Abstract An analytical solution is obtained for the 3D static deflection of variable stiffness composite beams subject to non-uniformly distributed loads. Governing differential equations with variable coefficients, reflecting the spatially variable stiffness properties, are presented in which four degrees of freedom are fully coupled. The general analytical solution in integral form is derived and closed-form expressions obtained using series expansion approximations. The static deflection of a number of variable stiffness composite beams that can be made by fibre steering are considered with various stacking sequences. The results obtained from the proposed method are validated against numerical results from the Chebyshev collocation method and excellent agreement is observed between the two. While the proposed methodology is applicable for variable stiffness composite beams with arbitrary span-wise variation of properties, it is also an efficient approach for capturing the complicated 3D static deflection of variable stiffness composite beams subject to non-uniformly distributed loads.

中文翻译：

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受非均匀分布载荷影响的变刚度复合梁：一种解析解

摘要 获得了非均匀分布载荷作用下变刚度组合梁的三维静态挠度的解析解。提出了具有可变系数的控制微分方程，反映了空间可变刚度特性，其中四个自由度完全耦合。推导出积分形式的一般解析解，并使用级数展开近似获得封闭形式的表达式。可以通过纤维转向制成的许多可变刚度复合梁的静态偏转考虑了各种堆叠顺序。从所提出的方法获得的结果与切比雪夫搭配方法的数值结果进行了验证，并且在两者之间观察到了极好的一致性。