Consider Saint-Venant’s Principle by Means of Chain Model
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摘要: 用泛函分析的双空间理论为计算力学构造了一个严密的背景理论,以此在链式模型上讨论圣文南原理,同时将传统的连分数扩展为算子连分式作为链式模型的本征关系式。平衡力系的影响在链式模型上由近及远的衰减受算子连分式的收敛性的控制,所以圣文南原理的合理成分体现为算子连分式的收敛性。发散的算子连分式对应着平衡力系的明显非零的影响可以传达到无穷远的场合,所以“圣文南原理”并不是普遍成立的原理。Abstract: A precise background theory of computational mechanics is formed.Saint-Venant's principle is discussed in chain model by means of this precise theory.The classical continued fraction is developed into operator continued fraction to be the constrictive formulation of the chain model.The decay of effect of a self-equilibrated system of forces in chain model is decided by the convergence of operator continued fraction,so the reasonable part of Saint-Venant's principle is described as the convergence of operator continued fraction.In case of divergence the effect of a self-equilibrated system of forces may be non-zero at even infinite distant sections,so Saint-Venant's principle is not a common principle.
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