Abstract

New higher-order models of orthotropic micropolar plates and shells have been developed using Carrera Unified Formulation (CUF). Here, a complete linear expansion case (CLEC) has been considered in detail. The stress and strain tensors, as well as the vectors of displacements and rotation, have been presented as linear expansion in terms of the shell thickness coordinates. Then, all the equations of the micropolar theory of elasticity (including generalized Hooke’s law) have been transformed to the corresponding equations for the coefficients of the expansion on the shell thickness coordinates. A system of differential equations in terms of the displacements and rotation vectors and natural boundary conditions for the coefficients of the expansion of the shell thickness coordinates has been obtained. All equations for the case of CLEC theory of micropolar plates and shells have been developed and presented here. The obtained equations can be used for calculating the stress-strain and for modeling thin walled structures in macro, micro, and nanoscale when taking into account micropolar couple stress and rotation effects.

摘要

使用 Carrera 统一公式 (CUF) 开发了正交各向异性微极板和壳的新高阶模型。在这里，已经详细考虑了完全线性膨胀情况（CLEC）。应力和应变张量，以及位移和旋转的向量，已根据壳厚度坐标表示为线性展开。然后，将微极弹性理论的所有方程（包括广义胡克定律）转化为相应的壳厚坐标膨胀系数方程。得到了壳厚度坐标膨胀系数的位移和旋转矢量以及自然边界条件的微分方程组。此处已开发和介绍了微极板和壳的 CLEC 理论案例的所有方程。当考虑到微极耦合应力和旋转效应时，获得的方程可用于计算应力应变和模拟宏观、微观和纳米尺度的薄壁结构。