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Composites Part C: Open Access 2025年 17卷

作者： Gholami, Y. Ansari, R. Rouhi, H. Faculty of Mechanical Engineering University of Guilan P.O. Box 3756 Rasht Iran Center of Excellence for Mathematical Modelling Optimization and Combinational Computing (MMOCC) University of Guilan Rasht Iran Department of Engineering Science Faculty of Technology and Engineering East of Guilan University of Guilan P.C. 44891-63157 Rudsar-Vajargah Iran

In this article, an efficient numerical approach is developed to study the primary resonant dynamics of rectangular plates with arbitrary boundary conditions made of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs). The problem is formulated in the context of three-dimensional (3d) elasticity theory. Also, a variational approach based on Hamilton's principle together with the variational differential quadrature (VdQ) method is proposed to obtain the discretized governing equations on space domain. Then, the solution procedure on the time domain is completed using the numerical Galerkin method, time periodic discretization method and pseudo arc-length continuation algorithm in order to find the frequency-response curves. It is considered that CNTs are distributed in the thickness direction based on an FG manner considering different patterns. After testing the convergence and validity of developed approach, numerical results are presented to investigate the influences of geometrical properties, CNT's volume fraction and distribution pattern on the nonlinear forced vibration response of plates. © 2025

关键词： 3d elasticity CNT-reinforced composite Forced vibration Plate Primary resonant dynamics VdQ

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3d elasticity analytical solution for bending of FG micro/nanoplates resting on elastic foundation using modified couple stress theory

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APPLIEd MATHEMATICAL MOdELLING 2017年 47卷 174-188页

作者： Salehipour, Hamzeh Nahvi, Hassan Shahidi, AliReza Mirdamadi, Hamid Reza Ilam Univ Dept Mech Engn Ilam 69315516 Iran Isfahan Univ Technol Dept Mech Engn Esfahan *** Iran

This paper addresses a 3d elasticity analytical solution for static deformation of a simply-supported rectangular micro/nanoplate made of both homogeneous and functionally graded (FG) material within the framework of modified couple stress theory. The plate is assumed to be resting on a Winkler-Pasternak elastic foundation, and its modulus of elasticity is assumed to vary exponentially along thickness. By expanding displacement components in double Fourier series along in-plane coordinates and imposing relevant boundary conditions, the boundary value problem (BVP) of plate system, including its governing partial differential equations (PdEs) of equilibrium are reduced to BVP consisting only ordinary ones (OdEs). Parametric studies are conducted among displacement and stress components developed in the plate and FG material gradient index, length scale parameter, and foundation stiffnesses. From the numerical results, it is concluded that the out-of-plane shear stresses are not necessarily zero at the top and bottom surfaces of plate. The results of this investigation may serve as a benchmark to verify further bending analyses of either homogeneous or FG micro/nanoplates on elastic foundation. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Analytical solution 3d elasticity Functionally graded micro/nanoplate Static deformation Winkler-Pasternak foundation Modified couple stress

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The multi-domain hybrid boundary node method for 3d elasticity

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ENGINEERING ANALYSIS WITH BOUNdARY ELEMENTS 2011年第6期35卷 803-810页

作者： Wang, Q. Zheng, J. J. Miao, Y. Lv, J. H. Huazhong Univ Sci & Technol Sch Civil Engn & Mech Wuhan 430074 Peoples R China

In this paper, a multi-domain technique for 3d elasticity problems is derived from the hybrid boundary node method (Hybrid BNM). The Hybrid BNM is based on the modified variational principle and the Moving Least Squares (MLS) approximation. It does not require a boundary element mesh, neither for the purpose of interpolation of the solution variables nor for the integration of energy. This method can reduce the human-labor costs of meshing, especially for complex construction. This paper presents a further development of the Hybrid BNM for multi-domain analysis in 3d elasticity. Using the equilibrium and continuity conditions on the interfaces, the final algebraic equation is obtained by assembling the algebraic equation for each single sub-domain. The proposed multi-domain technique is capable to deal with interface and multi-medium problems and results in a block sparsity of the coefficient matrix. Numerical examples demonstrate the accuracy of the proposed multi-domain technique. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Multi-domain 3d elasticity Hybrid boundary node method Modified variational principle Moving Least Squares approximation

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Graphics processing unit (GPU) accelerated fast multipole BEM with level-skip M2L for 3d elasticity problems

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AdVANCES IN ENGINEERING SOFTWARE 2015年 82卷 105-118页

作者： Wang, Yingjun Wang, Qifu deng, Xiaowei Xia, Zhaohui Yan, Jinhui Xu, Hua Univ Calif San Diego Dept Struct Engn La Jolla CA 92093 USA Huazhong Univ Sci & Technol Natl CAD Support Software Engn Res Ctr Wuhan 430074 Peoples R China Southwest Jiaotong Univ Sch Civil Engn Chengdu 610031 Peoples R China

In order to accelerate fast multipole boundary element method (FMBEM), in terms of the intrinsic parallelism of boundary elements and the FMBEM tree structure, a series of CUdA based GPU parallel algorithms for different parts of FMBEM with level-skip M2L for 3d elasticity are presented. A rigid body motion method (RBMM) for the FMBEM is proposed based on special displacement boundary conditions to deal with strongly singular integration and free term coefficients. The numerical example results show that our parallel algorithms obviously accelerates the FMBEM and can be used in large scale engineering problems with wide applications in the future. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Fast multipole method Boundary element method Parallel computing Graphics processing unit 3d elasticity Level-skip M2L

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An adaptive dual-information FMBEM for 3d elasticity and its GPU implementation

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ENGINEERING ANALYSIS WITH BOUNdARY ELEMENTS 2013年第2期37卷 236-249页

作者： Wang, Yingjun Wang, Qifu Wang, Gang Huang, Yunbao Wang, Shuting Huazhong Univ Sci & Technol Natl CAD Support Software Engn Res Ctr Wuhan 430074 Peoples R China

Combined the boundary element method (BEM) with the fast multipole method (FMM), the fast multipole BEM (FMBEM) is proposed to solve large scale problems. A key issue the FMBEM has to address is the element integrals, which usually consumes much time when the FMM for N-body problems is directly used. In order to accelerate element integrals, we present an adaptive FMBEM with a particular dual-information tree structure which contains both node and element information, and use it for 3d elasticity in this paper. In our adaptive FMBEM, the Multipole Expansions (ME), Moment-to-Local (M2L) translation, Local Expansions (LE), and the Near Field direct Computation (NFdC) are level independent so that they are suitable for parallel computing. The examples show that the time of ME and NFdC in our FMBEM is almost 1/3 and 1/2 compared with that in a node-based FMBEM which deals with FMBEM in a particle interaction mode. We develop two GPU parallel strategies to accelerate the processes of ME, M2L and NFdC and implement them on a NVIdIA GTX 285 GPU, and the speedups to an Intel Core2 Q9550 CPU using 4 cores can reach 10.7 for ME, 16.2 for M2L, and 3.6 for NFdC. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Fast multipole method Boundary element method dual-information Graphics processing unit 3d elasticity

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Large deformation analysis of shell-type structures using the VdQ-transformed scheme: A two-point formulation based on 3d elasticity

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ENGINEERING ANALYSIS WITH BOUNdARY ELEMENTS 2023年 146卷 306-317页

作者： Ansari, R. Hassani, R. Gholami, Y. Rouhi, H. Univ Guilan Fac Mech Engn POB 3756 Rasht Iran Univ Guilan Fac Technol & Engn Dept Engn Sci Rudsar Vajargah *** Iran

Shell-type structures are frequently used in aerospace, marine and civil engineering. In this paper, a numerical approach called as VdQ-transformed is introduced to analyze the large deformations of hyperelastic shell-type structures based on the Saint Venant-Kirchhoff constitutive model in the context of three-dimensional (3d) nonlinear elasticity. According to the Euler-Lagrange description, the kinetic first Piola-Kirchhoff tensor and kinematic deformation gradient tensor are considered for the stress and strain measures in the formulation. By replacing the tensor form of formulations with matricized ones, the governing equations are written in a novel vector-matrix format which can be readily exploited for programming in numerical approaches. Moreover, discretizing is carried out by the variational differential quadrature (VdQ) method as a point-wise numerical method. To apply the VdQ technique, a transformation is used to map the irregular domain into the regular one. Some well-known benchmark problems for the large deformations of shells are solved to assess the approach. Compact matricized formulation, simple implementation, being locking-free, computational efficiency and fast convergence rate can be mentioned as the main features of the introduced numerical approach.

关键词： Large deformation Shell -type structure Kirchhoff -St Venant material P -F formulation 3d elasticity VdQ-transformed approach

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The Hybrid Boundary Node Method Accelerated by Fast Multipole Expansion Technique for 3d elasticity

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CMES-COMPUTER MOdELING IN ENGINEERING & SCIENCES 2010年第2期70卷 123-151页

作者： Wang, Qiao Miao, Yu Zheng, Junjie Huazhong Univ Sci & Technol Sch Civil Engn & Mech Wuhan 430074 Peoples R China

In this paper, a fast formulation of the hybrid boundary node method (Hybrid BNM) for solving 3d elasticity is presented. Coupling modified variational principle with the Moving Least Squares (MLS) approximation, the Hybrid BNM only requires discrete nodes constructed on the surface of a domain. The preconditioned GMERS is employed to solve the resulting system of equations. At each iteration step of the GMERS, the matrix-vector multiplication is accelerated by the fast multipole method (FMM). The fundamental solution of three-dimensional elasticity problem is expanded in terms of series. An oct-tree data structure is adopted to subdivide the computational domain into well-separated cells hierarchically and to invoke the multipole expansion approximation. Formulations for the local and multipole expansions and conversion of multipole to local expansion are given. Nearly one million of total unknowns can be computed on a PC with 2.67GHz CPU and 2.0GB RAM. All the formulations are implemented in a computer code written in C++. Numerical examples demonstrate the accuracy and efficiency of the proposed approach.

关键词： meshless method hybrid boundary node method modified variational principle, moving least squares approximation fast multipole method 3d elasticity

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A dual interpolation boundary face method for 3d elasticity

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ENGINEERING ANALYSIS WITH BOUNdARY ELEMENTS 2021年 122卷 102-116页

作者： Zhang, Jianming Ju, Chuanming Wen, Pihua Shu, Xiaomin Lin, Weicheng Chi, Baotao Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Queen Mary Univ London Sch Engn & Mat Sci London E1 4NS England

The dual interpolation boundary face method (diBFM) proposed recently has been successfully applied to solve various problems in two dimensions. Compared with the conventional boundary element method (BEM), it has been proved that the diBFM has the advantages of higher accuracy, convergence rate and computational efficiency. In addition, the diBFM is suitable to unify the conforming and nonconforming elements in the BEM implementation, as well as to approximate both continuous and discontinuous fields. Moreover, there are no geometric errors by the diBFM in the computational process. In this paper, the diBFM is extended successfully to solve the elasticity problems in three-dimensions (3d) with formulations derived in details. A number of numerical examples are presented in order to validate the accuracy and convergence rate of the proposed method.

关键词： dual interpolation boundary face method 3d elasticity Boundary element method Moving least-squares approximation

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Efficient Solution of 3d elasticity Problems with Smoothed Aggregation Algebraic Multigrid and Block Arithmetics

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LOBACHEVSKII JOURNAL OF MATHEMATICS 2022年第4期43卷 948-958页

作者： demidov, d. E. Russian Acad Sci Kazan Branch Sci Res Inst Syst Anal Joint Supercomp Ctr Kazan 420111 Russia

Efficient solution of 3d elasticity problems is an important part of many industrial and scientific applications. Smoothed aggregation algebraic multigrid using rigid body modes for the tentative prolongation operator construction is an efficient and robust choice for the solution of linear systems arising from discretization of elasticity equations. The system matrices on every level of the multigrid hierarchy have block structure, so using block representation and block arithmetics should significantly improve the solver efficiency. However, the tentative prolongation operator construction may only be done using scalar representation. The paper proposes a couple of practical approaches for enabling the use of block arithmetics with smoothed aggregation algebraic multigrid based on the open-source AMGCL library. It is shown on the example of two real-world model problems that the suggested improvements may speed up the solution by 50% and reduce the memory requirements for the preconditioner by 30%. The implementation is straightforward and only requires a minimal amount of code.

关键词： Smoothed aggregation AMG 3d elasticity rigid body modes nullspace components block arithmetics

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The discrete spectrum of the Neumann-Poincare operator in 3d elasticity

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JOURNAL OF PSEUdO-dIFFERENTIAL OPERATORS ANd APPLICATIONS 2023年第2期14卷 1-36页

作者： Rozenblum, Grigori Chalmers Univ Technol Gothenburg Sweden St Petersburg State Univ St Petersburg Russia

For the Neumann-Poincare (double layer potential) operator in the three-dimensional elasticity we establish asymptotic formulas for eigenvalues converging to the points of the essential spectrum and discuss geometric and mechanical meaning of coefficients in these formulas. In particular, we establish that for any body, there are infinitely many eigenvalues converging from above to each point of the essential spectrum. On the other hand, if there is a point where the boundary is concave (in particular, if the body contains cavities) then for each point of the essential spectrum there exists a sequence of eigenvalues converging to this point from below. The reasoning is based upon the representation of the Neumann-Poincare operator as a zero order pseudodifferential operator on the boundary and the earlier results by the author on the eigenvalue asymptotics for polynomially compact pseudodifferential operators.

关键词： Eigenvalue asymptotics Pseudodifferential operators Neumann-Poincare operator 3d elasticity

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