The main objective of this study is to investigate the post-buckling thermal load–deflection path of rotating pre-twisted microblades/beams made of temperature-dependent functionally graded materials (FGMs) via nonlinear non-classical first-order shear deformation theory (FSDT). To this end, modified strain gradient theory (MSGT) as well as the von Karman geometric nonlinearity is used to develop the size-dependent nonlinear beam theory. Thermal loading is exerted by providing nonlinear (non-uniform) temperature rise across the microbeam thickness at steady-state condition. By using the principle of virtual work and Ritz method, the discretized form of nonlinear equations governing the post-buckling behavior of rotating pre-twisted functionally graded (FG) microbeams is achieved. To solve the obtained nonlinear equations numerically, Broyden’s method is employed. The effects of twist angle along the beam axis, angular velocity, index of the material gradient, length-scale parameter and thickness-to-length ratio on the post-buckling path of FG microbeams are carefully investigated. Findings show that making a correct assumption about the temperature dependence of material is an important factor to increase accuracy of results.

中文翻译：

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旋转预扭温度相关 FG 微刀片的非线性热稳定性

本研究的主要目的是通过非线性非经典一阶剪切变形理论 (FSDT) 研究由温度相关功能梯度材料 (FGM) 制成的旋转预扭曲微叶片/梁的屈曲后热载荷-挠曲路径。 ）。为此，使用修正应变梯度理论 (MSGT) 以及 von Karman 几何非线性来开发与尺寸相关的非线性梁理论。通过在稳态条件下提供跨微束厚度的非线性（非均匀）温升来施加热载荷。通过使用虚功原理和 Ritz 方法，实现了控制旋转预扭曲功能梯度 (FG) 微梁的后屈曲行为的非线性方程的离散形式。为了数值求解得到的非线性方程，采用布罗伊登的方法。仔细研究了沿梁轴的扭转角、角速度、材料梯度指数、长度尺度参数和厚长比对 FG 微梁后屈曲路径的影响。结果表明，对材料的温度依赖性做出正确的假设是提高结果准确性的重要因素。