Winkler地基上裂纹Timoshenko梁的弯曲解析解

将梁中裂纹等效为无质量线性扭转弹簧,研究了温克勒(Winkler)基础上具有任意开裂纹数目Timoshenko梁的弯曲变形．利用Delta广义函数和Heaviside函数以及Laplace变换,给出了Winkler基础上具有任意裂纹数目Timoshenko梁弯曲变形的解析通解．在此基础上,研究了Winkler基础上受均布荷载作用简支裂纹Timoshenko梁的弯曲变形,数值分析了裂纹数目和位置以及深度、梁剪切刚度和基础反力系数等对裂纹Timoshenko梁弯曲变形的影响．结果表明：在裂纹处,梁挠度存在尖点,转角存在跳跃;梁挠度随着裂纹深度和数目的增加而增加,但横截面弯矩和转角减小;随着基础反力系数的增加,梁挠度、弯矩和转角减小;随着剪切刚度的增加,梁挠度减少,弯矩和转角增大．     

CFRP布加固具有边缘裂纹板条的疲劳性能

将碳纤维增强复合材料(CFRP)布在板条两表面双面粘贴加固具有边缘穿透裂纹的板条,研究了加固板条在两端循环拉伸载荷作用下的断裂和疲劳性能.首先建立了CFRP布加固板条粘结层与CFRP布/板条的界面剪应力控制方程,并求得两端均布拉力作用下CFRP布加固具有边缘穿透裂纹的板条的界面剪应力解析解.其次,利用叠加原理推导了CFRP加固板条裂纹尖端的应力强度因子表达式,分别给出了其Paris和Elber模型疲劳寿命公式,通过与相关实验结果的比较,发现Elber模型的疲劳寿命公式与试验结果较吻合.最后的参数研究表明:CFRP布刚度对应力强度因子范围有显著的影响,且应力强度因子范围随CFRP布长度或粘贴层剪切模量的增加而减小,并趋于定值.同时,粘贴胶厚度对应力强度因子范围几乎没有影响.     

非线性粘弹性大挠度梁的动力学模型及其简化

本文建立了描述几何非线性均匀梁动力学行为的偏微分－－积分方程,梁的材料满足Ｌｅａｄｅｍａｎ非线性本构关系,对于两端简支的情形用Ｇａｌｅｒｋｉｎ方法进行了截断简化为常微分－－积分方程,然后引进附加变量的方法进一步简化为常微分方程组。     

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.     

THE GROWTH OF THE VOID IN A HYPERELASTIC RECTANOULAR PLATE UNDERA UNIAXIAL EXTENSION

1.IntroductionInrecenttenyears,thevoidformationandgrowthinhyperelasticmaterialhaveattractedmoreandmoreattentionandinterest.Theearliertestsfoundthatthenucleationofthemicro-voidwouldbepossibleduringthestretchingdeformationinmaterandrubbermaterials.However,t…     

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.     

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.     

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。     

轴向扩散下简支饱和多孔弹性梁的大挠度分析

基于多孔介质理论和弹性梁的大挠度理论,并考虑轴向变形,在孔隙流体仅沿轴向扩散的假设下,建立了微观不可压饱和多孔弹性梁大挠度弯曲变形的一维非线性数学模型.在此基础上,忽略饱和多孔弹性梁的轴向应变,并利用Galerkin截断法,研究了两端可渗透的简支饱和多孔弹性梁在突加横向均布载荷作用下的拟静态弯曲,给出了饱和多孔梁弯曲时挠度、弯矩和轴力以及孔隙流体压力等效力偶等沿轴线的分布曲线.揭示了大挠度非线性和小挠度线性模型的结果差异,指出大挠度非线性模型的结果小于相应小挠度线性模型的结果,并且这种差异随着载荷的增大而增大.计算表明:当无量纲载荷参数q>5时,应该采用大挠度非线性数学模型进行研究.     

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。