In the analysis of high-rise building, traditional displacement-based plane elements are often used to get the in-plane internal forces of the shear walls by stress integration. Limited by the singular problem produce...In the analysis of high-rise building, traditional displacement-based plane elements are often used to get the in-plane internal forces of the shear walls by stress integration. Limited by the singular problem produced by wall holes and the loss of precision induced by using differential method to derive strains, the displacement-based elements cannot always present accuracy enough for design. In this paper, the hybrid post-processing procedure based on the Hellinger-Reissner variational principle is used for improving the stress precision of two quadrilateral plane elements. In order to find the best stress field, three different forms are assumed for the displacement-based plane elements and with drilling DOF. Numerical results show that by using the proposed method, the accuracy of stress solutions of these two displacement-based plane elements can be improved.展开更多
A linear 4-node quadrilateral quasi-conforming plane element with internal parameters is proposed. The element preserves advantages of the quasi-conforming technique, including an explicit stiffness matrix, which can ...A linear 4-node quadrilateral quasi-conforming plane element with internal parameters is proposed. The element preserves advantages of the quasi-conforming technique, including an explicit stiffness matrix, which can be applied to nonlinear problems. The weak patch test guarantees the convergence of the element. Then the linear element is extended to the geometri- cally nonlinear analysis in the framework of Total Lagrangian （TL） formulation. The numerical tests indicate that the present element is accurate and insensitive to mesh distortion.展开更多
Shale contains distributed directional bedding planes,which make the shale transverse isotropic.To model shale with consideration of the bedding planes,a cohesive finite element method(CFEM)is developed based on the r...Shale contains distributed directional bedding planes,which make the shale transverse isotropic.To model shale with consideration of the bedding planes,a cohesive finite element method(CFEM)is developed based on the randomized triangular mesh.The interface orientation generated from such mesh tends to be uniformly distributed with the element number increasing.To represent the bedding plane,the interfaces aligned with the bedding plane are assigned the cohesive law that characterizes the bedding plane while the other interfaces are assigned the cohesive law that characterizes the matrix.By this means,the anisotropy characteristics of the stiffness and the strength of shale are well represented.The simulation examples demonstrate that the bedding plane has a significant influence on the fracture trajectory,which is consistent with the observation in the experiment.It is suggested that this modeling method of shale is feasible.It provides an alternative approach to fracture simulation in shale.展开更多
The analysis method of lattice dynamics in classical physics is extended to study the properties of in-plane wave motion in the hybrid-mass finite element model in this paper. The dispersion equations of P and SV wave...The analysis method of lattice dynamics in classical physics is extended to study the properties of in-plane wave motion in the hybrid-mass finite element model in this paper. The dispersion equations of P and SV waves in the discrete model are first obtained by means of separating the characteristic equation of the motion equation, and then used to analyse the properties of P-and SV-homogeneous, inhomogeneous waves and other types of motion in the model. The dispersion characters, cut-off frequencies of P and SV waves, the polarization drift and appendent anisotropic property of wave motion caused by the discretization are finally discussed.展开更多
The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurat...The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.展开更多
This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations s...This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.展开更多
In this paper, based on the step reduction method[1] and exact analytic method[2] anew method-exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational ...In this paper, based on the step reduction method[1] and exact analytic method[2] anew method-exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a quadrilateral noncompatible element with 8 degrees of freedom is derived for the solution of plane problem. Since Jacobi's transformation is not applied, the present element may degenerate into a triangle element. It is convenient to use the element in engineering. In this paper, the convergence is proved. Numerical examples are given at the endof this paper, which indicate satisfactory results of stress and displacements can be obtained and have higher numerical precision in nodes.展开更多
Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious...Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.展开更多
In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solutio...In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.展开更多
The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subj...The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.展开更多
In the paper, an improved algorithm is presented for Delaunay triangulation of the point-set in the plain. Based on the original algorithm, we propose the notion of removing circle. During the process of triangulation...In the paper, an improved algorithm is presented for Delaunay triangulation of the point-set in the plain. Based on the original algorithm, we propose the notion of removing circle. During the process of triangulation, and the circle dynamically moves, the algorithm which is simple and practical, therefore evidently accelerates the process of searching a new point, while generating a new triangle. Then it shows the effect of the algorithm in the finite element mesh.展开更多
As the continuation study on amplification of in-plane seismic ground motion by underground group cavities in layered half-space, this study extends to the case of poroelastic half-space with dry poroelastic and satur...As the continuation study on amplification of in-plane seismic ground motion by underground group cavities in layered half-space, this study extends to the case of poroelastic half-space with dry poroelastic and saturated poroelastic soil layers. The influence of poroelastic layers on the amplification of seismic ground motion is studied both in frequency domain and time domain using indirect boundary element method （IBEM）. It is shown that for the example of a saturated poroelastic site in Tianjin under the excitation of Taft wave and E1 Centro wave, the amplification of seismic ground motion in poroelastic case is slightly smaller than that in the elastic case, and the amplification of PGA （peak ground acceleration） and its PRS （peak response spectrum）.. can be increased up to 38.8% and 64.6%; the predominant period of response spectra in poroelastic case becomes shorter to some extent compared with that in the elastic case. It is suggested that the effect of underground group cavities in poroelastic half-space on design seismic ground motion should be considered.展开更多
To predict the behavior of geogrids embedded in sand under pullout loading conditions, the two dimensional plane-stress finite element model was presented. The interactions between soil and geogrid were simulated as ...To predict the behavior of geogrids embedded in sand under pullout loading conditions, the two dimensional plane-stress finite element model was presented. The interactions between soil and geogrid were simulated as non-linear springs, and the stiffness of the springs was determined from simple tests in the specially designed pullout box. The predicted behavior of the geogrid under pullout load agrees well with the observed data including the load-displacement properties, the displacement distribution along the longitudinal direction and the mobilization of the frictional and bearing resistance. (Edited author abstract) 8 Refs.展开更多
In this paper, linear and quadratic finite element models are devised for the three- dimensional Helmholtz problem by using a hybrid variational functional. In each element, contin- uous and discontinuous Helmholtz fi...In this paper, linear and quadratic finite element models are devised for the three- dimensional Helmholtz problem by using a hybrid variational functional. In each element, contin- uous and discontinuous Helmholtz fields are defined with their equality enforced over the element boundary in a weak sense. The continuous field is based on the C° nodal interpolation and the discontinuous field can be condensed before assemblage. Hence, the element can readily be in- corporated seamlessly into the standard finite element program framework. Discontinuous fields constructed by the plane-wave, Bessel and singular spherical-wave solutions are attempted. Nu- merical tests demonstrate that some of the element models are consistently and considerably more accurate than their conventional counterparts.展开更多
Amplification of in-plane seismic ground motion by underground group cavities in layered half-space is studied both in frequency domain and time domain by using indirect boundary element method （IBEM）, and the effec...Amplification of in-plane seismic ground motion by underground group cavities in layered half-space is studied both in frequency domain and time domain by using indirect boundary element method （IBEM）, and the effect of cavity interval and spectrum of incident waves on the amplification are studied by numerical examples. It is shown that there may be large interaction between cavities, and group cavities with certain intervals may have significant amplification to seismic ground motion. The amplification of PGA （peak ground acceleration） and its PRS （peak response spectrum） can be increased up to 45.2% and 84.4%, for an example site in Tianjin, under the excitation of Taft wave and E1 Centro wave; and group cavities may also affect the spectra of the seismic ground motion. It is suggested that the effect of underground group cavities on design seismic ground motion should be considered.展开更多
文摘In the analysis of high-rise building, traditional displacement-based plane elements are often used to get the in-plane internal forces of the shear walls by stress integration. Limited by the singular problem produced by wall holes and the loss of precision induced by using differential method to derive strains, the displacement-based elements cannot always present accuracy enough for design. In this paper, the hybrid post-processing procedure based on the Hellinger-Reissner variational principle is used for improving the stress precision of two quadrilateral plane elements. In order to find the best stress field, three different forms are assumed for the displacement-based plane elements and with drilling DOF. Numerical results show that by using the proposed method, the accuracy of stress solutions of these two displacement-based plane elements can be improved.
基金Project supported by the Fundamental Research Funds for the Central Universities(DUT14RC(3)092)the Key Project of the NSFC(Nos.11272075 and 11472071)+1 种基金the‘863’Project of China(No.2009AA04Z101)the‘973’National Basic Research Project of China(No.2010CB832700)
文摘A linear 4-node quadrilateral quasi-conforming plane element with internal parameters is proposed. The element preserves advantages of the quasi-conforming technique, including an explicit stiffness matrix, which can be applied to nonlinear problems. The weak patch test guarantees the convergence of the element. Then the linear element is extended to the geometri- cally nonlinear analysis in the framework of Total Lagrangian （TL） formulation. The numerical tests indicate that the present element is accurate and insensitive to mesh distortion.
基金supported by the National Natural Science Foundation of China(No.11772190)
文摘Shale contains distributed directional bedding planes,which make the shale transverse isotropic.To model shale with consideration of the bedding planes,a cohesive finite element method(CFEM)is developed based on the randomized triangular mesh.The interface orientation generated from such mesh tends to be uniformly distributed with the element number increasing.To represent the bedding plane,the interfaces aligned with the bedding plane are assigned the cohesive law that characterizes the bedding plane while the other interfaces are assigned the cohesive law that characterizes the matrix.By this means,the anisotropy characteristics of the stiffness and the strength of shale are well represented.The simulation examples demonstrate that the bedding plane has a significant influence on the fracture trajectory,which is consistent with the observation in the experiment.It is suggested that this modeling method of shale is feasible.It provides an alternative approach to fracture simulation in shale.
基金The project sponsored by the Earthquake Science Foundation under Contract No. 90141
文摘The analysis method of lattice dynamics in classical physics is extended to study the properties of in-plane wave motion in the hybrid-mass finite element model in this paper. The dispersion equations of P and SV waves in the discrete model are first obtained by means of separating the characteristic equation of the motion equation, and then used to analyse the properties of P-and SV-homogeneous, inhomogeneous waves and other types of motion in the model. The dispersion characters, cut-off frequencies of P and SV waves, the polarization drift and appendent anisotropic property of wave motion caused by the discretization are finally discussed.
基金the National Natural Science Foundation of China(No.11572210).
文摘The finite element method (FEM) plays a valuable role in computer modeling and is beneficial to the mechanicaldesign of various structural parts. However, the elements produced by conventional FEM are easily inaccurate andunstable when applied. Therefore, developing new elements within the framework of the generalized variationalprinciple is of great significance. In this paper, an 8-node plane hybrid finite element with 15 parameters (PHQ8-15β) is developed for structural mechanics problems based on the Hellinger-Reissner variational principle.According to the design principle of Pian, 15 unknown parameters are adopted in the selection of stress modes toavoid the zero energy modes.Meanwhile, the stress functions within each element satisfy both the equilibrium andthe compatibility relations of plane stress problems. Subsequently, numerical examples are presented to illustrate theeffectiveness and robustness of the proposed finite element. Numerical results show that various common lockingbehaviors of plane elements can be overcome. The PH-Q8-15β element has excellent performance in all benchmarkproblems, especially for structures with varying cross sections. Furthermore, in bending problems, the reasonablemesh shape of the new element for curved edge structures is analyzed in detail, which can be a useful means toimprove numerical accuracy.
基金supported by the National Natural Science Foundation of China (11172291)the National Science Foundation for Post-doctoral Scientists of China (2012M510162)the Fundamental Research Funds for the Central Universities (KB2090050024)
文摘This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/planesymmetric acoustic wave problems.The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only.Moreover,a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived,and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating,translating and saving the multipole/local expansion coefficients of the image domain.The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems.As for exterior acoustic problems,the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method.Details on the implementation of the present method are described,and numerical examples are given to demonstrate its accuracy and efficiency.
文摘In this paper, based on the step reduction method[1] and exact analytic method[2] anew method-exact element method for constructing finite element, is presented. Since the new method doesn 't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a quadrilateral noncompatible element with 8 degrees of freedom is derived for the solution of plane problem. Since Jacobi's transformation is not applied, the present element may degenerate into a triangle element. It is convenient to use the element in engineering. In this paper, the convergence is proved. Numerical examples are given at the endof this paper, which indicate satisfactory results of stress and displacements can be obtained and have higher numerical precision in nodes.
文摘Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.
文摘In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method （F2LFEM）. The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor （SIF）.
基金National Natural Science Foundation of China under Grant 51378384Key Project of Natural Science Foundation of Tianjin Municipality under Grant 12JCZDJC29000
文摘The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.
文摘In the paper, an improved algorithm is presented for Delaunay triangulation of the point-set in the plain. Based on the original algorithm, we propose the notion of removing circle. During the process of triangulation, and the circle dynamically moves, the algorithm which is simple and practical, therefore evidently accelerates the process of searching a new point, while generating a new triangle. Then it shows the effect of the algorithm in the finite element mesh.
基金supported by National Natural Science Foundation of China under grant No. 50978183Key Project for Applied Basic Research of Tianjin Municipality under Grant No. 12JCZDJC29000
文摘As the continuation study on amplification of in-plane seismic ground motion by underground group cavities in layered half-space, this study extends to the case of poroelastic half-space with dry poroelastic and saturated poroelastic soil layers. The influence of poroelastic layers on the amplification of seismic ground motion is studied both in frequency domain and time domain using indirect boundary element method （IBEM）. It is shown that for the example of a saturated poroelastic site in Tianjin under the excitation of Taft wave and E1 Centro wave, the amplification of seismic ground motion in poroelastic case is slightly smaller than that in the elastic case, and the amplification of PGA （peak ground acceleration） and its PRS （peak response spectrum）.. can be increased up to 38.8% and 64.6%; the predominant period of response spectra in poroelastic case becomes shorter to some extent compared with that in the elastic case. It is suggested that the effect of underground group cavities in poroelastic half-space on design seismic ground motion should be considered.
文摘To predict the behavior of geogrids embedded in sand under pullout loading conditions, the two dimensional plane-stress finite element model was presented. The interactions between soil and geogrid were simulated as non-linear springs, and the stiffness of the springs was determined from simple tests in the specially designed pullout box. The predicted behavior of the geogrid under pullout load agrees well with the observed data including the load-displacement properties, the displacement distribution along the longitudinal direction and the mobilization of the frictional and bearing resistance. (Edited author abstract) 8 Refs.
基金The support of Hong Kong Research Grant Council in the form of the GRF grant HKU 7167/08E
文摘In this paper, linear and quadratic finite element models are devised for the three- dimensional Helmholtz problem by using a hybrid variational functional. In each element, contin- uous and discontinuous Helmholtz fields are defined with their equality enforced over the element boundary in a weak sense. The continuous field is based on the C° nodal interpolation and the discontinuous field can be condensed before assemblage. Hence, the element can readily be in- corporated seamlessly into the standard finite element program framework. Discontinuous fields constructed by the plane-wave, Bessel and singular spherical-wave solutions are attempted. Nu- merical tests demonstrate that some of the element models are consistently and considerably more accurate than their conventional counterparts.
基金supported by National Natural Science Foundation of China under grant No. 50978183Tianjin Key Project for Applied Basic Research under grant No. 12JCZDJC29000
文摘Amplification of in-plane seismic ground motion by underground group cavities in layered half-space is studied both in frequency domain and time domain by using indirect boundary element method （IBEM）, and the effect of cavity interval and spectrum of incident waves on the amplification are studied by numerical examples. It is shown that there may be large interaction between cavities, and group cavities with certain intervals may have significant amplification to seismic ground motion. The amplification of PGA （peak ground acceleration） and its PRS （peak response spectrum） can be increased up to 45.2% and 84.4%, for an example site in Tianjin, under the excitation of Taft wave and E1 Centro wave; and group cavities may also affect the spectra of the seismic ground motion. It is suggested that the effect of underground group cavities on design seismic ground motion should be considered.
