粘弹性板大挠度蠕变屈曲的数值计算  

NUMERICAL CALCULATION OF CREEP BUCKLING FOR VISCOELASTIC PLATES CONSIDERING GEOMETRIC NONLINEARITY

作　　者：孙远翔[1] 徐琳[1] 

机构地区：[1]北京理工大学爆炸科学与技术国家重点实验室,北京100081

出　　处：《固体力学学报》2013年第S1期176-186,共11页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金资助项目(10572024)

摘　　要：研究了受轴向压力粘弹性板的蠕变屈曲问题.在建立控制方程时,引入von Karman应变-位移关系并考虑了初始挠度,采用标准线性固体模型描述粘弹性特性.所得控制方程是非线性积分方程.为了得到更精确的解,在计算时,挠度函数表达式取四项.在求解非线性积分方程时,利用梯形公式计算记忆积分式,将其转化为非线性代数方程组进行求解,得到了四个挠度系数与时间的关系曲线.通过对比四个挠度系数在不同载荷下随时间的变化曲线可知,板的挠度随时间的改变主要由挠度表达式中的某一项控制,即该项随时间增长的速度比其它项更快,当施加载荷较大时,此趋势更加明显.本文定量地分析了这个趋势随载荷的变化,分析结果对工程实际具有指导意义.The creep buckling analysis of viscoelastic rectangular plates under axial compression is analysised.A standard linear viscoelastic solid model is used and the von Karman nonlinear geometry equations are introduced in the governing equations.The governing equations are nonlinear integral equations.In order to obtain an accurate solution,the deflection function is expressed as four terms during the calculation.In order to change the nonlinear integral equations to a nonlinear algebraic equation which can be solved by using a standard subroutine,the trapezium method is used to calculate the hereditary integral expression.Four deflection coefficient-time curves are obtained.By comparing the four deflection coefficients that are under different loads,an important conclusion is gotten,deflection of the plate is controlled by one term of the deflection expression,i.e.the increase along with time of the term runs faster than any other terms.When the load is small,the tendency is not distinct.When the load is large,the tendency is more obvious.The conclusion is useful for engineering.

关 键 词：粘弹性板 蠕变屈曲 几何非线性 挠度函数 

分 类 号：O344.6[理学—固体力学]