三维高阶DDA方法的静力分析研究

STUDY OF STATIC ANALYSIS OF 3D HIGH-ORDER DDA

借助于DDA方法以"体"为研究对象的潜在优势进行连续结构的静力分析,突破网格相容条件的限制,有利于简化前处理。同时,采用高阶位移模式,在将空间几何形体简单地划分为单个或数个体的条件下,能获取较高的求解精度。遵循以上思路,定义"连接面"、"连接点对"的概念,给出DDA块体在连续系统中所需满足的变形协调条件,推导三维高阶DDA方法的基本公式,包括弹性子矩阵、初应力荷载矩阵、点荷载矩阵、体荷载矩阵和固定点矩阵及相邻块体间的连接矩阵,最终建立三维连续结构的高阶DDA整体平衡方程。最后编程实现上述思路,采用有解析解的经典算例并结合一定网格密度的有限元解进行比对分析,结果表明DDA方法应用于连续结构静力计算的可行性与优越性。

Applying three-dimensional high order discontinuous deformation analysis（DDA） with the volume- oriented advantage to structure static analysis gets rid of the limit of compatible mesh, which helps to simplify the preprocessing. Furthermore, by introducing high-order displacement mode, higher precision can be gained when the three-dimensional structure is simply divided into only one or few blocks. Based on above idea, the concepts of connecting face and connecting point pair is defined; and the deformation compatibility conditions of high-order DDA block in continuous structure computation are presented; then the principal formulas of three- dimensional high-order DDA are deduced, including elastic sub-matrix, initial stress load matrix, point load matrix, volume load matrix, fixed point matrix and the connecting matrix of adjacent blocks. The whole balance equations are established at last. Above thought is realized by program. Comparative analysis of some typical samples is applied between the method, analytic solution and finite element results. It shows the feasibility and advantage of DDA method in the static computation of continuous structure.