response of a heterogeneous piezoelectric sphere under thermal shock loading. Boundary conditions as well as loading are considered as symmetric; thus, the response of the sphere is expected to be symmetric. All of the properties of the thick-walled sphere, including mechanical, electrical and thermal properties, are considered dependent on the radial position, except for the relaxation time, which is considered a constant value along the radius. The governing equations of the sphere have been derived under heterogeneous anisotropic assumptions. The general form of the second law of thermodynamics, which is nonlinear in nature, and is called nonlinear energy equation is used. The number of the established equations is three, which includes the motion equation, energy equation and Maxwell electrostatic equation of Maxwell. These equations are obtained in terms of radial displacement, temperature difference and electric potential. The energy equation is derived based on Lord and Shulman theory with a single relaxation time. In the next step, by introducing dimensionless variables, the governing equations are provided in dimensionless presentation. Then these equations have been discretized using generalized differential quadrature method. Also, in order to follow the solution of the equations in time domain, Newmark method has been used. Since the system of equations is nonlinear, Picard algorithm is applied as a predictor-corrector mechanism to solve the nonlinear system of equations. Then numerical results are presented to investigate the propagation of mechanical, thermal and electric waves inside the heterogeneous sphere and also their reflection from the outer surface of the sphere. By examining the results, it can be seen that mechanical and thermal waves propagate with a limited speed, while the speed of electric wave propagation is infinite.
本研究探讨了异质压电球在热冲击加载下的热弹性响应。边界条件和加载被认为是对称的，因此球体的响应预计也是对称的。厚壁球体的所有特性，包括机械、电气和热特性，都被认为与径向位置有关，但弛豫时间除外，它被认为是沿半径的恒定值。球体的控制方程是在异质各向异性假设下推导出来的。热力学第二定律的一般形式在本质上是非线性的，被称为非线性能量方程。建立的方程有三个，包括运动方程、能量方程和麦克斯韦静电方程。这些方程是根据径向位移、温差和电动势得到的。能量方程是根据 Lord 和 Shulman 理论，在单一弛豫时间下导出的。下一步，通过引入无量纲变量，以无量纲形式给出了控制方程。然后使用广义微分正交法对这些方程进行离散化。此外，为了跟踪方程在时域中的求解，还使用了纽马克方法。由于方程组是非线性的，因此采用了 Picard 算法作为预测-修正机制来求解非线性方程组。然后给出了数值结果，以研究机械波、热波和电波在异质球体内部的传播，以及它们从球体外表面的反射。研究结果表明，机械波和热波的传播速度是有限的，而电波的传播速度是无限的。
{"title":"Nonlinear generalized piezothermoelasticity of spherical vessels made of functionally graded piezoelectric materials","authors":"S.M.H. Jani , Y. Kiani","doi":"10.1016/j.enganabound.2024.106010","DOIUrl":"10.1016/j.enganabound.2024.106010","url":null,"abstract":"<div><div>The present study investigates the thermoelastic response of a heterogeneous piezoelectric sphere under thermal shock loading. Boundary conditions as well as loading are considered as symmetric; thus, the response of the sphere is expected to be symmetric. All of the properties of the thick-walled sphere, including mechanical, electrical and thermal properties, are considered dependent on the radial position, except for the relaxation time, which is considered a constant value along the radius. The governing equations of the sphere have been derived under heterogeneous anisotropic assumptions. The general form of the second law of thermodynamics, which is nonlinear in nature, and is called nonlinear energy equation is used. The number of the established equations is three, which includes the motion equation, energy equation and Maxwell electrostatic equation of Maxwell. These equations are obtained in terms of radial displacement, temperature difference and electric potential. The energy equation is derived based on Lord and Shulman theory with a single relaxation time. In the next step, by introducing dimensionless variables, the governing equations are provided in dimensionless presentation. Then these equations have been discretized using generalized differential quadrature method. Also, in order to follow the solution of the equations in time domain, Newmark method has been used. Since the system of equations is nonlinear, Picard algorithm is applied as a predictor-corrector mechanism to solve the nonlinear system of equations. Then numerical results are presented to investigate the propagation of mechanical, thermal and electric waves inside the heterogeneous sphere and also their reflection from the outer surface of the sphere. By examining the results, it can be seen that mechanical and thermal waves propagate with a limited speed, while the speed of electric wave propagation is infinite.</div></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"169 ","pages":"Article 106010"},"PeriodicalIF":4.2,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142555010","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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