计算力学中的静力衰减
The Theory of Static Decay in Computational Mechanics
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摘要: 本文在计算力学范围内证明了,平衡力系的影响,由近及远按矩阵连分式的规律衰减.该衰减往往不慢于,但并非总是不慢于指数衰减或幂次衰减.本文结果可用于估计某些简化假定在计算中引入的误差.Abstract: In this paper,a new mathematical form,matrix,continued fraction(MCF) is introduced to describe the decay of effects of an equilibrant system of forces acting on a sphere of an elastic body.By this way,the famous Saint-Venant's principle is proved often but not always valid in computational mechanics.
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[1] Fung,Y.C.,Foundation of Solid Mechanics,Prentice-Hall,Inc.,New Jersey(1965),300-309. [2] Horgan,C.O.and J.K.Knowles,Recent development concerning Saint-Venant's principle,Advances in Applied Mechanics,23,Academic Press Inc.(1983),179-269. [3] 橘英三郎,Two theorems on Saint-Venant's principle in discrete structural model,日本AIJ構造系论文报告集,351(1985),55-64. [4] 武建勋、堤一,离散系にする Saint-Venant の原理の反例,日本AIJ構造系论文银告集,374(1987)57-62. [5] 武建勋、堤一,同じりンクの细长ン構造物にわける变形の相似性,日本·宫崎大学工学部纪要,33(1987). [6] 普齐米尼斯基,J.S.,《矩阵结构分析理论》,王德荣译校,国防工业出版社(ISSB),157-158. -
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