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Analysis Of An Initially Stressed Laminated Plate Based On Elasticity Theory

机译：基于弹性理论的初始应力层合板分析

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摘要

The governing equations of elasticity theory for natural vibration and buckling are derived from Hellin-ger-Reissner's variational principle with nonlinear strain-displacement relations. Simply supported rectangular laminated plates based on exact theory of elasticity are studied by precise integration method. This method, in contrast to the traditional finite-difference approximation, gives highly precise numerical result, which approaches the full computer precision. So the results for natural vibration and buckling of cross-ply laminated plates, angle-ply laminated plates and hybrid plates presented in the paper can be regarded as analytical solutions. These results can be taken as a standard for both thin plates and moderately thick plates theory considering the effect of shear deformation. The several types of coupling effects, such as coupling between bending and twisting, coupling between extension and bending, etc. when the layer stacking sequence is not symmetric, are considered by only one set of governing equations.
机译：自然振动和屈曲的弹性理论的控制方程是从Hellin-ger-Reissner的具有非线性应变-位移关系的变分原理导出的。通过精确积分方法研究了基于精确弹性理论的简支矩形层压板。与传统的有限差分近似法相比，该方法可提供高度精确的数值结果，接近整个计算机的精度。因此，本文中提出的交叉层板，角层层板和混合板的自然振动和屈曲结果可以视为解析解。考虑到剪切变形的影响，这些结果可以作为薄板和中厚板理论的标准。仅在一组控制方程中考虑了几种类型的耦合效应，例如，弯曲和扭曲之间的耦合，延伸和弯曲之间的耦合等。

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