Abstract Present paper deals with the nonlinear thermal bending response, thermal postbuckling behavior, and snap-through phenomenon due to lateral mechanical load in a thermally preloaded functionally graded (FG) porous perfect/imperfect nanobeam subjected to two types of thermal loading, including heat conduction across the thickness and uniform temperature rise. Heterogenous material properties of the porous nanobeams are assumed to be position/temperature-dependent, where dependency is obtained according to the modified rule of mixture and Touloukian formulation. Two types of porosity distribution and also geometrical imperfection of the nanobeam are considered. Assuming the Timoshenko beam model and von-Karman nonlinearity, the nonlinear equilibrium equations are extracted on the basis of the nonlocal theory of elasticity. With the establishment of the principle of virtual displacement and Chebyshev polynomial of the first kind as the basic functions, the Ritz method is utilized to obtain the matrix form of the nonlocal governing equations. Two different strategies, including the Newton-Raphson technique and direct displacement control scheme, are first proposed to extract the nonlinear bending and postbuckling trajectories of the graded porous nanobeam. Afterwards, to trace the snapping behavior beyond limit loads of the graded porous nanobeam with thermal preloading, the cylindrical arch-length scheme as a path-following method is adopted. Numerical parametric investigations are given to discuss the influences of the power-law index, two types of porosity distribution and thermal loads, size-dependent nonlocal parameter, imperfection amplitude, and boundary conditions on the snap-through behavior and the nonlinear thermal stability of the FG nanobeam.

中文翻译：

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具有几何缺陷的剪切变形 FG 多孔纳米梁的非线性热行为：快速通过和后屈曲分析

摘要 本论文讨论了热预加载功能梯度 (FG) 多孔完美/不完美纳米梁中由于横向机械载荷引起的非线性热弯曲响应、热后屈曲行为和瞬穿现象，这些纳米梁受到两种类型的热载荷，包括热传导。整个厚度和均匀的温升。假设多孔纳米梁的异质材料特性与位置/温度有关，其中相关性是根据混合和 Touloukian 公式的修改规则获得的。考虑了纳米束的两种孔隙率分布和几何缺陷。假设Timoshenko梁模型和von-Karman非线性，基于非局部弹性理论提取非线性平衡方程。以虚位移原理和第一类切比雪夫多项式为基本函数，利用Ritz方法得到非局部控制方程的矩阵形式。两种不同的策略，包括 Newton-Raphson 技术和直接位移控制方案，首先被提出来提取梯度多孔纳米梁的非线性弯曲和后屈曲轨迹。然后，为了追踪具有热预加载的分级多孔纳米梁超出极限载荷的咬合行为，采用圆柱拱长方案作为路径跟踪方法。数值参数研究讨论了幂律指数、两种类型的孔隙度分布和热载荷、尺寸相关的非局部参数、缺陷幅度、