Author’s response to Comment by Yang Gao and Min-Zhong Wang on “Stress boundary conditions for plate bending” by F.Y.M. Wan [Int. J. Solids Struct. 40 (2003) 4107–4123]
Author’s response to Comment by Yang Gao and Min-Zhong Wang on “Stress boundary conditions for plate bending” by F.Y.M. Wan [Int. J. Solids Struct. 40 (2003) 4107–4123]
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DOI：
10.1016/j.ijsolstr.2005.07.032
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发表时间：
2006-03
影响因子：
3.6
通讯作者：
F. Wan
中科院分区：
文献类型：
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作者：
F. Wan
作者非常感谢王教授（他对弹性理论包括与本文有关的板理论方面作出了许多有价值的贡献）和高博士对他最近在《国际固体与结构杂志》上发表的文章的兴趣和评论。作者同意王教授和高博士的观点，即板的中面位移表达式中的常数a0可以用问题的另一个奇异解来确定（正如他们所做的那样）。所得的解将对应于一个内部解，其边缘应力与边缘数据的偏差仅引起边界层，这是Gregory和Wan理论中残余状态快速衰减条件所要求的。另一方面，线弹性力学中任何应力边值问题的解仅在刚体运动之前确定。在所讨论的论文中，作者只是指出，对于轴对称载荷作用下的板，在厚度方向上的刚性平移总是可以加到应力边值问题的任何解上（因此不确定a0也不是不合理的）。同时，垂直平移不是边界层现象。如果我们坚持只得到一个真正的内部解（而不是弹性问题的实际解），任何额外的刚性平移将是不适当的，并且通过在理论中施加在剩余边界值上的快速衰减的剩余状态要求来消除，我们得到了一个内部解，a0由王教授和高博士使用衰减中的另一个奇异解导出的表达式给出剩余状态要求
The author appreciates very much the interest and comments on his recent article in the International Journal of Solids and Structures by Professor Wang (who has made many valuable contributions to elasticity theory including aspects of plate theory related to the present article) and Dr. Gao. The author agrees with Professor Wang and Dr. Gao that the constant a0 in the expression for the midplane displacement of the plate can be determined using the other singular solution of the problem (as they have done). The resulting solution would correspond to an interior solution with deviations of its edge stresses from the edge data inducing only a boundary layer as required by the condition of rapidly decaying residual state in the theory developed by Gregory and Wan.On the other hand, the solution of any stress boundary value problem in linear elasticity is determined only up to a rigid body motion. In the paper being discussed, the author merely pointed out that for plates under axi-symmetric loading, a rigid translation in the thickness direction can always be added to any solution of the stress boundary value problem (and hence it would not be unreasonable not to determine a0). At the same time, a vertical translation is not a boundary layer phenomenon. If we insist on getting only a true interior solution (and not the actual solution of the elasticity problem), any additional rigid translation would be inappropriate and eliminated by the rapidly decaying residual state requirement imposed on the residual boundary value in the theory, leaving us with an interior solution with a0 given by the expression derived by Professor Wang and Dr. Gao using the other singular solution in the decaying residual state requirement.