Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with inte...Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with interpolation points mutual iterative between odd and even sequences in boundary region is provided, as well as the conformal mapping function which can be described by real number region between complicated region and unit dish region is carried out. Furthermore, in the in-plane state of constant stress, vibrating function is completed by unit dish region method for simple-supported elastic plates with concentrated substance of complicated vibrating region, and the coefficient of fundamental frequency of the plate is analyzed. Meanwhile, taking simple-supported elastic ellipse-plates as an example, the effects on fundamental frequency caused by eccentric ratio, the coefficient of constant in-plane stress, as well as the concentrated substance mass and positions are analyzed respectively.展开更多
By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between...By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between complicated region and unite dish region was carried out. Aiming at calculating the vibrating fundamental frequency of special-shaped, elastic simple-supported rectangle-plates, in the in-plane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region. The coefficient of fundamental frequency was calculated. Whilst, taking simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio of the length to width of rectangle, as well as the coefficient of constant in-plane stress were analyzed respectively.展开更多
Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved ...Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.展开更多
We extend the differential quadrature element method (DQEM) to the buckling analysis of uniformly in-plane loaded functionally graded (FG) plates fully or partially resting on the Pasternak model of elastic support. M...We extend the differential quadrature element method (DQEM) to the buckling analysis of uniformly in-plane loaded functionally graded (FG) plates fully or partially resting on the Pasternak model of elastic support. Material properties of the FG plate are graded in the thickness direction and assumed to obey a power law distribution of the volume fraction of the constituents. To set up the global eigenvalue equation, the plate is divided into sub-domains or elements and the generalized differential quadrature procedure is applied to discretize the governing, boundary and compatibility equations. By assembling discrete equations at all nodal points, the weighting coefficient and force matrices are derived. To validate the accuracy of this method, the results are compared with those of the exact solution and the finite element method. At the end, the effects of different variables and local elastic support arrangements on the buckling load factor are investigated.展开更多
Coupled-plate structures are widely used in the practical engineering such as aeronautical,civil and naval engineering etc.Limited works can be found on the vibration of the coupled-plate structure due to the increase...Coupled-plate structures are widely used in the practical engineering such as aeronautical,civil and naval engineering etc.Limited works can be found on the vibration of the coupled-plate structure due to the increased mathematical complexity compared with the single plate structure.In order to study analytically the vibration characteristics and power transmission of the coupled-plate structure,an analytical model consisting of three coupled plates elastically restrained along boundary edges and elastically coupled with arbitrary angle is considered,in which four groups of springs are distributed consistently along each edge of the model to simulate the transverse shearing forces,bending moments,in-plane longitudinal forces and in-plane shearing forces separately.With elastic coupling condition and general boundary condition of both flexural and in-plane vibrations taken into account by setting the stiffness of corresponding springs,the double Fourier series solution to the dynamic response of the structure was obtained by employing the Rayleigh-Ritz method.In order to validate the model,the natural frequency and velocity response of the model are firstly checked against results published in literatures and the ANSYS data,and good agreement was observed.Then,numerical simulation of the effects of several relevant parameters on the vibration characteristics and power transmission of the coupled structure were performed,including boundary conditions,coupling conditions,coupling angle,and location of the external forces.Vibration and energy transmission behaviors were analyzed numerically.The results show that the power transmission can be significantly influenced by the boundary restraints and the location of excitation.When the excitation is located at the central symmetry point of the model,the energy flow shows a symmetrical distribution.Once the location deviates from the central symmetry point,the power circumfluence occurs and the vortex energy field is formed at high frequency.展开更多
The paper proposes a new approach of predicting the bifurcation points of elastic-plasticbuckling of plates and shells,which is obtained from the natural combination of the Lyaponov’s dy-namic criterion on stability ...The paper proposes a new approach of predicting the bifurcation points of elastic-plasticbuckling of plates and shells,which is obtained from the natural combination of the Lyaponov’s dy-namic criterion on stability and the modified adaptive Dynamic Relaxation(maDR)method developedrecently by the authors.This new method can overcome the difficulties in the applications of the dy-namic criterion.Numerical results show that the theoretically predicted bifurcation points are in verygood agreement with the corresponding experimental ones.The paper also provides a new means forfurther research on the plastic buckling paradox of plates and shells.展开更多
In this paper, some deformation patterns defined by differential equations of the elastic system are introduced into the revised functional for the incompatible elements. And therefore the rational FEM, which is perfe...In this paper, some deformation patterns defined by differential equations of the elastic system are introduced into the revised functional for the incompatible elements. And therefore the rational FEM, which is perfect combination of the analytic methods and numeric methods, has been presented. This new approach satisfies not only the mechanical requirement of the elements but also the geometric requirement of the complex structures. What’ s more the quadrilateral element obtained accordingly for the elastic bending of thick plates demonstrates such advantages as high precision for computation and availability of accurate integration for stiffness matrices.展开更多
The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi_Laplace equations of the first kind as well as of the sec...The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi_Laplace equations of the first kind as well as of the second.展开更多
The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton's principle fo...The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton's principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.展开更多
Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-para...Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack's continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.展开更多
By using complex variable methods, the houndary value problem for biharmonic functions arisen from the theory of clamped elastic thin plate is shown to be equivalent to the first fundamental problem in plane elasticit...By using complex variable methods, the houndary value problem for biharmonic functions arisen from the theory of clamped elastic thin plate is shown to be equivalent to the first fundamental problem in plane elasticity which, as well-known,may be easily solved by reduction to a Fredholm integral equation. The case of circular plate is illustrated in detail,the solution of which is obtained in closed form.展开更多
In this paper an accurate solution for the thick rectangular plate with free edges laid onelastic foundation is presented.The superposition method of trigonometric series is used.The method can solve this kind of plat...In this paper an accurate solution for the thick rectangular plate with free edges laid onelastic foundation is presented.The superposition method of trigonometric series is used.The method can solve this kind of plates directly and simply.Its results completely satisfythe boundary conditions of the four free edges and nicely agree with the solutions by WangKe-lin and Huang Yi.展开更多
In this paper,applying the method of reciprocal theorem,we give the distributions ofthe amplitude of bending moments along clamped edges and the amplitude of deflectionsalong free edges of rectangular plates with two ...In this paper,applying the method of reciprocal theorem,we give the distributions ofthe amplitude of bending moments along clamped edges and the amplitude of deflectionsalong free edges of rectangular plates with two adjacent clamped edges under harmonicdistributed and concentrated loads.展开更多
Based on the generalized England-Spencer plate theory, the equilibrium of a transversely isotropic functionally graded plate containing an elastic inclusion is studied.The general solutions of the governing equations ...Based on the generalized England-Spencer plate theory, the equilibrium of a transversely isotropic functionally graded plate containing an elastic inclusion is studied.The general solutions of the governing equations are expressed by four analytic functionsα(ζ), β(ζ), φ(ζ), and ψ(ζ) when no transverse forces are acting on the surfaces of the plate. Axisymmetric problems of a functionally graded circular plate and an infinite functionally graded plate containing a circular hole subject to loads applied on the cylindrical boundaries of the plate are firstly investigated. On this basis, the three-dimensional(3D)elasticity solutions are then obtained for a functionally graded infinite plate containing an elastic circular inclusion. When the material is degenerated into the homogeneous one,the present elasticity solutions are exactly the same as the ones obtained based on the plane stress elasticity, thus validating the present analysis in a certain sense.展开更多
文摘Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with interpolation points mutual iterative between odd and even sequences in boundary region is provided, as well as the conformal mapping function which can be described by real number region between complicated region and unit dish region is carried out. Furthermore, in the in-plane state of constant stress, vibrating function is completed by unit dish region method for simple-supported elastic plates with concentrated substance of complicated vibrating region, and the coefficient of fundamental frequency of the plate is analyzed. Meanwhile, taking simple-supported elastic ellipse-plates as an example, the effects on fundamental frequency caused by eccentric ratio, the coefficient of constant in-plane stress, as well as the concentrated substance mass and positions are analyzed respectively.
文摘By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between complicated region and unite dish region was carried out. Aiming at calculating the vibrating fundamental frequency of special-shaped, elastic simple-supported rectangle-plates, in the in-plane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region. The coefficient of fundamental frequency was calculated. Whilst, taking simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio of the length to width of rectangle, as well as the coefficient of constant in-plane stress were analyzed respectively.
基金support of this work by the National Natural Science Foundation of China(No.51405096)the Fundamental Research Funds for the Central Universities(HEUCF210710).
文摘Based on Kirchhoff plate theory and the Rayleigh-Ritz method,the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method(ICCM).The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate.The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method.From the continuity condition of the vibration displacement function at the cutout,the transition matrix between the two coordinate systems is constructed,and the mass and stiffness matrices are completely obtained.As a result,the calculation is simplified and the computational efficiency of the solution is improved.In this paper,numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods,and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.
文摘We extend the differential quadrature element method (DQEM) to the buckling analysis of uniformly in-plane loaded functionally graded (FG) plates fully or partially resting on the Pasternak model of elastic support. Material properties of the FG plate are graded in the thickness direction and assumed to obey a power law distribution of the volume fraction of the constituents. To set up the global eigenvalue equation, the plate is divided into sub-domains or elements and the generalized differential quadrature procedure is applied to discretize the governing, boundary and compatibility equations. By assembling discrete equations at all nodal points, the weighting coefficient and force matrices are derived. To validate the accuracy of this method, the results are compared with those of the exact solution and the finite element method. At the end, the effects of different variables and local elastic support arrangements on the buckling load factor are investigated.
基金supported by National Natural Science Foundation of China (Grant No. 10802024)Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200802171009)Innovative Talents Fund of Harbin of China(Grant No.2009RFQXG211)
文摘Coupled-plate structures are widely used in the practical engineering such as aeronautical,civil and naval engineering etc.Limited works can be found on the vibration of the coupled-plate structure due to the increased mathematical complexity compared with the single plate structure.In order to study analytically the vibration characteristics and power transmission of the coupled-plate structure,an analytical model consisting of three coupled plates elastically restrained along boundary edges and elastically coupled with arbitrary angle is considered,in which four groups of springs are distributed consistently along each edge of the model to simulate the transverse shearing forces,bending moments,in-plane longitudinal forces and in-plane shearing forces separately.With elastic coupling condition and general boundary condition of both flexural and in-plane vibrations taken into account by setting the stiffness of corresponding springs,the double Fourier series solution to the dynamic response of the structure was obtained by employing the Rayleigh-Ritz method.In order to validate the model,the natural frequency and velocity response of the model are firstly checked against results published in literatures and the ANSYS data,and good agreement was observed.Then,numerical simulation of the effects of several relevant parameters on the vibration characteristics and power transmission of the coupled structure were performed,including boundary conditions,coupling conditions,coupling angle,and location of the external forces.Vibration and energy transmission behaviors were analyzed numerically.The results show that the power transmission can be significantly influenced by the boundary restraints and the location of excitation.When the excitation is located at the central symmetry point of the model,the energy flow shows a symmetrical distribution.Once the location deviates from the central symmetry point,the power circumfluence occurs and the vortex energy field is formed at high frequency.
文摘The paper proposes a new approach of predicting the bifurcation points of elastic-plasticbuckling of plates and shells,which is obtained from the natural combination of the Lyaponov’s dy-namic criterion on stability and the modified adaptive Dynamic Relaxation(maDR)method developedrecently by the authors.This new method can overcome the difficulties in the applications of the dy-namic criterion.Numerical results show that the theoretically predicted bifurcation points are in verygood agreement with the corresponding experimental ones.The paper also provides a new means forfurther research on the plastic buckling paradox of plates and shells.
文摘In this paper, some deformation patterns defined by differential equations of the elastic system are introduced into the revised functional for the incompatible elements. And therefore the rational FEM, which is perfect combination of the analytic methods and numeric methods, has been presented. This new approach satisfies not only the mechanical requirement of the elements but also the geometric requirement of the complex structures. What’ s more the quadrilateral element obtained accordingly for the elastic bending of thick plates demonstrates such advantages as high precision for computation and availability of accurate integration for stiffness matrices.
基金theResearchFoundationofEducationalCommitteeofYunnanProvince China
文摘The uniqueness for the solutions mentioned in the subject is proved by using the uniqueness of the solution for the internal boundary problem of Laplace and bi_Laplace equations of the first kind as well as of the second.
基金Project supported by the National Natural Science Foundation of China (Grant No.10872163)the Natural Science Foundation of Education Department of Shaanxi Province (Grant No.08JK394)
文摘The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton's principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.
基金国家自然科学基金，Technology Item of Ministry of Communications of China
文摘Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack's continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.
文摘By using complex variable methods, the houndary value problem for biharmonic functions arisen from the theory of clamped elastic thin plate is shown to be equivalent to the first fundamental problem in plane elasticity which, as well-known,may be easily solved by reduction to a Fredholm integral equation. The case of circular plate is illustrated in detail,the solution of which is obtained in closed form.
文摘In this paper an accurate solution for the thick rectangular plate with free edges laid onelastic foundation is presented.The superposition method of trigonometric series is used.The method can solve this kind of plates directly and simply.Its results completely satisfythe boundary conditions of the four free edges and nicely agree with the solutions by WangKe-lin and Huang Yi.
文摘In this paper,applying the method of reciprocal theorem,we give the distributions ofthe amplitude of bending moments along clamped edges and the amplitude of deflectionsalong free edges of rectangular plates with two adjacent clamped edges under harmonicdistributed and concentrated loads.
基金Project supported by the National Natural Science Foundation of China(Nos.11202188,11321202,and 11172263)
文摘Based on the generalized England-Spencer plate theory, the equilibrium of a transversely isotropic functionally graded plate containing an elastic inclusion is studied.The general solutions of the governing equations are expressed by four analytic functionsα(ζ), β(ζ), φ(ζ), and ψ(ζ) when no transverse forces are acting on the surfaces of the plate. Axisymmetric problems of a functionally graded circular plate and an infinite functionally graded plate containing a circular hole subject to loads applied on the cylindrical boundaries of the plate are firstly investigated. On this basis, the three-dimensional(3D)elasticity solutions are then obtained for a functionally graded infinite plate containing an elastic circular inclusion. When the material is degenerated into the homogeneous one,the present elasticity solutions are exactly the same as the ones obtained based on the plane stress elasticity, thus validating the present analysis in a certain sense.
