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Exact model for the response of moderately thick laminates to transverse forces

机译：中等厚度层压板对横向力响应的精确模型

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摘要

Under the premise of homogeneous force, or curvature-gradient, distribution, a solution for transverse-shear strains and stresses, warping functions, and through-thickness displacements is derived by satisfying all relations and conditions of linear elasticity. Only for calculating the substitute-plate transverse-stiffness matrix the principle of the minimum of the total potential energy is used as a scheme for correctly combining energetically conjugate components of stresses and strains for the entries of the substitute-plate transverse stiffness matrix. The model is valid for all laminate and sandwich designs. The said premise renders the model a point theory rather than a structural theory, so that it is a complement to the classical theory of laminated plates in the sense of mapping substitute-plate properties and distribution of state variables through the laminate thickness. This paper explains the modeling ideas and derivations in detail. Predictions of the responses for a set of sample laminates of varying complexity, and comparison of stiffness values with those obtained by a dedicated FEM formulation, verify the model.
机译：在均质力或曲率梯度分布的前提下，通过满足线​​性弹性的所有关系和条件，可以得出横向剪切应变和应力，翘曲函数和厚度方向位移的解决方案。仅为了计算替代板横向刚度矩阵，才使用总势能最小值的原理作为正确组合应力和应变的能量共轭分量的方案，以替代替代板横向刚度矩阵。该模型对所有层压板和三明治设计均有效。所述前提使模型成为点理论，而不是结构理论，因此在映射替代板特性和通过层压板厚度分布状态变量的意义上，它是对层压板经典理论的补充。本文详细解释了建模思想和派生方法。预测一组复杂程度各异的样品层压板的响应，并将刚度值与通过专用FEM公式获得的刚度值进行比较，以验证该模型。

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