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Fourier analysis of thick cross-ply Levy type clamped doubly-curved panels

机译：厚交叉层Levy型夹紧双曲面板的傅立叶分析

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摘要

A hitherto unavailable Levy type analytical solution to the problem of deformation of a finite-dimensional general cross-ply thick doubly-curved panel of rectangular plan-form, modeled using a higher order shear deformation theory (HSDT), is presented. A solution methodology, based on a boundary-discontinuous generalized double Fourier series approach is used to solve a system of five highly coupled linear partial differential equations, generated by the HSDT-based laminated shell analysis, with the C4-type simply supported boundary condition prescribed on two opposite edges, while the remaining two edges are subjected to the SS3-type constraint. The numerical accuracy of the solution is ascertained by studying the convergence characteristics of the deflection and moment of a cross-ply spherical panel, and also by comparison with the available FSDT (first-order shear deformation theory) based analytical solution. Additionally, numerical results pertaining to flat symmetric and antisymmetric cross-ply plates with the same boundary conditions have also been reproduced. Hitherto unavailable important numerical results presented include sensitivity of the predicted response quantities of interest to shell geometry (cylindrical and spherical), lamination, lamina material property, and thickness effects, as well as their interactions. Comparison with their SS2 counterparts demonstrates the effect of end clamping on the deflections and moments of thin to thick singly- and doubly-curved cross-ply panels.
机译：针对高阶剪切变形理论（HSDT）建模，提出了迄今无法获得的Levy型解析方法，用于求解有限平面的矩形平面多层双曲面板的变形问题。基于边界不连续的广义双傅立叶级数方法的求解方法用于求解由基于HSDT的叠层壳分析生成的五个高度耦合的线性偏微分方程组，其中规定了C4型简单支撑边界条件在两个相对的边缘上，其余的两个边缘则受SS3类型约束。通过研究交叉层球形板的挠度和弯矩的收敛特性，并与基于FSDT（一阶剪切变形理论）的解析解进行比较，可以确定解的数值精度。另外，还得到了关于具有相同边界条件的平面对称和反对称交叉板的数值结果。迄今为止，尚无可用的重要数值结果包括对壳几何形状（圆柱和球形）的预期响应量的敏感性，叠层，薄片材料特性和厚度效应以及它们之间的相互作用。与它们的SS2同类产品的比较表明，端部夹紧对薄到厚的单弯和双弯交叉层板的挠度和弯矩的影响。

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