摘要
介绍了非连续变形分析 (DDA)方法的原理、特点及适用范围 ,分析了DDA方法较常用的有限元法的优越性 ,进一步提出把现有平面DDA方程推广到球面DDA方程的基本思路 ,希望为在大范围内研究地壳运动找到突破口。在此基础上 ,结合目前我国地学研究的热点 ,提出了三类最具代表性的实际问题 。
This paper discusses the application of discontinuous deformation analysis (DDA),a powerful numerical method,to the simulation of crustal movement problems.The problems of crustal movement contain the movement of large plates to small active faults.Usually,finite element (FE) method is used to the simulation of crustal movement problems,but discontinuous faults exist in plates and discontinuous medium exist in rocks.So traditional numerical methods (especial for finite element method) are not efficient to simulate crustal movement.DDA method is better than FE method. This paper introduces the principle of DDA method.After DDA method compared with FE method,the advantage and limitation of DDA method discussed. For efficiently using DDA method in the simulation of crustal movement,the idea of developing DDA method in 2D plane coordinate system to a new DDA method in 2D spherical coordinate system is shown for the first time. 1) Establishing the function equation between displacement and its invariant of any point of the blocks on the spherical surface.Based on the basic relation formula of displacement and strain on the spherical coordinate system,the function equation of displacement (u,v) and its invariant (u 0,v 0,r 0,ε ,ε θ,γ θ ) on the spherical surface can be set up.The linear approximately expression of deformation of blocks will be assumed. 2) Establishing the relation equation of the blocks on spherical surface depending on the theory of Least Potential Energy.The potential energy expression will be separately resolved,including the stiffness stress,initial stress,points loading,volume force,inertial stress,fixed displacement of points etc.By differencing the equation,the coefficient child matrix can be got,and then added to the relation equation. 3) Establishing the kinematics equation of block system formed by a lot of blocks on the spherical surface.A mathematic expression must be achieved to describe the relation between the nearby blocks.The invasion is not allowed among the blocks.The problem of no invasion can be well resolved in high precise through adding rigidity spring on the edge of blocks.The appending of rigidity spring is judged by distance of invasion on the edge of the nearby blocks.The calculation of distance invasion will be very complex on spherical coordinate system.In order to make the calculation simple and highly efficient,local plane projection coordinate system is chose and the problem of spherical surface becomes as easy as the situation of plane coordinate. In the fourth part of the paper,focusing on researching region of geosciences,three kinds of problem of crustal movement are mentioned,and a working plan is shown.DDA method can play an important part in the areas.
出处
《武汉大学学报（信息科学版）》
EI
CSCD
北大核心
2001年第2期122-126,共5页
Geomatics and Information Science of Wuhan University
基金
国家攀登计划 (现代地壳运动和地球动力学研究 )资助项目 ( 970 2 310 0 2 )
国家自然科学基金资助项目 ( 4 990 40 0 1)。
