The thermal conduction behavior of the three-dimensional axisymmetric functionally graded circular plate was studied under thermal loads on its top and bottom surfaces. Material properties were taken to be arbitrary d...The thermal conduction behavior of the three-dimensional axisymmetric functionally graded circular plate was studied under thermal loads on its top and bottom surfaces. Material properties were taken to be arbitrary distribution functions of the thickness. A temperature function that satisfies thermal boundary conditions at the edges and the variable separation method were used to reduce equation governing the steady state heat conduction to an ordinary differential equation (ODE) in the thickness coordinate which was solved analytically. Next, resulting variable coefficients ODE due to arbitrary distribution of material properties along thickness coordinate was also solved by the Peano-Baker series. Some numerical examples were given to demonstrate the accuracy, efficiency of the present model, mad to investigate the influence of different distributions of material properties on the temperature field. The numerical results confirm that the influence of different material distributions, gradient indices and thickness of plate to temperature field in plate can not be ignored.展开更多
Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using ...Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.展开更多
The problem of a transversely isotropic functionally graded material (FGM) plate welded with a circular inclusion is considered. The analysis starts with the general- ized England-Spencer plate theory for transverse...The problem of a transversely isotropic functionally graded material (FGM) plate welded with a circular inclusion is considered. The analysis starts with the general- ized England-Spencer plate theory for transversely isotropic FGM plates, which expresses a three-dimensional (3D) general solution in terms of four analytic functions. Several analytical solutions are then obtained for an infinite FGM plate welded with a circular inclusion and subjected to the loads at infinity. Three different cases are considered, i.e., a rigid circular inclusion fixed in the space, a rigid circular inclusion rotating about the x-, y-, and z-axes, and an elastic circular inclusion with different material constants from the plate itself. The static responses of the plate and/or the inclusion are investigated through numerical examples.展开更多
Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied...Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied on its top surface. The material prop- erties can continuously and arbitrarily vary along the thickness direction. By virtue of the generalized England's method, the problem can be solved by determining the expres- sions of four analytic functions. Expanding the transverse loarl in Fourier series along the circumferential direction eases the theoretical construction of the four analytic functions for a series of important biharmonic loads. Certain boundary conditions are then used to determine the unknown constants that are involved in the four constructed analytic functions. Numerical examples are presented to validate the proposed method. Then, we scrutinize the asymmetric bending behavior of a transversely isotropic functionally graded solid circular plate with different geometric and material parameters.展开更多
Büeckner Rice weight function method was used to analyse mixed mode fracture of center cracked circular disk subjected to uniaxial compression. Based on Wu Carlsson procedure semi analytical modes Ⅰ and Ⅱ weigh...Büeckner Rice weight function method was used to analyse mixed mode fracture of center cracked circular disk subjected to uniaxial compression. Based on Wu Carlsson procedure semi analytical modes Ⅰ and Ⅱ weight functions were derived from corresponding reference displacement fields and stress intensity factors calculated by finite element method. Normalized mode Ⅰ and mode Ⅱ stress intensity factors, f Ⅰ, f Ⅱ , were derived from the obtained semi analytical weight functions. The results were then fitted into polynomials, the precision is within 0.5%. It is interesting to note that when the inclined angle θ of a crack is less than 15°, the f Ⅰvalues are positive. when θ =15°, the f Ⅰ values are positive for the crack length a varying from 0.1 to 0.7, but when a =0.8, the f Ⅰ takes the negative value -0.51. When θ >15°, all the f Ⅰ values become negative, which denotes that the compression shear mode is achieved at crack tips. These results are very useful in the investigation of mixed mode fracture of brittle materials.展开更多
This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement res...This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.展开更多
Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So ...Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So the Hamiltonian system can also be applied to plate bending problems by introducing bending moment functions. The new method presents the analytical solution for the circular sector plate. The results show that the new method is effective.展开更多
A system of Mathieu–Hill equations have been obtained for the dynamic stability analysis of electrical graded piezoelectric circular cylindrical shells subjected to the combined loading of periodic axial compressio...A system of Mathieu–Hill equations have been obtained for the dynamic stability analysis of electrical graded piezoelectric circular cylindrical shells subjected to the combined loading of periodic axial compression and radial pressure and electric ?eld. Bolotin’s method is then employed to obtain the dynamic instability regions. It is revealed that the piezoelectric e?ect, the piezoelectric graded e?ect and the electric ?eld only have minor e?ect on the unstable region. In contrast, the geometric parameters, the rigidity of constituent materials and the external loading play a dominant role in determining the unstable region.展开更多
This paper investigates the static behavior of a functionally graded circular plate made of magneto-electro-elastic(MEE) materials under tension and bending.The analysis is directly based on the three-dimensional go...This paper investigates the static behavior of a functionally graded circular plate made of magneto-electro-elastic(MEE) materials under tension and bending.The analysis is directly based on the three-dimensional governing equations for magnetoelectro-elasticity, with the boundary conditions on the upper and lower surfaces satisfied exactly and those on the cylindrical surface satisfied approximately(in the Saint Venant sense). The analytical solutions, derived with a direct displacement method, are valid for any functionally graded material(FGM) with its properties varying independently in a continuous manner along the thickness direction. For homogeneous materials, these solutions are degenerated to the ones available in the literature. Interesting relations are also found between the solutions for a functionally graded magneto-electro-elastic(FGMEE) circular plate and those for an FGMEE rectangular beam, and even those for a functionally graded elastic beam when only the elastic displacements are considered. The beam solutions are also derived using a direct displacement method. Numerical examples are presented to verify the present analytical solutions, show the effects of material heterogeneity and multi-field coupling, and indicate the correspondence between the plate solutions and beam solutions.展开更多
In this paper the complete double-series in the closed region expressing the double-variable functions and their partial derivatives are derived by the H-transforniution and Stockes transformation. Using the double-se...In this paper the complete double-series in the closed region expressing the double-variable functions and their partial derivatives are derived by the H-transforniution and Stockes transformation. Using the double-series, a series solution for the axisyinmetric boundary value problem of the elastic circular cylinder with finite length is presented.In a numerical example, the cylinder subjected to the axisymmetric traellens with various loaded regions is investigated and the distributions of the displacement sand stresses are obtained.It is possible to solve the axisymmetric boundary value problems in the eylinderical coordinates for other scientific fields by use of the method presented in this paper.展开更多
基金Project(11102136)supported by the National Natural Science Foundation of ChinaProject(2012ZDK04)supported by the Open Project of Guangxi Key Laboratory of Disaster Prevention and Structural Safety,China
文摘The thermal conduction behavior of the three-dimensional axisymmetric functionally graded circular plate was studied under thermal loads on its top and bottom surfaces. Material properties were taken to be arbitrary distribution functions of the thickness. A temperature function that satisfies thermal boundary conditions at the edges and the variable separation method were used to reduce equation governing the steady state heat conduction to an ordinary differential equation (ODE) in the thickness coordinate which was solved analytically. Next, resulting variable coefficients ODE due to arbitrary distribution of material properties along thickness coordinate was also solved by the Peano-Baker series. Some numerical examples were given to demonstrate the accuracy, efficiency of the present model, mad to investigate the influence of different distributions of material properties on the temperature field. The numerical results confirm that the influence of different material distributions, gradient indices and thickness of plate to temperature field in plate can not be ignored.
基金Project supported by the National Natural Science Foundation of China (No.10432030).
文摘Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.
基金supported by the National Natural Science Foundation of China(Nos.11202188,11321202,and 11172263)the Program for Innovative Research Team of Zhejiang Sci-Tech University
文摘The problem of a transversely isotropic functionally graded material (FGM) plate welded with a circular inclusion is considered. The analysis starts with the general- ized England-Spencer plate theory for transversely isotropic FGM plates, which expresses a three-dimensional (3D) general solution in terms of four analytic functions. Several analytical solutions are then obtained for an infinite FGM plate welded with a circular inclusion and subjected to the loads at infinity. Three different cases are considered, i.e., a rigid circular inclusion fixed in the space, a rigid circular inclusion rotating about the x-, y-, and z-axes, and an elastic circular inclusion with different material constants from the plate itself. The static responses of the plate and/or the inclusion are investigated through numerical examples.
基金Project supported by the National Natural Science Foundation of China(No.11621062)the Natural Science Foundation of Zhejiang Province(No.LY18A020009)+1 种基金the Science and Technology Project of Ministry of Housing and Urban and Rural Development(No.2016-K5-052)the Science Foundation of Zhejiang Sci-Tech University(No.16052188-Y)
文摘Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied on its top surface. The material prop- erties can continuously and arbitrarily vary along the thickness direction. By virtue of the generalized England's method, the problem can be solved by determining the expres- sions of four analytic functions. Expanding the transverse loarl in Fourier series along the circumferential direction eases the theoretical construction of the four analytic functions for a series of important biharmonic loads. Certain boundary conditions are then used to determine the unknown constants that are involved in the four constructed analytic functions. Numerical examples are presented to validate the proposed method. Then, we scrutinize the asymmetric bending behavior of a transversely isotropic functionally graded solid circular plate with different geometric and material parameters.
文摘Büeckner Rice weight function method was used to analyse mixed mode fracture of center cracked circular disk subjected to uniaxial compression. Based on Wu Carlsson procedure semi analytical modes Ⅰ and Ⅱ weight functions were derived from corresponding reference displacement fields and stress intensity factors calculated by finite element method. Normalized mode Ⅰ and mode Ⅱ stress intensity factors, f Ⅰ, f Ⅱ , were derived from the obtained semi analytical weight functions. The results were then fitted into polynomials, the precision is within 0.5%. It is interesting to note that when the inclined angle θ of a crack is less than 15°, the f Ⅰvalues are positive. when θ =15°, the f Ⅰ values are positive for the crack length a varying from 0.1 to 0.7, but when a =0.8, the f Ⅰ takes the negative value -0.51. When θ >15°, all the f Ⅰ values become negative, which denotes that the compression shear mode is achieved at crack tips. These results are very useful in the investigation of mixed mode fracture of brittle materials.
基金supported by National Natural Science Foundation of China (No. 50978183)Tianjin Natural Science Foundation (No. 07JCZDJC10100)
文摘This paper presents a closed-form solution for diffraction of plane SH waves by a semi-circular cavity in half-space by using wave function expansion method. Accuracy of the solution is checked by the displacement residual and stress residual along the boundaries. Numerical results show that there are notable differences for response amplitudes between a semi-circular cavity and a whole-circular cavity in a half-space.
基金National Natural Science Foundation(No.19732020)the Doctoral Research Foundation of China
文摘Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So the Hamiltonian system can also be applied to plate bending problems by introducing bending moment functions. The new method presents the analytical solution for the circular sector plate. The results show that the new method is effective.
基金Project supported by the the Natural Science Foundation of China (Nos. 10132010 and 50135030).
文摘A system of Mathieu–Hill equations have been obtained for the dynamic stability analysis of electrical graded piezoelectric circular cylindrical shells subjected to the combined loading of periodic axial compression and radial pressure and electric ?eld. Bolotin’s method is then employed to obtain the dynamic instability regions. It is revealed that the piezoelectric e?ect, the piezoelectric graded e?ect and the electric ?eld only have minor e?ect on the unstable region. In contrast, the geometric parameters, the rigidity of constituent materials and the external loading play a dominant role in determining the unstable region.
基金Project supported by the National Natural Science Foundation of China(Nos.11321202 and11272281)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20130101110120)+2 种基金the Program for New Century Excellent Talents in University of Ministry of Education of China(No.NCET-13-0973)the Program for Sichuan Provincial Youth Science and Technology Innovation Team(No.2013-TD-0004)the Scientific Research Foundation for Returned Scholars(Ministry of Education of China)
文摘This paper investigates the static behavior of a functionally graded circular plate made of magneto-electro-elastic(MEE) materials under tension and bending.The analysis is directly based on the three-dimensional governing equations for magnetoelectro-elasticity, with the boundary conditions on the upper and lower surfaces satisfied exactly and those on the cylindrical surface satisfied approximately(in the Saint Venant sense). The analytical solutions, derived with a direct displacement method, are valid for any functionally graded material(FGM) with its properties varying independently in a continuous manner along the thickness direction. For homogeneous materials, these solutions are degenerated to the ones available in the literature. Interesting relations are also found between the solutions for a functionally graded magneto-electro-elastic(FGMEE) circular plate and those for an FGMEE rectangular beam, and even those for a functionally graded elastic beam when only the elastic displacements are considered. The beam solutions are also derived using a direct displacement method. Numerical examples are presented to verify the present analytical solutions, show the effects of material heterogeneity and multi-field coupling, and indicate the correspondence between the plate solutions and beam solutions.
文摘In this paper the complete double-series in the closed region expressing the double-variable functions and their partial derivatives are derived by the H-transforniution and Stockes transformation. Using the double-series, a series solution for the axisyinmetric boundary value problem of the elastic circular cylinder with finite length is presented.In a numerical example, the cylinder subjected to the axisymmetric traellens with various loaded regions is investigated and the distributions of the displacement sand stresses are obtained.It is possible to solve the axisymmetric boundary value problems in the eylinderical coordinates for other scientific fields by use of the method presented in this paper.