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首页> 外文会议>The 2001 ASME International Mechanical Engineering Congress and Exposition, 2001, Nov 11-16, 2001, New York, New York >Asymptotic Construction of Reissner-like Models for Composite Plates with Accurate Strain Recovery
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Asymptotic Construction of Reissner-like Models for Composite Plates with Accurate Strain Recovery

机译：具有精确应变恢复的复合板Reissner样模型的渐近构造

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摘要

The focus of this paper is to develop an asymptotically correct theory for composite laminated plates when each lamina exhibits monoclinic material symmetry. The development starts with formulation of the three-dimensional, anisotropic elasticity problem in which the deformation of the reference surface is expressed in terms of intrinsic two-dimensional variables. The Variational Asymptotic Method is then used to rigorously split this three-dimensional problem into a linear one-dimensional normal-line analysis and a nonlinear two-dimensional "plate" analysis accounting for transverse shear deformation. The normal-line analysis provides a constitutive law between the generalized, two-dimensional strains and stress resultants as well as recovering relations to approximately express the three-dimensional displacement, strain and stress fields in terms of plate variables calculated in the "plate" analysis. It is known that more than one theory that is correct to a given asymptotic order may exist. This nonuniqueness is used to cast a strain energy functional that is asymptotically correct through the second order into a simple "Reissner-like" plate theory. Although it is true that it is not possible to construct an asymptotically correct Reissner-like composite plate theory in general, an optimization procedure is used to drive the present theory as close to being asymptotically correct as possible while maintaining the beauty of Reissner-like formulation. Numerical results are presented to compare with the exact solution as well as a previous similar yet very different theory. The present theory has excellent agreement with the previous theory and exact results.
机译：本文的重点是为每块薄板表现出单斜材料对称性的复合层压板开发一种渐近正确的理论。发展始于提出三维各向异性弹性问题，其中参考表面的变形用固有的二维变量表示。然后使用变分渐近方法将这个三维问题严格分解为线性一维法线分析和考虑横向剪切变形的非线性二维“板”分析。法线分析提供了广义二维应变和应力结果之间的本构定律，并提供了恢复关系，以根据“板”分析中计算出的板变量来近似表示三维位移，应变和应力场。 。众所周知，可能存在不止一个对给定渐近阶正确的理论。这种非唯一性用于将通过二阶渐近校正的应变能函数转换为简单的“类似于Reissner的”板理论。尽管确实不可能一般地构造渐近正确的类似Reissner的复合板理论，但是在保持Reissner形式之美的同时，仍使用优化程序来驱动本理论尽可能接近渐近正确。 。给出了数值结果，以与精确的解决方案以及先前类似但非常不同的理论进行比较。本理论与先前的理论和精确的结果有很好的一致性。

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