湿热环境下多孔功能梯度圆管的非线性弯曲行为
NONLINEAR BENDING BEHAVIOR OF POROUS FUNCTIONALLY GRADED MATERIAL TUBES IN HYGRO-THERMAL ENVIRONMENT
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摘要: 圆管作为重要的工程结构, 广泛应用于各个领域, 其几何特征特殊, 传统的梁理论不能满足其内外表面切应力为0的边界条件, 采用合适的梁理论对其进行研究至关重要. 文章采用一种修正的高阶剪切变形梁理论, 研究了湿热环境下多孔功能梯度圆管的非线性弯曲行为. 考虑材料物性与温度相关, 基于修正的高阶剪切变形梁理论和von Kármán非线性理论, 利用最小势能原理, 建立了多孔功能梯度圆管的非线性弯曲控制方程, 采用二次摄动法对控制方程进行求解, 通过数值算例讨论了孔隙分布模型、孔隙率、梯度指数、内半径、湿度和温度对多孔功能梯度圆管非线性弯曲行为的影响. 提出了针对湿热环境下多孔功能梯度圆管的非线性弯曲行为分析方法, 得到了该问题的半解析解, 将为优化多孔功能梯度圆管的结构和材料参数提供理论依据. 结果表明: 当孔隙率较大时, 非均匀孔隙分布模型比均匀孔隙分布模型的多孔功能梯度圆管具有更好的抗弯曲变形能力, 因此在实际轻量化设计过程中, 孔隙分布应优先采用非均匀分布模型.Abstract: Tubes, as important engineering structures, are widely used in various fields, its geometric characteristics are special, and the traditional beam theory can not satisfy the boundary condition that the shear stress on its inner and outer surfaces is zero. It is crucial to adopt a suitable beam theory to study it. A modified high-order shear deformation beam theory was used to study the nonlinear bending behavior of porous functionally graded material tubes under the hygro-thermal environment. Considering temperature-dependent material properties, basing on the modified high-order shear deformation beam theory and von Kármán nonlinear theory, the nonlinear bending control equations of porous functionally graded material tubes were derived by the principle of minimum potential energy. The control equations were solved by the two-step perturbation technique. The effects of porosity distribution types, porosity, gradient index, inner radius, humidity and temperature on the nonlinear bending behavior of the tubes were discussed by numerical examples. The nonlinear bending behavior analysis method of porous functionally graded tubes under hygro-thermal environment was proposed, and the semi-analytical solution of this problem was obtained, which will provide a theoretical basis for optimizing the structure and material parameters of porous functionally graded material tubes. The results show that when the porosity is relatively high, the porous functionally graded material tubes with uneven pore distribution models exhibit superior resistance to bending deformation compared to those with even pore distribution models. Consequently, in practical lightweight design processes, uneven pore distribution models are preferably adopted.