Abstract

This study deals with the nonlinear bending analysis of elastic tubes made of functionally graded (FG) porous material based on modified couple stress theory. Immovable simply supported and clamped boundary conditions are assumed for the FG porous microtubes resting on nonlinear elastic foundation. Transverse pressure load is applied uniformly on the upper surface of the microtube which is exposed to uniform temperature field. Temperature-dependent material properties of the microtube with uniformly distributed porosity are graded across the radius of the cross-section. The higher-order shear deformation theory of circular beams is presented to approximate the displacement field. The von Kármán type of kinematic assumptions is utilized for nonlinear strain-displacement relations. The uncoupled thermoelasticity theory is used to derive the constitutive equations. With the establishment of the virtual displacement principle, nonlinear differential equations governing the equilibrium position of the microtube are extracted. These equilibrium equations are analytically solved by means of the two-step perturbation technique and Galerkin procedure. Parametric investigations are performed to demonstrate the size-dependent nonlinear bending responses of an FG porous microtube on nonlinear elastic foundation in thermal environment.

摘要

本研究基于修正耦合应力理论对由功能梯度 (FG) 多孔材料制成的弹性管进行非线性弯曲分析。对于基于非线性弹性基础的 FG 多孔微管，假设了不可移动的简支和夹紧边界条件。横向压力载荷均匀地施加在暴露于均匀温度场的微管的上表面。具有均匀分布孔隙率的微管的与温度相关的材料特性在横截面的半径上分级。提出了圆梁的高阶剪切变形理论来近似位移场。von Kármán 类型的运动学假设用于非线性应变-位移关系。非耦合热弹性理论用于推导本构方程。随着虚位移原理的建立，提取了控制微管平衡位置的非线性微分方程。这些平衡方程通过两步微扰技术和 Galerkin 程序解析求解。进行参数研究以证明 FG 多孔微管在热环境中非线性弹性基础上的尺寸相关非线性弯曲响应。