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R·M·琼斯在他所著的“复合材料力学”一书中,对层合板的柔度矩阵进行了讨论。指出在正交铺设和角铺设的两种情况下,层合板的柔度矩阵有如下形式[A′B′H′D′]琼斯进一步谈到,因为层合板的刚度矩阵是对称的,所以它的逆阵即柔度矩阵也是对称的。以此为理由,琼斯得出了H′必须等于B′的结论。本文指出,对于正交铺设和角铺设的层合板,琼斯关于H′=B′的结论虽然是对的,但其论证显然是错误的。因为在柔度矩阵也是对称的情况下,其子块B′未必对称,因此只能推出H′=B′~T,而不是H′必然等于B′的结论。琼斯此书在国内影响甚广,由于书中对柔度矩阵论证的弊病,致使国内有的复合材料力学教材中,错误地把H′=B′不加限制地当成层合板柔度矩阵的一般结论来论述,更扩大了错误。本文对正交各向异性简单层组成的层合板,论证了在一般情况下其柔度矩阵应该是[A′B′B′~T D′]而对琼斯一书中提到的各种正交铺设和角铺设层合板的柔度矩阵[A′B′B′D′]给出了严格的证明。
In his book “Composites Mechanics,” R. M. Jones discusses the flexibility matrix of laminates. It is pointed out that in the two cases of orthogonal paving and corner paving, the pliability matrix of the plywood has the following form [A’B’H’D’] Jones further mentioned because the stiffness matrix of the plywood is symmetrical, so it The inverse matrix, the flexibility matrix, is also symmetric. For this reason, Jones came to the conclusion that H’ must equal B’. This article points out that Jones’s conclusion about H’=B’ is correct for the orthogonally laid and angled laminates, but its argument is obviously wrong. Because in the case that the flexibility matrix is also symmetric, its sub-block B’ is not necessarily symmetric, so only H’=B’~T can be pushed out instead of the conclusion that H’ must be equal to B’. Jones’s book has a wide range of impacts in the country. Due to the shortcomings of the flexibility matrix argument in the book, some textbooks in composite materials mechanics in China mistakenly regard H′=B′ as a general rule for the flexibility matrix of laminated plates. As a result of the discussion, the error has been expanded. In this paper, a laminate consisting of simple layers with orthotropic layers is demonstrated. In general, the flexibility matrix should be [A’B’B’~TD’] and the various orthogonality mentioned in Jones’s book. The rigorous proof is given by the flexibility matrix [A’B’B’D’] for laying and corner laying laminates.