Based on B-spline wavelet on the interval （BSWI） and the multivariable generalized variational principle, the multivariable wavelet finite element for flat shell is constructed by combining the elastic plate element...Based on B-spline wavelet on the interval （BSWI） and the multivariable generalized variational principle, the multivariable wavelet finite element for flat shell is constructed by combining the elastic plate element and the Mindlin plate element together. First, the elastic plate element formulation is derived from the generalized potential energy function. Due to its excellent numerical approximation property, BSWI is used as the interpolation function to separate the solving field variables. Second, the multivariable wavelet Mindlin plate element is deduced and constructed according to the multivariable generalized variational principle and BSWI. Third, by following the displacement compatibility requirement and the coordinate transformation method, the multivariable wavelet finite element for fiat shell is constructed. The novel advantage of the constructed element is that the solving precision and efficiency can be improved because the generalized displacement field variables and stress field variables are interpolated and solved independently. Finally, several numerical examples including bending and vibration analyses are given to verify the constructed element and method.展开更多
Topology optimization of continuum structures with design-dependent loads has long been a challenge. In this paper, the topology optimization of 3D structures subjected to design-dependent loads is investigated. A bou...Topology optimization of continuum structures with design-dependent loads has long been a challenge. In this paper, the topology optimization of 3D structures subjected to design-dependent loads is investigated. A boundary search scheme is proposed for 3D problems, by means of which the load surface can be identified effectively and efficiently, and the difficulties arising in other approaches can be overcome. The load surfaces are made up of the boundaries of finite elements and the loads can be directly applied to corresponding element nodes, which leads to great convenience in the application of this method. Finally, the effectiveness and efficiency of the proposed method is validated by several numerical examples.展开更多
The numerical solutions for uncertain viscoelastic problems have important theo- retical and practical significance. The paper develops a new approach by combining the scaled boundary finite element method （SBFEM） a...The numerical solutions for uncertain viscoelastic problems have important theo- retical and practical significance. The paper develops a new approach by combining the scaled boundary finite element method （SBFEM） and fuzzy arithmetic. For the viscoelastic problems with zero uncertainty, the SBFEM and the temporally piecewise adaptive algorithm is employed in the space domain and the time domain, respectively, in order to provide an accurate semi- analytical boundary-based approach and to ensure the accuracy of discretization in the time domain with different sizes of time step at the same time. The fuzzy arithmetic is used to address the uncertainty analysis of viscoelastic material parameters, and the transformation method is used for computation with the advantages of effectively avoiding overestimation and reducing the computational costs. Numerical examples are provided to test the performance of the proposed method. By comparing with the analytical solutions and the Monte Carlo method, satisfactory results are achieved.展开更多
To facilitate long term infrastructure asset management systems, it is necessary to determine the bearing capacity of pavements. Currently it is common to conduct such measurements in a stationary manner, however the ...To facilitate long term infrastructure asset management systems, it is necessary to determine the bearing capacity of pavements. Currently it is common to conduct such measurements in a stationary manner, however the evaluation with stationary loading does not correspond to reality a tendency towards continuous and high speed measurements in recent years can be observed. The computational program SAFEM was developed with the objective of evaluating the dynamic response of asphalt under moving loads and is based on a semi-analytic element method. In this research project SAFEM is compared to commercial finite element software ABAQUS and field measurements to verify the computational accuracy. The computational accuracy of SAFEM was found to be high enough to be viable whilst boasting a computational time far shorter than ABAQUS. Thus, SAFEM appears to be a feasible approach to determine the dynamic response of pavements under dynamic loads and is a useful tool for infrastructure administrations to analyze the pavement bearing capacity.展开更多
In this paper, we study Nitsche extended finite element method （XFEM） for the inter- face problem of a two dimensional diffusion equation. Specifically, we study the quadratic XFEM scheme on some shape-regular famil...In this paper, we study Nitsche extended finite element method （XFEM） for the inter- face problem of a two dimensional diffusion equation. Specifically, we study the quadratic XFEM scheme on some shape-regular family of grids and prove the optimal convergence rate of the scheme with respect to the mesh size. Main efforts are devoted onto classifying the cases of intersection between the elements and the interface and prove a weighted trace inequality for the extended finite element functions needed, and the general framework of analysing XFEM c^n be implemented then.展开更多
This paper proves the saturation assumption for the nonconforming Morley finite ele- ment discretization of the biharmonic equation. This asserts that the error of the Morley approximation under uniform refinement is ...This paper proves the saturation assumption for the nonconforming Morley finite ele- ment discretization of the biharmonic equation. This asserts that the error of the Morley approximation under uniform refinement is strictly reduced by a contraction factor smaller than one up to explicit higher-order data approximation terms. The refinement has at least to bisect any edge such as red refinement or 3-bisections on any triangle. This justifies a hierarchical error estimator for the Morley finite element method, which simply compares the discrete solutions of one mesh and its red-refinement. The related adaptive mesh-refining strategy performs optimally in numerical experiments. A remark for Crouzeix-Raviart nonconforming finite element error control is included.展开更多
Slippage corresponds to the relative displacement of a bolted joint subjected to shear loads since the construction clearance between the bolt shank and the bolthole at assembly can cause joint slip. Deflections of to...Slippage corresponds to the relative displacement of a bolted joint subjected to shear loads since the construction clearance between the bolt shank and the bolthole at assembly can cause joint slip. Deflections of towers with joint slippage effects is up to 1.9 times greater than the displacements obtained by linear analytical methods. In this study, 8 different types of joints are modelled and studied in the finite element program, and the results are verified by the experimental results which have been done in the laboratory. Moreover, several types of joints have been modelled and studied and load-deformation curves have also been presented. Finally, joint slip data for different types of angles, bolt diameter and bolt arrangements are generated. Thereupon, damping ratios （ζ） for different types of connections are reported. The study can be useful to help in designing of wind turbine towers with a higher level of accuracy and safety.展开更多
This paper is concerned with the finite elements approximation for the Steklov eigen- value problem on concave polygonal domain. We make full use of the regularity estimate and the characteristic of edge average inter...This paper is concerned with the finite elements approximation for the Steklov eigen- value problem on concave polygonal domain. We make full use of the regularity estimate and the characteristic of edge average interpolation operator of nonconforming Crouzeix- Raviart element, and prove a new and optimal error estimate in ｜｜ ｜｜o,δΩ for the eigenfunc- tion of linear conforming finite element and the nonconforming Crouzeix-Raviart element. Finally, we present some numerical results to support the theoretical analysis.展开更多
The electromagnetic wave propagation in the chiral medium is governed by Maxwell＇s equations together with the Drude-Born-Fedorov （constitutive） equations. The problem is simplified to a two-dimensional scattering ...The electromagnetic wave propagation in the chiral medium is governed by Maxwell＇s equations together with the Drude-Born-Fedorov （constitutive） equations. The problem is simplified to a two-dimensional scattering problem, and is formulated in a bounded domain by introducing two pairs of transparent boundary conditions. An a posteriori error estimate associated with the truncation of the nonlocal boundary operators is established. Based on the a posteriori error control, a finite element adaptive strategy is presented for computing the diffraction problem. The truncation parameter is determined through sharp a posteriori error estimate. Numerical experiments are included to illustrate the robustness and effectiveness of our error estimate and the proposed adaptive algorithm.展开更多
In this paper, we propose a multilevel preconditioner for the Crouzeix-Raviart finite element approximation of second-order elliptic partial differential equations with discontinuous coefficients. Since the finite ele...In this paper, we propose a multilevel preconditioner for the Crouzeix-Raviart finite element approximation of second-order elliptic partial differential equations with discontinuous coefficients. Since the finite element spaces are nonnested, weighted intergrid transfer operators, which are stable under the weighted L2 norm, are introduced to exchange information between different meshes. By analyzing the eigenvalue distribution of the preconditioned system, we prove that except a few small eigenvalues, all the other eigenvalues are bounded below and above nearly uniformly with respect to the jump and the mesh size. As a result, we get that the convergence rate of the preconditioned conjugate gradient method is quasi-uniform with respect to the jump and the mesh size. Numerical experiments are presented to confirm our theoretical analysis.展开更多
基金This work was supported by the National Natural Science Foundation of China （No. 51775408）, the Project funded by the Key Laboratory of Product Quality Assurance ＆ Diagnosis （No. 2014SZS14-P05）
文摘Based on B-spline wavelet on the interval （BSWI） and the multivariable generalized variational principle, the multivariable wavelet finite element for flat shell is constructed by combining the elastic plate element and the Mindlin plate element together. First, the elastic plate element formulation is derived from the generalized potential energy function. Due to its excellent numerical approximation property, BSWI is used as the interpolation function to separate the solving field variables. Second, the multivariable wavelet Mindlin plate element is deduced and constructed according to the multivariable generalized variational principle and BSWI. Third, by following the displacement compatibility requirement and the coordinate transformation method, the multivariable wavelet finite element for fiat shell is constructed. The novel advantage of the constructed element is that the solving precision and efficiency can be improved because the generalized displacement field variables and stress field variables are interpolated and solved independently. Finally, several numerical examples including bending and vibration analyses are given to verify the constructed element and method.
基金supported by the National Natural Science Foundation of China(90816025,10721062)National Basic Research Program of China(2006CB601205)Program for New Century Excellent Talents in University of the Ministry of Education of China(NCET-04-0272)
文摘Topology optimization of continuum structures with design-dependent loads has long been a challenge. In this paper, the topology optimization of 3D structures subjected to design-dependent loads is investigated. A boundary search scheme is proposed for 3D problems, by means of which the load surface can be identified effectively and efficiently, and the difficulties arising in other approaches can be overcome. The load surfaces are made up of the boundaries of finite elements and the loads can be directly applied to corresponding element nodes, which leads to great convenience in the application of this method. Finally, the effectiveness and efficiency of the proposed method is validated by several numerical examples.
文摘The numerical solutions for uncertain viscoelastic problems have important theo- retical and practical significance. The paper develops a new approach by combining the scaled boundary finite element method （SBFEM） and fuzzy arithmetic. For the viscoelastic problems with zero uncertainty, the SBFEM and the temporally piecewise adaptive algorithm is employed in the space domain and the time domain, respectively, in order to provide an accurate semi- analytical boundary-based approach and to ensure the accuracy of discretization in the time domain with different sizes of time step at the same time. The fuzzy arithmetic is used to address the uncertainty analysis of viscoelastic material parameters, and the transformation method is used for computation with the advantages of effectively avoiding overestimation and reducing the computational costs. Numerical examples are provided to test the performance of the proposed method. By comparing with the analytical solutions and the Monte Carlo method, satisfactory results are achieved.
文摘To facilitate long term infrastructure asset management systems, it is necessary to determine the bearing capacity of pavements. Currently it is common to conduct such measurements in a stationary manner, however the evaluation with stationary loading does not correspond to reality a tendency towards continuous and high speed measurements in recent years can be observed. The computational program SAFEM was developed with the objective of evaluating the dynamic response of asphalt under moving loads and is based on a semi-analytic element method. In this research project SAFEM is compared to commercial finite element software ABAQUS and field measurements to verify the computational accuracy. The computational accuracy of SAFEM was found to be high enough to be viable whilst boasting a computational time far shorter than ABAQUS. Thus, SAFEM appears to be a feasible approach to determine the dynamic response of pavements under dynamic loads and is a useful tool for infrastructure administrations to analyze the pavement bearing capacity.
基金The first author is partially supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials under Award Number DE-SC-0009249, and the Key Program of National Natural Science Foundation of China with Grant No. 91430215. The second author is supported by State Key Laboratory of Scientific and Engineering Computing （LSEC）, National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences （NCMIS）, and National Natural Science Foundation of China with Grant No. 11471026 he is thankful to the Center for Computational Mathematics and Applications, the Pennsylvania State University, where he worked on this manuscript as a visiting scholar. The authors are grateful to Professor Jinchao Xu, Dr. Yuanming Xiao and Dr. Maximilian Metti for their valuable suggestions and discussions, to Professor Haijun Wu for his valuable help on preparing the numerical example, and to the anonymous referee for the valuable comments and suggestion which lead to improvements of the paper.
文摘In this paper, we study Nitsche extended finite element method （XFEM） for the inter- face problem of a two dimensional diffusion equation. Specifically, we study the quadratic XFEM scheme on some shape-regular family of grids and prove the optimal convergence rate of the scheme with respect to the mesh size. Main efforts are devoted onto classifying the cases of intersection between the elements and the interface and prove a weighted trace inequality for the extended finite element functions needed, and the general framework of analysing XFEM c^n be implemented then.
文摘This paper proves the saturation assumption for the nonconforming Morley finite ele- ment discretization of the biharmonic equation. This asserts that the error of the Morley approximation under uniform refinement is strictly reduced by a contraction factor smaller than one up to explicit higher-order data approximation terms. The refinement has at least to bisect any edge such as red refinement or 3-bisections on any triangle. This justifies a hierarchical error estimator for the Morley finite element method, which simply compares the discrete solutions of one mesh and its red-refinement. The related adaptive mesh-refining strategy performs optimally in numerical experiments. A remark for Crouzeix-Raviart nonconforming finite element error control is included.
文摘Slippage corresponds to the relative displacement of a bolted joint subjected to shear loads since the construction clearance between the bolt shank and the bolthole at assembly can cause joint slip. Deflections of towers with joint slippage effects is up to 1.9 times greater than the displacements obtained by linear analytical methods. In this study, 8 different types of joints are modelled and studied in the finite element program, and the results are verified by the experimental results which have been done in the laboratory. Moreover, several types of joints have been modelled and studied and load-deformation curves have also been presented. Finally, joint slip data for different types of angles, bolt diameter and bolt arrangements are generated. Thereupon, damping ratios （ζ） for different types of connections are reported. The study can be useful to help in designing of wind turbine towers with a higher level of accuracy and safety.
文摘This paper is concerned with the finite elements approximation for the Steklov eigen- value problem on concave polygonal domain. We make full use of the regularity estimate and the characteristic of edge average interpolation operator of nonconforming Crouzeix- Raviart element, and prove a new and optimal error estimate in ｜｜ ｜｜o,δΩ for the eigenfunc- tion of linear conforming finite element and the nonconforming Crouzeix-Raviart element. Finally, we present some numerical results to support the theoretical analysis.
基金The work of the second author was supported by the NSFC （No. 11301267） and by the Natural Science Foundation for Colleges and Universities in Jiangsu Province （No.12KJB110007）.
文摘The electromagnetic wave propagation in the chiral medium is governed by Maxwell＇s equations together with the Drude-Born-Fedorov （constitutive） equations. The problem is simplified to a two-dimensional scattering problem, and is formulated in a bounded domain by introducing two pairs of transparent boundary conditions. An a posteriori error estimate associated with the truncation of the nonlocal boundary operators is established. Based on the a posteriori error control, a finite element adaptive strategy is presented for computing the diffraction problem. The truncation parameter is determined through sharp a posteriori error estimate. Numerical experiments are included to illustrate the robustness and effectiveness of our error estimate and the proposed adaptive algorithm.
基金supported by National Natural Science Foundation of China (Grant Nos.10871100 and 11071124)
文摘In this paper, we propose a multilevel preconditioner for the Crouzeix-Raviart finite element approximation of second-order elliptic partial differential equations with discontinuous coefficients. Since the finite element spaces are nonnested, weighted intergrid transfer operators, which are stable under the weighted L2 norm, are introduced to exchange information between different meshes. By analyzing the eigenvalue distribution of the preconditioned system, we prove that except a few small eigenvalues, all the other eigenvalues are bounded below and above nearly uniformly with respect to the jump and the mesh size. As a result, we get that the convergence rate of the preconditioned conjugate gradient method is quasi-uniform with respect to the jump and the mesh size. Numerical experiments are presented to confirm our theoretical analysis.
