Modified Bolle - Reissner Theory of Plates Including Transverse Shear Deformations

AbstractIn this work, new equations for first-order shear deformation plates are deduced taking into account the kinematic assumptions of the Bolle-Reissner theory but considering the equilibrium equations in the deformed configuration for the plate. The system of differential equations deduced is applicable to the calculation of the stresses in isotropic plates and is valid for thin and moderately thick plates. Analytical solutions are also presented in this work which are compared, when possible, with the ones obtained with other refined shear deformation plate theories.

摘要：本文基于Bolle-Reissner理论的运动学假设，同时考虑板在变形构型中的平衡方程，推导得到一阶剪切变形板（first-order shear deformation plates）的全新控制方程。所推导得到的微分方程组可用于各向同性板的应力计算，且适用于薄板与中厚板场景。本文同时给出了对应的解析解，并在可行范围内将其与其他精细化剪切变形板理论（refined shear deformation plate theories）所得结果进行对比验证。