两种矩形板考虑初始恒载效应的位移伽辽金近似解  

Galerkin Approximate Solutions of Displacement Including the Effect of Dead Loads for Two Kinds of Rectangular Plates

作　　者：刘德贵[1] 周世军[1] 

机构地区：[1]重庆大学土木工程学院,重庆400045

出　　处：《土木建筑与环境工程》2013年第6期58-66,130,共10页Journal of Civil,Architectural & Environment Engineering

摘　　要：基于板考虑初始恒载效应的应变能表达,运用变分原理导出了静力平衡控制微分方程。运用伽辽金法求解得到了四边固支、简支矩形板考虑初始恒载效应的近似活载(或后期荷载)位移表达式,并运用有限元法验证了公式的正确性。各近似位移表达式简单明了,清楚地反映了前期恒载和各因素对活载位移的影响,更为直观地说明了板的恒载效应这一概念。计算分析表明:初始恒载的存在增加了板的弯曲刚度,减小了活载位移;板的恒载效应主要受恒载大小、跨厚比和边界条件等因素的影响;对于较薄或弯曲刚度较小的板,在计算分析和结构设计中应考虑这种恒载效应对承受活载(或后期荷载)作用的受力行为影响。Based on the strain energy considering the effect of dead loads, the general form static equilibrium differential equations were formulated by means of the potential energy principle. The approximate solutions of live load or later load displacement including the effect of dead loads for the clamped rectangular plate and the simply supported rectangular plate were generated by the Galerkin method. These formulas are simple and clear, and their physical concepts are explicit. The correctness of these formulas was verified by the finite element method. The dead loads and other factors that influence the effect of dead loads are shown by these formulas. The effect of dead loads on the two different boundary condition rectangular plate were analyzed by these approximate solutions. The effect of dead loads improves the bending stiffness of plate and minimizes the displacement of live loads or later loads. The key physical factors governing the effects of dead loads on plates are the dead load, the ration of span to thickness and boundary condition etc. This effect of dead loads is not negligible, especial in thinner plates or plates with smaller stiffness, more attention should be paid to the effect of dead load in the calculation and analysis for plates

关 键 词：近似解 恒载效应 位移 板 

分 类 号：TU313[建筑科学—结构工程]