求解几何非线性桩-土耦合系统的微分求积单元法  

DQEM FOR SOLVING PILE-SOIL COUPLING SYSTEMS WITH GEOMETRICAL NONLINEARITY

作　　者：胡育佳[1] 朱媛媛[2] 程昌钧[1] 

机构地区：[1]上海大学,上海市应用数学和力学研究所,力学系,上海200072 [2]上海师范大学,计算机科学与技术系,上海200234

出　　处：《固体力学学报》2008年第2期141-148,共8页Chinese Journal of Solid Mechanics

基　　金：上海市浦江人才计划(07pj14073);市重点学科建设项目(Y0103);上海高校选拔培养优秀青年教师科研专项基金资助

摘　　要：将桩-土系统看成在土层中嵌入了一根等圆截面桩的空间轴对称弹性体,在几何非线性的条件下建立了具有间断性条件的桩-土系统的非线性控制方程,并运用微分求积方法(DQEM)来求解了该问题.提出了利用DQEM求解非线性空间轴对称问题中处理单元之间连接条件(包括间断性条件)及边界条件的离散化方法,最终得到了一组离散化的非线性DQEM代数方程,运用Newton-Raphson迭代方法求解非线性代数方程组可以得到每个节点处的位移,进一步可以得到系统的应力和应变.给出了两个数值算例,并与有限元解进行了比较,它们是非常吻合的.将看到,由于在采用DQEM求解时只布置了较少的节点,因此,该文方法具有较小的计算工作量、较高的精度、良好的收敛性以及应用广泛等优点.该文提出的处理连接条件的方法是一个一般的方法,由于它在数学上遵循了求解边值问题的思路,因此,数学上也是严谨的.A pile-soil system is regarded as an axisymmetric space elastic body in which a pile with circular cross-section is embedded. A nonlinear mathematical model of the pile-soil system with discontinuity conditions is established under the condition of geometrical nonlinearity. The differential quadrature element method （DQEM） is applied to solve the problem. A discretization method is presented to deal with the junction conditions （included discontinuity conditions） at the interface between the pile and the soil as well as the boundary conditions in the application of the DQEM to solving nonlinear axisymmetric prob lems. A set of DQEM discretization equations are obtained. The Newton-Raphson method is used to solve the system of discretized nonlinear algebraic equations and the nodal displacements are obtained, further the stresses and the strains of the system can be yielded. Two numerical examples are presented. The obtained results are compared with those obtained by FEM and they are comparatively accordant. Due to fe wer nodes applied, the method presented in this paper is with the advantages of little amount in computa- tion, higher precision, better stability and convergence, broader application and so on, compared to the other comparation techniques. At the same time, The method for dealing with the junction conditions presented in this paper is also a general method, and it follows the theory and the principle solving the boundary value problem with discontinuity conditions.

关 键 词：桩-土耦合系统 几何非线性 间断性条件 微分求积方法 

分 类 号：O175[理学—数学]