单层双曲抛物面网壳的建模方法及力学特性的研究.pdf

摘要摘要网壳结构良好的力学特性及形式各异的外观造型使它们逐渐成为一个城市,甚至一个国家的标志。大部分专家和学者着重研究球面网壳、椭圆抛物面网壳等正高斯曲率网壳,使这类网壳的力学理论越来越成熟。相比而言,人们对单层双曲抛物面网壳等负高斯曲率网壳的力学特性研究还不够充分。网壳结构由于杆件数量庞大,节点数目繁多,加上本身就是呈现几何非线性的外观形式,使得其模型的建立存在一定的难度。根据单层双曲抛物面网壳自身的特性,参照标准规范设定尺寸大小,引入Maple计算软件编程求解出网壳结构所有节点的坐标值,代入Ansys有限元分析软件实现单层双曲抛物面网壳的快速准确建模。通过对比分析证明运用该类方法建立网壳结构模型完全达到设计与施工的要求。同时通过建立其他形式网壳模型证明了该方法具有全面性和推广性。考虑网壳结构的矢跨比、长跨比、边梁侧向刚度等结构参数对单层双曲抛物面网壳力学特性的影响。利用最小二乘法拟合出该网壳的极限荷载计算公式, 将其结果与有限元结果进行比较,证明了该公式具有误差小、计算简便的优点, 具有较好的实用价值。利用基于有矩理论的拟壳法对单层双曲抛物面网壳力学特性进行研究。首先将单层双曲抛物面网壳的网格单元划分成覆盖物单元以及杆单元,对结构的薄膜刚度进行修正;其次建立该网壳结构的基本微分方程;再次利用基于薄膜理论的拟壳法得出该网壳的内力求解公式,该公式作为网壳结构基本微分方程的特解;最后求解网壳结构基本微分方程的通解,综合方程的特解得到单层双曲抛物面网壳结构基本微分方程的解。为研究该类网壳的力学特性提供了一定的理论依据。关键词:单层双曲抛物面网壳;网壳建模;结构参数;公式拟合;拟壳法; ABSTRACT ABSTRACT Shell structures haveexcellentmechanical characteristicanddifferentforms SO that廿ley e acity,or even experts and scholars focused on thespherical shell,theellipticparabolic shell and other positive Gaussian curvature shells,make themechanics theory oftheseshellsmore andmore contrast,People research themechanical theory of thesinglehyperbolic parabolic shellandothernegative Gaussian curvature shells which is notsufficient Because theshell structures have alargenumber ofbars,a lotofnodes,and own theappearance ofgeometric non-linearform,making theirmodel must bedifficult. According tosinglehyperbolicparabolic shell itsown characteristicsandreferencing standards themaple calculationsoftwareprogram tosolve theshell structure coordinates of laSt,take the shell structure coordinates ofall nodes intotheAnsys finiteelement analysissoftware,achieve singlehyperbolic parabolic shellof fastand accurate and analyzing shows that theuse ofsuchmethods tOestablish shell structure models fully meets the requirements of the design through the establishment ofotherforms of shellmodel proved thatthe method hasthepromotion prehensive. Consider thestructuralparameters such aSthespan