用Rayleigh-Ritz法求含裂纹偏心柱的弹性挠度  

LATERAL FLEXURE ANALYSIS OF CRACKED ECCENTRIC COLUMN WITH RAYLEIGH-ROTZ ENERGY METHOD

作　　者：周利[1] 

机构地区：[1]五邑大学土木工程系,广东江门529020

出　　处：《工程力学》2000年第4期109-116,共8页Engineering Mechanics

摘　　要：本文采用Ｒａｙｌｅｉｇｈ－Ｒｉｔｚ能量变分法，计算分析了两端铰支含裂纹偏心受压柱的弹性挠度，其中重点研究了裂纹对最大挠度的影响。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的弯曲变形能和裂纹引起的变形能增量及外力势能，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级数解。文中还以含Ⅰ型裂纹箱形截面偏心柱为例，具体地应用上述解分析了裂纹对柱最大挠度的影响。数值结果表明，用上述级数解的首项进行工程近似计算具有良好的精度。The lateral flexure of cracked eccentrically compressed column is analyzed and the effects of crack on lateral flexure are studied in this paper. For a cracked column with both ends pinned. the elastic lateral flexure equation is derived by means of Rayleigh-Ritz energy method. The flexure function is assumed as a trigonometric series. The change in elastic energy caused by. introducing the crack is expressed under the fixed grip condition and the flexure coefficient C is determined by use of minimum potential energy principle. Consequently, a series solution of elastic flexure, that satisfies the compatibility of deformation, is obtained analytically. As an example, a box column that contains a through-wall mode I crack situated on the middle across section is studied to verify the solution In addition the influences of crack size on maximum lateral flexure for various loads or eccentricity are investigated The numerical results show that the first term of the series can be used in engineering with satisfactory accuracy.

关 键 词：裂纹 偏心柱 弹性挠度 Rayleigh-Ritz变分法 

分 类 号：TU323.1[建筑科学—结构工程] TU311.2