Determination of Non-Linear Buckling Load for Simple Supported Beam with Bounded Initial Imperfection
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摘要: 给出了初缺陷简支梁非线性屈曲载荷的一种计算方法,这种方法避免了求解常微分方程组初值问题,节约了计算工作量.并将描述初缺陷的傅里叶系数视为有界随机变量,提出了计算屈曲载荷界限的区间方法.当初缺陷统计数据较充分时,用概率统计法计算了一定可靠度下屈曲载荷的界限.最后,对两种方法的结果进行了比较,定性地给出了各自的适用范围.Abstract: A method to obtain non-linear buckling loads of simple supported beam with initial imperfection is presented,Which avoids differential equation sets initial value problems resulting from another definition of buckling load,and the proposed method save computational cost. Fourier series to describe initial imperfection is viewed bounded variables followed a certain probability distribution,the range of buckling load under a certain reliability is obtained via statistical method,and a non-stochastic interval method to determine the range of buckling load is presented to describe a situation when only limited information is available on initial imperfection. Finally,the results from both approaches are critically contrasted,the scope of application is given qualitatively for each approach.
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Key words:
- uncertain systems /
- interval mathematics /
- non-linear structural analysis /
- buckling
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[1] Ben H Y,Elishakoff I. Convex models of uncertainty in applied mechanics[M]. Amsterdam:Elsevier Science Publishers,1990. 231~234． [2]Lindberg H E .Dynamic response and buckling failure measured for structures with bounded and random imperfections[J]. J Applied Mechanics,1991,58:1092~1095． [3]Elishakoff I. Probabilistic methods in the theory of structures[M].Oxford:A Wiley-interscience Publication, 1986. 326~327． [4]Rao S S. Analysis of uncertain structural systems using interval analysis[J]. AIAA J,1997,35:727~734． [5]Hansen J S, Roorda J .On a probabilistic stability theory for imperfection sensitive structures[J]. J Solids Structures,1974,10(6):341~359． -
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