QUALITATIVE ANALYSIS OF DYNAMICAL BEHAVIOR FOR AN IMPERFECT INCOMPRESSIBLE NEO-HOOKEAN SPHERICAL SHELL

IntroductionIn applications, it is commonly considered that the phenomena of cavity formation,growth and run-through of adjacent cavities occur in materials as precursors to failure. Thesephenomena are mainly due to instability of materials. On the other …     

环形板的非轴对称屈曲分析

本文利用打靶法研究了内外边界固支且在外边界受均匀径向压力作用下的极正交各向异性环形板的非轴对称屈曲和过屈曲,计算了临界载荷,讨论了分支解的存在性,得到了分支解的渐近表达式,分析了环形板的屈曲性态。     

DYNAMICAL FORMATION OF CAVITY FOR COMPOSED THERMAL HYPERELASTIC SPHERES IN NONUNIFORM TEMPERATURE FIELDS

Dynamical formation and growth of cavity in a sphere composed of two incompressible thermal-hyperelastic Gent-Thomas materials were discussed under the case of a non-uniform temperature field and the surface dead loading. The mathematical model was first presented based on the dynamical theory of finite deformations. An exact differential relation between the void radius and surface load was obtained by using the variable transformation method. By numerical computation, critical loads and cavitation growth curves were obtained for different temperatures. The influence of the temperature and material parameters of the composed sphere on the void formation and growth was considered and compared with those for static analysis. The results show that the cavity occurs suddenly with a finite radius and its evolvement with time displays a non-linear periodic vibration and that the critical load decreases with the increase of temperature and also the dynamical critical load is lower than the static critical load under the same conditions.     

开孔粘弹性薄板的非线性数学模型

应力函数的多值性和位移单值性要求，是开孔薄板大挠度问题中必须注意的两个方面。本文利用线粘性力学中的Ｂｏｌｔｚｍａｎｎ蠕变律，把开孔弹性薄板大挠度问题的一般数学理论推广到开孔弹性薄板。在考察应力函数的多值性和位移单值性条件的基础上，提出了开孔粘弹性薄板的控制方程和初、边值条件，系统地建立了开也粘弹性薄板非线性分析的三类初一边值问题。     

INSTABILITY OF TOROIDAL MEMBRANE WITH LARGE TENSILE DEFORMATION

In this paper,the problem of large axisymmetric deformation of hyperelasticmembrane is reformulated on the basis of the general theory of finite elasticity.From thefundamental equations derived here,the tensile instability of toroidal rubberlike membranewith Mooney-Rivlin’s model constitutive relation is solved by using the shooting method.The upper and lower limit loads and the response curve of the displacement to the load aregiven.     

A METHOD OF DETERMINING BUCKLED STATES OF THIN PLATES AT A DOUBLE EIGENVALUE

A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method. By using the present method, the buckled states of rectangular plates at a double eigenvalue are numerically analyzed. The results show that this method is effective.     

热环境中粘贴压电层功能梯度材料梁的自由振动

研究了上下表面粘贴压电层的功能梯度材料Euler-Bernoulli梁在升温及电场作用下的屈曲和自由振动行为.在精确考虑轴线伸长基础上,建立了压电功能梯度材料层合梁在热-电-机载荷作用下的几何非线性动力学控制方程.其中,假设功能梯度材料性质沿厚度方向按照幂函数连续变化,上下压电层为各向同性均匀材料.在小振幅和谐振动假设下,上述非线性偏微分方程组被转化为两套相互耦合的常微分方程组,即过屈曲问题的控制方程和过屈曲构形附近的线性振动控制方程.采用打靶法数值求解上述两个耦合的常微分方程边值问题,获得了在均匀电场和横向非均匀升温场作用下两端固定压电.功能梯度材料层合梁在屈曲前和过屈曲构型附近的自由振动响应.绘出了梁的过屈曲平衡路径以及前3阶固有频率随热、电载荷及材料梯度参数变化的特性曲线.结果表明,梁的前3阶频率在屈曲前随着温度升高而减小,在进入过屈曲后它们却随着温度升高而增加.通过施加电压在压电层产生拉应力可有效地提高粱的热屈曲临界载荷,从而提高其固有频率.     

THE BENDING OF A THICK RECTANGULAR PLATE WITH THREE CLAMPED EDGES AND ONE FREE EDGE

The exact solution of the bending of a thick rectangular plate with three clamped edgesand one free edge under a uniform transverse load is obtained by means of the concept ofgeneralized simply-supported boundary in Reissner’s theory of thick plates.The effect ofthe thickness h of a plate on the bending is studied and the applicable range of Kirchhoffstheory for bending of thin plates is considered.     

Dynamical behavior of nonlinear viscoelastic beams

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非线性粘弹性平面问题的数学模型及其失记效应

本文以位移为基本未知量,利用非线性粘弹性力学中的Leaderman本构关系和线性几何假设,建立了非线性粘弹性平面问题的数学模型;在粘弹性泊松比为常数的情况下,利用Titchmarsh定理和Laplace变换法证明了非线性粘弹性平面问题与非线性弹性平面问题之间存在着某些对应关系,对应关系为粘弹性问题的求解提供了一种新的思路,利用这些关系可直接从相应弹性问题获得粘弹性平面问题的部分响应,与传统的时域有限差分法相比,计算时间明显缩短,另外,对应关系也揭示了粘弹性结构的失记效应,即结构的部分响应仅与外部输入的现时值有关,而与其历史无关。