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首页> 外文会议>AD-vol.69; American Society of Mechanical Engineers(ASME) International Mechanical Engineering Congress and Exposition; 20041113-19; Anaheim,CA(US) >AN IMPROVED REISSNER-MINDLIN PLATE THEORY FOR COMPOSITE LAMINATES
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AN IMPROVED REISSNER-MINDLIN PLATE THEORY FOR COMPOSITE LAMINATES

机译：复合板的改进的Reissner-Mindlin板理论

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摘要

An improved Reissner-Mindlin theory for composite laminates without invoking ad hoc kinematic assumptions is constructed using the variational-asymptotic method. Instead of assuming a priori the distribution of three-dimensional displacements in terms of two-dimensional plate displacements as what is usually done in typical plate theories, an exact intrinsic formulation has been achieved by introducing unknown three-dimensional warping functions. Then the variational-asymptotic method is applied to systematically decouple the original three-dimensional problem into a one-dimensional through-the-thickness analysis and a two-dimensional plate analysis. The resulting theory is an equivalent single-layer Reissner-Mindlin theory with an excellent accuracy comparable to that of higher-order, layerwise theories. The present work is extended from the previous theory developed by the writer and his co-workers with two sizable contributions: (a) six more constants (33 in total) are introduced to allow maximum freedom to transform the asymptotically correct energy into a Reissner-Mindlin model; and (b) the semi-definite programming technique is used to seek the optimum Reissner-Mindlin model. Furthermore, it is proved the first time that the recovered three-dimensional quantities exactly satisfy the continuity conditions on the interface between different layers and traction boundary conditions on the bottom and top surfaces. It is also shown that that two of the equilibrium equations of three-dimensional elasticity can be satisfied asymptotically, and the third one can be satisfied approximately so that the difference between the Reissner-Mindlin model and the second order asymptotical energy can be minimized. Numerical exam- ples are presented to compare with the exact solution as well as the classical lamination theory and first-order shear-deformation, demonstrating that the present theory has an excellent agreement with the exact solution.
机译：使用变分渐近方法构造了一种改进的Reissner-Mindlin理论，用于复合材料层合板，无需调用特殊的运动学假设。代替了通常按照典型板理论通常按照二维板位移来假设三维位移的分布的方式，通过引入未知的三维翘曲函数已经获得了精确的内在公式。然后应用变分渐近方法将原始的三维问题系统地解耦为一维厚度分析和二维板分析。由此产生的理论是等效的单层Reissner-Mindlin理论，其精度可与高阶分层理论相媲美。本工作是从作者和他的同事以前的理论发展而来的，并有两个可观的贡献：（a）引入了另外六个常数（总共33个），以允许最大的自由度将渐近正确的能量转换为Reissner- Mindlin模型； （b）使用半定规划技术来寻求最佳的Reissner-Mindlin模型。此外，首次证明了恢复的三维量完全满足不同层之间的界面上的连续性条件以及底面和顶面的牵引边界条件。还表明，可以渐近地满足两个三维弹性平衡方程，并且可以近似地满足第三个方程，从而可以最小化Reissner-Mindlin模型与二阶渐近能量之间的差异。数值例子与精确解，经典层合理论和一阶剪切变形进行了比较，证明了本理论与精确解有很好的一致性。

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