应力协调迭代法在高速冲击动力有限元中的应用
The Application of Compatible Stress Iterative Method in Dynamic Finite Element Analysis of High Velocity Impact
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摘要: 在EPIC[2][3],NONSAP[4]等弹塑性撞击动力有限元程序中,有一个共同的弱点是都采取了静力有限元方法,把位移函数用线性插值表示.单元之间应力是非协调的.因此应用虚功原理的基础不合理.为了克服以上困难,本文引入一个新的方法,即协调应力迭代法.实例表明,这种方法在冲击动力有限元计算中是稳定和精确的,同时具有减小单元刚度的作用.Abstract: There is a common difficulty in elastic-plastic impact codes such as EPIC[2,3] NONSAP[4], etc.. Most of these codes use the simple linear functions usually taken from static problem to represent the displacement components. In such finite element formulation, the stress components are constant in each element and they are discontinuous in any two neighboring elements. Therefore, the bases of using the virtual work principle in such elements are unreliable. In this paper, we introduce a new method, namely, the compatible stress iterative method, to eliminate the above-said difficulty. The calculated examples show that the calculation using the new method in dynamic finite element analysis of high velocity impact is valid and stable, and the element stiffness can be somewhat reduced.
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[1] 钱伟长,《穿甲力学》,国防工业出版社(1984) [2] Johnson,G.R.,Analysis of elastic-plastic impact involving severe distortions,Journal of Applied Mechanics,Trans.ASME,43,3(1976),98. [3] Johnson,G.R.,High velocity impact calculations in three dimensions,Journal of Applied Mechanics,Trans.ASME.44. 1(1976),99. [4] Bath,K.J.and E.L.Nilson,NONSAP-A general finite element programme for nonlinear dynamic analysis of complex structure,Paper M3/1,Proc.2nd Int.Conf.Struct.Mech.Reactor Technology,Berlin(1973). [5] von Neumann,J.and R.D.Richtmyer,A method for the numerical calculation of hydrodynamics shocks,Journal of Applied Physics,21(1950). [6] Wilkins,M.L.,Calculation of elastic-plastic flow,Methods in Computational Physics,3. eds.,B.Alden,S.Fernbach and M.Rotenberg,Academic Press,New York(1964),211-263. -
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