The equivalent elastic modulus of cracked bodies with orderly distributed cracks was computed with the boundary element method. A practical self-consistent scheme has been proposed in consideration of the mutual inter...The equivalent elastic modulus of cracked bodies with orderly distributed cracks was computed with the boundary element method. A practical self-consistent scheme has been proposed in consideration of the mutual interaction effects of the cracks. The Influence of friction coefficients and orientation of cracks has been investigated. Some computational examples have been given, and the results show that the proposed method is adequate and the scheme is efficient.展开更多
Computational analysis of electrostatic microelectromechanical systems （MEMS） requires an electrostatic analysis to compute the electrostatic forces acting on micromechanical structures and a mechanical analysis to ...Computational analysis of electrostatic microelectromechanical systems （MEMS） requires an electrostatic analysis to compute the electrostatic forces acting on micromechanical structures and a mechanical analysis to compute the deformation of micromechanical structures. Typically, the mechanical analysis is performed on an undeformed geometry. However, the electrostatic analysis is performed on the deformed position of microstructures. In this paper, a new efficient approach to self-consistent analysis of electrostatic MEMS in the small deformation case is presented. In this approach, when the microstructures undergo small deformations, the surface charge densities on the deformed geometry can be computed without updating the geometry of the microstructures. This algorithm is based on the linear mode shapes of a microstructure as basis functions. A boundary integral equation for the electrostatic problem is expanded into a Taylor series around the undeformed configuration, and a new coupled-field equation is presented. This approach is validated by comparing its results with the results available in the literature and ANSYS solutions, and shows attractive features comparable to ANSYS.展开更多
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide...We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly, we introduce the ongoing project SCRIMP (Simulation and Control of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available.展开更多
We consider the approximation of systems of reaction-diffusion equations, with the finite element method. The highest derivative in each equation is multiplied by a parameter ε∈ （0, 1], and as ε → 0 the solution ...We consider the approximation of systems of reaction-diffusion equations, with the finite element method. The highest derivative in each equation is multiplied by a parameter ε∈ （0, 1], and as ε → 0 the solution of the system will contain boundary layers. We extend the analysis of the corresponding scalar problem from [Melenk, IMA J. Numer. Anal. 17（1997）, pp. 577-601], to construct a finite element scheme which includes elements of size O（εp） near the boundary, where p is the degree of the approximating polynomials. We show that, under the assumption of analytic input data, the method yields exponential rates of convergence, independently of ε, when the error is measured in the energy norm associated with the problem. Numerical computations supporting the theory are also presented, which also show that the method yields robust exponential convergence rates when the error in the maximum norm is used.展开更多
The Kaohsiung light rail transit (LRT) system first introduced embedded rail system in Taiwan. However, domestic engineering consultants are still lacking in experience of analysis, design and construction of embedded...The Kaohsiung light rail transit (LRT) system first introduced embedded rail system in Taiwan. However, domestic engineering consultants are still lacking in experience of analysis, design and construction of embedded rail systems. Noise and vibration of the mass rapid transit system is an important environmental issue in an urban environment. In order to understand the environmental impact of noise due to structural vibrations caused by a train running on the rail system, this paper establishes a numerical analysis procedure to perform a simulation. There are two fundamental parts to the numerical simulation: 1) vibration response due to a moving load and 2) radiation propagation of noise induced by structural vibration. The Kaohsiung LRT is used as a case study. The real embedded rail track system is modeled using ANSYS software with finite element analysis and the dynamic time history of the vibration response of the rail caused by a moving load is obtained. Secondly, the dynamic vibration response of the rail outputted by ANSYS is then imported into the software LMS Virtual.Lab to obtain the external radiation and sound field pressure distribution transferred from the rail to a specific monitoring point, based on the boundary element method. This paper also conducts field measurements of vibration velocity and sound pressure as a train passes. Both the experimental and analytical results for noise at specific points are compared and discussed. The proposed procedure promises to be suitable for practical vibration and noise analyses for rail systems.展开更多
基金the National Natural Science Foundation of China
文摘The equivalent elastic modulus of cracked bodies with orderly distributed cracks was computed with the boundary element method. A practical self-consistent scheme has been proposed in consideration of the mutual interaction effects of the cracks. The Influence of friction coefficients and orientation of cracks has been investigated. Some computational examples have been given, and the results show that the proposed method is adequate and the scheme is efficient.
基金Project supported by the National Natural Science Foundation of China (Grant No 50675034)the Natural Science Foundation of Jiangsu Province of China (Grant No SBK200920386)
文摘Computational analysis of electrostatic microelectromechanical systems （MEMS） requires an electrostatic analysis to compute the electrostatic forces acting on micromechanical structures and a mechanical analysis to compute the deformation of micromechanical structures. Typically, the mechanical analysis is performed on an undeformed geometry. However, the electrostatic analysis is performed on the deformed position of microstructures. In this paper, a new efficient approach to self-consistent analysis of electrostatic MEMS in the small deformation case is presented. In this approach, when the microstructures undergo small deformations, the surface charge densities on the deformed geometry can be computed without updating the geometry of the microstructures. This algorithm is based on the linear mode shapes of a microstructure as basis functions. A boundary integral equation for the electrostatic problem is expanded into a Taylor series around the undeformed configuration, and a new coupled-field equation is presented. This approach is validated by comparing its results with the results available in the literature and ANSYS solutions, and shows attractive features comparable to ANSYS.
文摘We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general structure of infinite-dimensional port-Hamiltonian systems (pHs) for which the Partitioned Finite Element Method (PFEM) straightforwardly applies. The proposed strategy is applied to abstract multidimensional linear hyperbolic and parabolic systems of PDEs. Then we show that instructional model problems based on the wave equation, Mindlin equation and heat equation fit within this unified framework. Secondly, we introduce the ongoing project SCRIMP (Simulation and Control of Interactions in Multi-Physics) developed for the numerical simulation of infinite-dimensional pHs. SCRIMP notably relies on the FEniCS open-source computing platform for the finite element spatial discretization. Finally, we illustrate how to solve the considered model problems within this framework by carefully explaining the methodology. As additional support, companion interactive Jupyter notebooks are available.
文摘We consider the approximation of systems of reaction-diffusion equations, with the finite element method. The highest derivative in each equation is multiplied by a parameter ε∈ （0, 1], and as ε → 0 the solution of the system will contain boundary layers. We extend the analysis of the corresponding scalar problem from [Melenk, IMA J. Numer. Anal. 17（1997）, pp. 577-601], to construct a finite element scheme which includes elements of size O（εp） near the boundary, where p is the degree of the approximating polynomials. We show that, under the assumption of analytic input data, the method yields exponential rates of convergence, independently of ε, when the error is measured in the energy norm associated with the problem. Numerical computations supporting the theory are also presented, which also show that the method yields robust exponential convergence rates when the error in the maximum norm is used.
文摘The Kaohsiung light rail transit (LRT) system first introduced embedded rail system in Taiwan. However, domestic engineering consultants are still lacking in experience of analysis, design and construction of embedded rail systems. Noise and vibration of the mass rapid transit system is an important environmental issue in an urban environment. In order to understand the environmental impact of noise due to structural vibrations caused by a train running on the rail system, this paper establishes a numerical analysis procedure to perform a simulation. There are two fundamental parts to the numerical simulation: 1) vibration response due to a moving load and 2) radiation propagation of noise induced by structural vibration. The Kaohsiung LRT is used as a case study. The real embedded rail track system is modeled using ANSYS software with finite element analysis and the dynamic time history of the vibration response of the rail caused by a moving load is obtained. Secondly, the dynamic vibration response of the rail outputted by ANSYS is then imported into the software LMS Virtual.Lab to obtain the external radiation and sound field pressure distribution transferred from the rail to a specific monitoring point, based on the boundary element method. This paper also conducts field measurements of vibration velocity and sound pressure as a train passes. Both the experimental and analytical results for noise at specific points are compared and discussed. The proposed procedure promises to be suitable for practical vibration and noise analyses for rail systems.
