The bending problem of a thin rectangular plate with in-plane variable stiffness is studied. The basic equation is formulated for the two-opposite-edge simply supported rectangular plate under the distributed loads. The formulation is based on the assumption that the flexural rigidity of the plate varies in the plane following a power form, and Poisson's ratio is constant. A fourth-order partial differential equation with variable coefficients is derived by assuming a Levy-type form for the transverse displacement. The governing equation can be transformed into a Whittaker equation, and an analytical solution is obtained for a thin rectangular plate subjected to the distributed loads. The validity of the present solution is shown by comparing the present results with those of the classical solution. The influence of in-plane variable stiffness on the deflection and bending moment is studied by numerical examples. The analytical solution presented here is useful in the design of rectangular plates with in-plane variable stiffness.
连续丝束剪切(Continuous Tow Shearing, CTS)铺放技术是一种新的变角度层合板制作技术,这种新技术能显著减少丝束铺放过程中产生的丝束重叠和间隙等缺陷,然而,采用CTS技术铺设时,层合板的厚度将随着纤维角度的变化而变化.本文基于一阶剪切变形理论并应用Chebyshev-Ritz法对这种变厚度的变角度复合材料层合板的热屈曲问题进行了研究.假设纤维方向角沿板的长度方向按照线性变化,获得了均匀温度变化时变厚度层合板的临界热屈曲荷载.通过与现有文献的比较验证了本文方法的正确性,并进一步讨论了纤维铺设技术、纤维方向角的变化以及边界条件的不同对变角度复合材料层合板的临界屈曲温度的影响.研究结果表明,在体积相同的情况下,采用CTS铺设较传统的自动丝束铺放(AFP)可以进一步提升变角度层合板的临界屈曲温度.本文的研究结果可为变角度复合材料的设计提供一定的参考.
