Stability and chaotic motion in columns of nonlinear viscoelastic material

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On The Reissner Theory of Bending of Flastic Plates

The Reissner equations of elastic plates are rederived on the bases of the incomplete generalizedvariational principle of Complementary energy.The Stress function to is naturally obtained from thevariational Calculation in the form of Lagrange multiplier.The stucture of solutions of the Reissnerequations is thus defined.On the bases of these discussions,a simplified theory has been put forward,in which the equations of equilibrium involving the shearing influence can be reduced into a fourthorder differential equation similar to those of the Classical theory of plates.     

极正交各向异性圆薄膜大挠度问题

本文主要用摄动法和积分方程的数值积分方法求解受预加张力的极正交各向异性圆薄膜在均布荷载作用下的轴对称大挠度问题,得到了荷载、薄膜力及挠度与中心挠度的关系,它们与材料系数的比K=E_■|E_r~(1/2)有关.当K→时,所得结果与各向同性圆薄膜的结果相吻合。     

环形板的屈曲状态

本文研究了内边界固定、外边界可移夹紧并受面内径向均匀压缩推力p作用的环形板的轴对称屈曲状态。首先论述了问题的合理提法,给出了未屈曲板的平凡解的解析公式;得到了在平凡解处线性化问题的特征方程,并对某些参数值给出了前两个特征值(即临界载荷)。然后,在一个适度的假设下,证明了所有的临界载荷都是分支点,并给出了临界载荷附近屈曲解的渐近公式。     

热超弹性薄板非对称拉伸的分岔和稳定性

本文应用超弹性材料的有限变形理论分析了在面内等双向拉伸死载荷作用下不可压热超弹性方形薄板发生非对称变形的分岔及其稳定性问题.给出了方板变形的分岔曲线和临界载荷,发现对受面内等双向拉伸载荷作用的均匀方板,当拉伸载荷值较小时,方板双向等伸长变形,发生对称的拉伸变形;但当此载荷值大于某一临界值时,从方板的对称拉伸变形中分岔出非对称的变形,方板在两个方向的变形不再相等.通过变形发生分岔前后的能量比较发现,分岔后的对称变形是不稳定的,而非对称变形是稳定的.同时,给出了板中的应力分布曲线,并由不同温度下变形的分岔曲线和应力分布曲线讨论了温度对方板变形和板中的应力分布的影响.     

理性力学关于塑性本构关系的研究概况

塑性行为是金属、岩土、聚合物、复合材料等众多物质的基本属性之一.自从十九世纪Tresca,Saintvenant 和Lévy 建立了第一个塑性经典理论以来,大批力学家和物理学家投入了这一领域的研究工作.到目前为止,经典塑性理论大致可分为以下几类: ...     

联合载荷作用下简支矩形板的屈曲和过屈曲

本文研究了简支正交各向异性矩形板在两对板受中面压力作用下的屈曲和过屈曲性态,得到了载荷的稳定性区域,证明了临界载荷最多为二重的。利用多参数摄动方法求得临界载荷附近板的过屈曲状态的渐近解,分析了在二重临界载荷附近,当载荷按比例变化时,板的可能的过屈曲状态及其与参数的依赖关系。     

环形板屈曲与过屈曲的横向剪切效应

本文应用分支理论和打靶法研究了环形板屈曲与过屈曲的横向剪切效应     

Dynamical formation of cavity in transversely isotropic hyper-elastic spheres

The cavity formation in a radial transversely isotropic hyper-elastic sphere of an incompressible Ogden material, subjected to a suddenly applied uniform radial tensile boundary dead-load, is studied fllowing the theory of finite deformation dynamics. A cavity forms at the center of the sphere when the tensile load is greater than its critical value. It is proved that the evolution of the cavity radius with time follows that of nonlinear periodic oscillations. The project supported by the National Natural Science Foundation of China (10272069) and Shanghai Key Subject Program     

QUASI-STATIC ANALYSIS FOR VISCOELASTIC TIMOSHENKO BEAMS WITH DAMAGE

Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams, the equations governing quasi-static and dynamical behavior of Timoshenko beams with damage were first derived. The quasi-static behavior of the viscoelastic Timoshenko beam under step loading was analyzed and the analytical solution was obtained in the Laplace transformation domain. The deflection and damage curves at different time were obtained by using the numerical inverse transform and the influences of material parameters on the quasi-static behavior of the beam were investigated in detail.