含边裂纹矩形截面偏心柱最大挠度的一个解析解

本文采用Rayleigh-Ritz能量变分法，计算分析了两端铰支含边裂纹矩形截面偏心柱的弹性挠度。首先选取三角函数级数作为柱挠度的试函数；然后分别计算弹性体系弯曲变形能和裂纹引起的变形能增量以及外边势能，进而得到体系的总势能；最终根据势能驻值条件确定挠度系数，从而得到一个在裂纹截面满足变形协调条件的挠度方程级数解。在假设裂纹位于柱中间截面的基础上，进一步分析推出了最大挠度的解析公式。文中还就本文解与相应的Okamura解进行了对比分析，指出了Okamura解存在的缺点和适用范围。

An Analytical Solution of Maximum Lateral Flexure for Side-cracked Eccentric Rectangular Column

The lateral flexure of side-cracked eccentric rectangular column was analyzed and the effects of crack on lateral flexure were studied in this paper. For a cracked column with both ends pinned, the elastic lateral flexure equation was derived by mean of Rayleigh-Ritz energy method. The flexure function was assumed as a trigonometric series. The change in elastic energy caused by introducing the crack was expressed under the fixed grip condition and the flexure coefficient Cm was determined by use of minimum potential energy principle. Consequently, a series solution of elastic flexure equation, that fulfils the compatibility of deformation, was obtained analytically. According above series solution, an analytical formulation of the maximum lateral flexure was derived and an improved computing method and its program were suggested. In comparison with Okamura's solution, the advantages of the solution in this paper is discussed summarily and the range of crack-load states of using Okamura's solution is given numerically under the 5% relative error conditions.