初始荷载效应对板的稳定性影响分析  

Analysis for the effect of initial loads on the buckling of plates

作　　者：刘德贵[1] 周世军[2] 王宁[1] 

机构地区：[1]西南科技大学土木工程与建筑学院,绵阳621010 [2]重庆大学土木工程学院,重庆400044

出　　处：《应用力学学报》2015年第6期895-900 1095,1095,共7页Chinese Journal of Applied Mechanics

基　　金：四川省教育厅项目(15ZB0122);西南科技大学博士基金项目(14zx7138)

摘　　要：运用变分原理,推导了考虑初始荷载效应情况下板的屈曲控制微分方程。以微分方程为基础,运用伽辽金法解得了简支矩形板考虑初始荷载效应的屈曲临界荷载系数近似解;同时,提出了考虑初始荷载效应情况下板的稳定有限元公式。对比验证了考虑初始荷载效应情况下,简支矩形板的屈曲临界荷载系数近似解和稳定有限元公式的正确性。并通过本文建立的有限元公式深入分析了考虑初始荷载效应情况下,初始荷载、板的厚度对板稳定性的影响,得到了如下结论:初始荷载效应提高了板的屈曲临界荷载;初始荷载越大,或板的厚度越薄,或边界约束越弱,初始荷载效应对板的屈曲临界荷载提高越明显。General buckling differential equations of plate considering initial load effect are formulated by means of the variational principle. Based on the differential equations, the approximate solutions of buckling critical load coefficient considering initial load effect for simply supported rectangular plate are derived by the Galerkin method. Meanwhile, the FEM for analyzing the buckling of plate is presented. The correctness of the coefficients of buckling critical load approximate solutions and the presented FEM are verified by comparing the results calculated by above two methods. Further analysis is conducted by the presented FEM to better insight into the effect of initial loads on buckling of plates, useful conclusions are obtained. The buckling critical loads are increased by the initial load effect. The bigger initial load is, or the smaller thickness of plates is, or weaker boundary condition is, the more apparent effect of the initial load on buckling of plates is.

关 键 词：初始荷载效应 板 屈曲临界荷载 近似解 有限元法 

分 类 号：TU311.2[建筑科学—结构工程]