Abstract

Two-variable sinusoidal shear and normal deformation theory is used in this paper for elastic analysis of doubly curved nanoshells resting on elastic foundation. Thickness stretching effect is accounted based on higher-order shear and normal deformation theory. The transverse displacement is decomposed into bending and stretching components based on two-variable sinusoidal shear deformation theory. Unlike classical structural theories for plates and shells, the present theory considers an extra variable as transverse displacement along the thickness direction. 3D constitutive relations are presented based on generalized Hooke’s law. The principle of virtual work is used for derivation of governing equations and proper boundary conditions. An extensive parametric analysis is performed to present variation of in-plane and transverse displacements along the thickness direction in terms of the nonlocal parameter, opening angles and foundation characteristics. Comparison of results with and without thickness stretching effect show that the present theory improves results about 4% with respect to the structural theories without stretching effect.

摘要

本文使用二变量正弦剪切和法向变形理论对基于弹性基础的双弯曲纳米壳进行弹性分析。基于高阶剪切和法向变形理论计算厚度拉伸效应。基于二变量正弦剪切变形理论将横向位移分解为弯曲和拉伸分量。与板壳的经典结构理论不同，本理论将额外变量视为沿厚度方向的横向位移。3D 本构关系基于广义胡克定律呈现。虚功原理用于推导控制方程和适当的边界条件。进行了广泛的参数分析，以根据非局部参数、张角和基础特性呈现沿厚度方向的平面内和横向位移的变化。比较有和没有厚度拉伸效应的结果表明，相对于没有拉伸效应的结构理论，本理论提高了大约 4% 的结果。