4-node, 8-node and 8(4)-node quadrilateral plane isoparametric elements are used for the solution of boundary value problems in linear isotropic Cosserat elasticity. The patch test is applied to validate the finite ...4-node, 8-node and 8(4)-node quadrilateral plane isoparametric elements are used for the solution of boundary value problems in linear isotropic Cosserat elasticity. The patch test is applied to validate the finite elements. Engineering problems of stress concentration around a circular hole in plane strain condition and mechanical behaviors of heterogeneous materials with rigid inclusions and pores are computed to test the accuracy and capability of these three types of finite elements.展开更多
A second order isoparametric finite element method (IPFEM) is proposed for elliptic interface problems. It yields better accuracy than some existing second-order methods, when the coefficients or the flux across the...A second order isoparametric finite element method (IPFEM) is proposed for elliptic interface problems. It yields better accuracy than some existing second-order methods, when the coefficients or the flux across the immersed curved interface is discontinuous. Based on an initial Cartesian mesh, a mesh optimization strategy is presented by employing curved boundary elements at the interface, and an incomplete quadratic finite element space is constructed on the optimized mesh. It turns out that the number of curved boundary elements is far less than that of the straight one, and the total degree of freedom is almost the same as the uniform Cartesian mesh. Numerical examples with simple and complicated geometrical interfaces demonstrate the efficiency of the proposed method.展开更多
We consider the quadrilateral Q1 isoparametric element and establish an optimal error estimate in H^1 norm for the interpolation operator under a weaker mesh condition which admits anisotropic quadrilaterals and allow...We consider the quadrilateral Q1 isoparametric element and establish an optimal error estimate in H^1 norm for the interpolation operator under a weaker mesh condition which admits anisotropic quadrilaterals and allows the quadrilateral to become a regular triangle in the sense of maximum angle condition [5, 11].展开更多
An 8-noded locking-free degenerated isoparametric shell element is presented. A revised interpolation for shear strain terms was constructed in natural co-ordinate system such that all necessary modes (translation, ro...An 8-noded locking-free degenerated isoparametric shell element is presented. A revised interpolation for shear strain terms was constructed in natural co-ordinate system such that all necessary modes (translation, rotation and constant curvature) are preserved, which can be used to eliminate shear locking. A revised interpolation for membrane strains was produced in the local Cartesian co-ordinate system to overcome membrane locking behavior. The new 8-noded element has the proper rank, with the requisite number of zero eigenvalues each associated with a rigid mode. The element does not exhibit membrane or shear locking for large span-thickness ratio. The element does not form element mechanisms or extra spurious zero energy modes. Therefore, it can be used for both thin and thick shells.展开更多
In this paper, the hydrodynamic characteristics and flow field around rectangular and delta hydrofoils, moving with a constant speed beneath the free surface are numerically studied by means of isoparametric boundary ...In this paper, the hydrodynamic characteristics and flow field around rectangular and delta hydrofoils, moving with a constant speed beneath the free surface are numerically studied by means of isoparametric boundary element method (IBEM). The quantities (source and dipole strengths) and the geometry of the dements are represented by a linear distribution. Two types of three-dimensional hydrofoils (rectangular and delta) are selected with NACA4412 and symmetric Joukowski sections. Some numerical results of pressure distribution, lift, wave-making drag coefficients and velocity field around the hydrofoils are presented. Also, the wave pattern due to moving hydrofoil is predicted at different operational conditions. Comparisons are made between computational results obtained through this method and those from the experimental measurements and other numerical results which reveal good agreement.展开更多
Based on the Hellinger-Reissner (H-R) mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is established. A new semi-analyt...Based on the Hellinger-Reissner (H-R) mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient response of the laminated cantilever with piezoelectric patch is presented. The major steps of mathematical model are as follows: the piezoelectric layer and host layer of laminated plate are considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure is derived by considering the compatibility of generalized displacements and generalized stresses on the interface between layers. There is no restriction for the side-face geometrical boundaries, the thickness and the number of layers of plate by the use of the present isoparametric element. Present method has wide application area.展开更多
The mold filling of RTM was simulated based on the control volume finite element method (CV/FEM). The formulat ion using isoparametric transformation was discussed in detail and a computation al code based on isopara...The mold filling of RTM was simulated based on the control volume finite element method (CV/FEM). The formulat ion using isoparametric transformation was discussed in detail and a computation al code based on isoparametric technique was developed. The simulation results w ere compared with experimental data. Different isoparametric elements, quadrilat eral and triangular, were compared in the simulation.It demonstrates that the us e of bilinear quadrilateral isoparametric elements in simulating the process can produce a higher precision and cost a less time than the use of triangular ones .展开更多
A finite element method is developed for simulating frequency domain electromagnetic responses due to a dipole source in the 2-D conductive structures. Computing costs are considerably minimized by reducing the full t...A finite element method is developed for simulating frequency domain electromagnetic responses due to a dipole source in the 2-D conductive structures. Computing costs are considerably minimized by reducing the full three-dimensional problem to a series of two-dimensional problems. This is accomplished by transforming the problem into y-wave number (Ky) domain using Fourier transform and the y-axis is parallel to the structural strike. In the Ky domain, two coupled partial differential equations for magnetic field Hy and electric field Ey are derived. For a specific value of Ky, the coupled equations are solved by the finite element method with isoparametric elements in the x-z plane. Application of the inverse Fourier transform to the Ky, domain provides the electric and magnetic fields in real space. The equations derived can be applied to general complex two-dimensional structures containing either electric or magnetic dipole source in any direction. In the modeling of the electromagnetic measurement, we adopted a pseudo-delta function to distribute the dipole source current and circumvent the problem of singularity at the source point. Moreover, the suggested method used isoparametric finite elements to accommodate the complex subsurface formation. For the large scale linear system derived from the discretization of the Maxwell's equations, several iterative solvers were used and compared to select the optimal one. A quantitative test of accuracy was presented which compared the finite element results with analytic solutions for a dipole source in homogeneous space for different ranges and different wave numbers Ky. to validate the addressed the effects of the distribution range τ of the homogeneous medium. code and check its effectiveness. In addition, we pseudo-delta function on the numerical results in展开更多
The use of finite element method leads to replacing the initial domain by an approaching domain. Under some appropriate assumptions, we prove that there exists a W1,+∞-diffeomorphism from the original domain to the a...The use of finite element method leads to replacing the initial domain by an approaching domain. Under some appropriate assumptions, we prove that there exists a W1,+∞-diffeomorphism from the original domain to the approaching domain.展开更多
Combining the symplectic variations theory, the homogeneous control equation and isopaxametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the gene...Combining the symplectic variations theory, the homogeneous control equation and isopaxametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isopaxametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which axe often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.展开更多
Aiming at the isoparametric bilinear finite volume element scheme,we initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise by employing the energ...Aiming at the isoparametric bilinear finite volume element scheme,we initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise by employing the energy-embedded method on uniform grids.Furthermore,we prove that the approximate derivatives are convergent of order two.Finally,numerical examples verify the theoretical results.展开更多
The main aim of this paper is to show that the quadrilateral mesh condition RDP(N, ψ) is only sufficient but not necessary for the optimal order error estimate of the Q isoparametric element in the Hi norm.
In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws.High order accuracy in space is obtain...In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws.High order accuracy in space is obtained with a standard WENO reconstruction algorithm and high order in time is obtained using the local space-time discontinuous Galerkinmethod recently proposed in[20].In the Lagrangian framework considered here,the local space-time DG predictor is based on a weak formulation of the governing PDE on a moving space-time element.For the spacetime basis and test functions we use Lagrange interpolation polynomials defined by tensor-product Gauss-Legendre quadrature points.The moving space-time elements are mapped to a reference element using an isoparametric approach,i.e.the spacetime mapping is defined by the same basis functions as the weak solution of the PDE.We show some computational examples in one space-dimension for non-stiff and for stiff balance laws,in particular for the Euler equations of compressible gas dynamics,for the resistive relativistic MHD equations,and for the relativistic radiation hydrodynamics equations.Numerical convergence results are presented for the stiff case up to sixth order of accuracy in space and time and for the non-stiff case up to eighth order of accuracy in space and time.展开更多
基金The project supported by the National Natural Science Foundation of China(10225212,50178016,10421002)the Program for Changjiang Scholars and Innovative Research Team in University of China
文摘4-node, 8-node and 8(4)-node quadrilateral plane isoparametric elements are used for the solution of boundary value problems in linear isotropic Cosserat elasticity. The patch test is applied to validate the finite elements. Engineering problems of stress concentration around a circular hole in plane strain condition and mechanical behaviors of heterogeneous materials with rigid inclusions and pores are computed to test the accuracy and capability of these three types of finite elements.
基金Supported by the National Natural Science Foundation of China (11071216 and 11101361)
文摘A second order isoparametric finite element method (IPFEM) is proposed for elliptic interface problems. It yields better accuracy than some existing second-order methods, when the coefficients or the flux across the immersed curved interface is discontinuous. Based on an initial Cartesian mesh, a mesh optimization strategy is presented by employing curved boundary elements at the interface, and an incomplete quadratic finite element space is constructed on the optimized mesh. It turns out that the number of curved boundary elements is far less than that of the straight one, and the total degree of freedom is almost the same as the uniform Cartesian mesh. Numerical examples with simple and complicated geometrical interfaces demonstrate the efficiency of the proposed method.
文摘We consider the quadrilateral Q1 isoparametric element and establish an optimal error estimate in H^1 norm for the interpolation operator under a weaker mesh condition which admits anisotropic quadrilaterals and allows the quadrilateral to become a regular triangle in the sense of maximum angle condition [5, 11].
文摘An 8-noded locking-free degenerated isoparametric shell element is presented. A revised interpolation for shear strain terms was constructed in natural co-ordinate system such that all necessary modes (translation, rotation and constant curvature) are preserved, which can be used to eliminate shear locking. A revised interpolation for membrane strains was produced in the local Cartesian co-ordinate system to overcome membrane locking behavior. The new 8-noded element has the proper rank, with the requisite number of zero eigenvalues each associated with a rigid mode. The element does not exhibit membrane or shear locking for large span-thickness ratio. The element does not form element mechanisms or extra spurious zero energy modes. Therefore, it can be used for both thin and thick shells.
文摘In this paper, the hydrodynamic characteristics and flow field around rectangular and delta hydrofoils, moving with a constant speed beneath the free surface are numerically studied by means of isoparametric boundary element method (IBEM). The quantities (source and dipole strengths) and the geometry of the dements are represented by a linear distribution. Two types of three-dimensional hydrofoils (rectangular and delta) are selected with NACA4412 and symmetric Joukowski sections. Some numerical results of pressure distribution, lift, wave-making drag coefficients and velocity field around the hydrofoils are presented. Also, the wave pattern due to moving hydrofoil is predicted at different operational conditions. Comparisons are made between computational results obtained through this method and those from the experimental measurements and other numerical results which reveal good agreement.
基金Project supported by the National Natural Science Foundation of China (No. 10072038)
文摘Based on the Hellinger-Reissner (H-R) mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient response of the laminated cantilever with piezoelectric patch is presented. The major steps of mathematical model are as follows: the piezoelectric layer and host layer of laminated plate are considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure is derived by considering the compatibility of generalized displacements and generalized stresses on the interface between layers. There is no restriction for the side-face geometrical boundaries, the thickness and the number of layers of plate by the use of the present isoparametric element. Present method has wide application area.
基金Funded by the National Natural Science Foundation of China ( 19872051 ) and the National "863" H tech Foundation(2001AA335020)
文摘The mold filling of RTM was simulated based on the control volume finite element method (CV/FEM). The formulat ion using isoparametric transformation was discussed in detail and a computation al code based on isoparametric technique was developed. The simulation results w ere compared with experimental data. Different isoparametric elements, quadrilat eral and triangular, were compared in the simulation.It demonstrates that the us e of bilinear quadrilateral isoparametric elements in simulating the process can produce a higher precision and cost a less time than the use of triangular ones .
文摘A finite element method is developed for simulating frequency domain electromagnetic responses due to a dipole source in the 2-D conductive structures. Computing costs are considerably minimized by reducing the full three-dimensional problem to a series of two-dimensional problems. This is accomplished by transforming the problem into y-wave number (Ky) domain using Fourier transform and the y-axis is parallel to the structural strike. In the Ky domain, two coupled partial differential equations for magnetic field Hy and electric field Ey are derived. For a specific value of Ky, the coupled equations are solved by the finite element method with isoparametric elements in the x-z plane. Application of the inverse Fourier transform to the Ky, domain provides the electric and magnetic fields in real space. The equations derived can be applied to general complex two-dimensional structures containing either electric or magnetic dipole source in any direction. In the modeling of the electromagnetic measurement, we adopted a pseudo-delta function to distribute the dipole source current and circumvent the problem of singularity at the source point. Moreover, the suggested method used isoparametric finite elements to accommodate the complex subsurface formation. For the large scale linear system derived from the discretization of the Maxwell's equations, several iterative solvers were used and compared to select the optimal one. A quantitative test of accuracy was presented which compared the finite element results with analytic solutions for a dipole source in homogeneous space for different ranges and different wave numbers Ky. to validate the addressed the effects of the distribution range τ of the homogeneous medium. code and check its effectiveness. In addition, we pseudo-delta function on the numerical results in
基金Partially supported by Professor Xu Yuesheng and his program "One hundred distinguished Young Scientists" Partially supported by "Programme Sino-Francais de Recherches Advancees(PRA).
文摘The use of finite element method leads to replacing the initial domain by an approaching domain. Under some appropriate assumptions, we prove that there exists a W1,+∞-diffeomorphism from the original domain to the approaching domain.
基金Project supported by the National Natural Science Foundation of China(No.50276041)
文摘Combining the symplectic variations theory, the homogeneous control equation and isopaxametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isopaxametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which axe often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.
基金supported by NSFC Project(Grant No.11031006,91130002,11171281)the Key Project of Scientific Research Fund of Hunan Provincial Science and Technology Department(Grant No.2011FJ2011)+2 种基金Specialized research Fund for the Doctoral Program of Higher Education(Grant No.20124301110003)Program for Changjiang Scholars and Innovative Research Team in University of China(No.IRT1179)Hunan Provincial Natural Science Foundation of China(Grant No.12JJ3010)。
文摘Aiming at the isoparametric bilinear finite volume element scheme,we initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise by employing the energy-embedded method on uniform grids.Furthermore,we prove that the approximate derivatives are convergent of order two.Finally,numerical examples verify the theoretical results.
基金This research is supported by the National Science Fbundation of China(No.10371113).
文摘The main aim of this paper is to show that the quadrilateral mesh condition RDP(N, ψ) is only sufficient but not necessary for the optimal order error estimate of the Q isoparametric element in the Hi norm.
基金the European Research Council under the European Union’s Seventh Framework Programme(FP7/2007-2013)under the research project STiMulUs,ERC Grant agreement no.278267.
文摘In this article we present a new family of high order accurate Arbitrary Lagrangian-Eulerian one-step WENO finite volume schemes for the solution of stiff hyperbolic balance laws.High order accuracy in space is obtained with a standard WENO reconstruction algorithm and high order in time is obtained using the local space-time discontinuous Galerkinmethod recently proposed in[20].In the Lagrangian framework considered here,the local space-time DG predictor is based on a weak formulation of the governing PDE on a moving space-time element.For the spacetime basis and test functions we use Lagrange interpolation polynomials defined by tensor-product Gauss-Legendre quadrature points.The moving space-time elements are mapped to a reference element using an isoparametric approach,i.e.the spacetime mapping is defined by the same basis functions as the weak solution of the PDE.We show some computational examples in one space-dimension for non-stiff and for stiff balance laws,in particular for the Euler equations of compressible gas dynamics,for the resistive relativistic MHD equations,and for the relativistic radiation hydrodynamics equations.Numerical convergence results are presented for the stiff case up to sixth order of accuracy in space and time and for the non-stiff case up to eighth order of accuracy in space and time.