直角坐标系下层状地基力学计算中的传递矩阵技术-工程力学.PDFVIP

第24 卷增刊I Vol.24 Sup. I 工 程 力 学 2007 年 6 月 June 2007 ENGINEERING MECHANICS 83 文章编号：1000-4750(2007)Sup.I-0083-04 直角坐标系下层状地基力学 计算中的传递矩阵技术 *王有凯，牛婷婷 (河南理工大学土木工程学院，河南 焦作 454000) 摘 要：给出了在直角坐标系下计算层状地基力学问题的传递矩阵技术，改变了过去只能在柱坐标系下求解层状 地基力学问题的状况，大大地简化了任意荷载作用下层状地基力学问题的计算。从直角坐标系下弹性问题的基本 方程出发，通过改变坐标系的常规位置，成功地利用 Laplace 变换及其微分性质，首次推导出直角坐标系下的状 态控制方程和对应的传递矩阵，并给出了利用该方法的求解过程。 关键词：层状地基；Laplace 变换；状态空间；传递矩阵；直角坐标系 中图分类号：TU470; TU311 文献标识码：A THE METHOD OF TRANSFERRING MATRIX FOR MULTI-LAYERED HALF SPACE ELASTIC PROBLEMS IN RECTANGULAR COORDINATE SYSTEM * WANG You-kai , NIU Ting-ting (School of Civil Engineering, Henan Polytechnic University, Jiaozuo, Henan 454000, China) Abstract: A new method is proposed for solving the problem of non-axisymmetric elastic problems in multi-layered foundation with rectangular coordinate system. The method is simple and effective, which changes the situation that elastic multi-layered foundation problems could only be solved in cylindrical coordinate system. The location of rectangular coordinate system is changed so that Laplace transform and its differential properties can be used. Starting from the fundamental equations of elastic mechanics in rectangular coordinates, the state equations of one elastic layer and the state space transferring matrix are derived in rectangular coordinates. The procedure of solving the problem with this method is given. Key words: multi-layered half space; Laplace transform; the state space; transferring matrix; rectangular coordinate system 用状态空间法中的传递矩阵技术求解层状地 Hankle 变换进行求解，这种级数解法的推导过程和 基的受力问题已有许多研究成果，这些研究基本上