Based on the assumption of finite deformation, the Hamilton variational principle is extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation. The corresponding three-...Based on the assumption of finite deformation, the Hamilton variational principle is extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation. The corresponding three-dimensional （3D） mathematical model for analyzing the nonlinear mechanical behaviors of structures is established, in which the effects of the rotation inertia and the nonlinearity of material and geometry are considered. As an application, the nonlinear stability and the post-buckling for a linear elastic beam with the equal cross-section located on an elastic foundation are analyzed. One end of the beam is fully fixed, and the other end is partially fixed and subjected to an axial force. A new numerical technique is proposed to calculate the trivial solution, bifurcation points, and bifurcation solutions by the shooting method and the Newton- Raphson iterative method. The first and second bifurcation points and the corresponding bifurcation solutions are calculated successfully. The effects of the foundation resistances and the inertia moments on the bifurcation points are considered.展开更多
The finite element equations considering the geometrical nonlinearity of piezoelectric smart structures are derived based on the total Lagrange method under the assumption of weak coupling between electricity and mech...The finite element equations considering the geometrical nonlinearity of piezoelectric smart structures are derived based on the total Lagrange method under the assumption of weak coupling between electricity and mechanics. Buckling and post-buckling of piezoelectric-plate with various boundary conditions are investigated. The calculated results show that piezoelectric effects and external voltage can hardly affect the buckling and post-bucking characteristics of piezoelectric-plate under uniaxial pressure while the buckling caused by displacement in-plane has much to do with the electric field.展开更多
This paper is concerned with the nonlinear vibration problems of circular plates with variable thickness.The nonlinear equations of plates with variable thickness are extended to the dynamic case.The resulting equatio...This paper is concerned with the nonlinear vibration problems of circular plates with variable thickness.The nonlinear equations of plates with variable thickness are extended to the dynamic case.The resulting equations can be solved by using an iterative method,a Galerkin's approach and a perturbation method.Detailed solutions and numerical results are given for two kinds of boundary conditions,the clamped edge and the supported edge.The results show that the solutions for the case of the plates with uniform thickness can be included in the solution herin as a special case.The effect of various thickness parameters is investigated in detail.Also,a Runge Kutta method is used to solve the free and forced vibrations of plates with variable thickness,and the results are obtained firstly.It has shown that the adoption of variable thickness plate would be useful in engineering design.展开更多
A theoretical analysis is presented to predict the nonlinear thermo-structural response of metallicsandwich panels with truss cores under through-thickness gradient temperature field, which is acommon service condit...A theoretical analysis is presented to predict the nonlinear thermo-structural response of metallicsandwich panels with truss cores under through-thickness gradient temperature field, which is acommon service condition for metallic thermal protection system （TPS）. The in-planetemperature distribution is assumed to be uniform, and through-thickness temperature field isdetermined by heat conduction. Two typical conditions are analyzed： nonlinear thermal bendingin fixed inside surface temperature, and thermal post-buckling in fixed temperature differencebetween two surfaces. Temperature-dependent mechanical properties are considered, andgradient shear stiffness and bending stiffness due to non-uniform temperature is included. Resultsindicate that the temperature-dependent material properties obviously affect bending resistance;however, the effect is negligible on post-buckling behavior. Influences of geometric parameters onthe thermo-structural behavior of the sandwich panel according to the present theoretical modelare discussed.展开更多
基金Project supported by the National Science Foundation for Distinguished Young Scholars of China(No. 11002084)the Shanghai Pujiang Program (No. 07pj14073)the Scientific Research Projectof Shanghai Normal University (No. SK201032)
文摘Based on the assumption of finite deformation, the Hamilton variational principle is extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation. The corresponding three-dimensional （3D） mathematical model for analyzing the nonlinear mechanical behaviors of structures is established, in which the effects of the rotation inertia and the nonlinearity of material and geometry are considered. As an application, the nonlinear stability and the post-buckling for a linear elastic beam with the equal cross-section located on an elastic foundation are analyzed. One end of the beam is fully fixed, and the other end is partially fixed and subjected to an axial force. A new numerical technique is proposed to calculate the trivial solution, bifurcation points, and bifurcation solutions by the shooting method and the Newton- Raphson iterative method. The first and second bifurcation points and the corresponding bifurcation solutions are calculated successfully. The effects of the foundation resistances and the inertia moments on the bifurcation points are considered.
基金the National Natural Science Foundation of China(No.59635140)
文摘The finite element equations considering the geometrical nonlinearity of piezoelectric smart structures are derived based on the total Lagrange method under the assumption of weak coupling between electricity and mechanics. Buckling and post-buckling of piezoelectric-plate with various boundary conditions are investigated. The calculated results show that piezoelectric effects and external voltage can hardly affect the buckling and post-bucking characteristics of piezoelectric-plate under uniaxial pressure while the buckling caused by displacement in-plane has much to do with the electric field.
文摘This paper is concerned with the nonlinear vibration problems of circular plates with variable thickness.The nonlinear equations of plates with variable thickness are extended to the dynamic case.The resulting equations can be solved by using an iterative method,a Galerkin's approach and a perturbation method.Detailed solutions and numerical results are given for two kinds of boundary conditions,the clamped edge and the supported edge.The results show that the solutions for the case of the plates with uniform thickness can be included in the solution herin as a special case.The effect of various thickness parameters is investigated in detail.Also,a Runge Kutta method is used to solve the free and forced vibrations of plates with variable thickness,and the results are obtained firstly.It has shown that the adoption of variable thickness plate would be useful in engineering design.
基金The financial support from the National Natural Science Foundation of China (91016025, 11472276, 11602271, and 11332011)the Defense Industrial Technology Development Program of China (JCKY2016130B009)
文摘A theoretical analysis is presented to predict the nonlinear thermo-structural response of metallicsandwich panels with truss cores under through-thickness gradient temperature field, which is acommon service condition for metallic thermal protection system （TPS）. The in-planetemperature distribution is assumed to be uniform, and through-thickness temperature field isdetermined by heat conduction. Two typical conditions are analyzed： nonlinear thermal bendingin fixed inside surface temperature, and thermal post-buckling in fixed temperature differencebetween two surfaces. Temperature-dependent mechanical properties are considered, andgradient shear stiffness and bending stiffness due to non-uniform temperature is included. Resultsindicate that the temperature-dependent material properties obviously affect bending resistance;however, the effect is negligible on post-buckling behavior. Influences of geometric parameters onthe thermo-structural behavior of the sandwich panel according to the present theoretical modelare discussed.
