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考虑尺度影响的平面正交各向异性功能梯度微梁的屈曲分析
Size-dependent buckling analysis of plane orthotropic functionally graded micro-beams
投稿时间:2018-05-31  修订日期:2018-07-10
DOI:
中文关键词:  新修正偶应力理论  功能梯度材料  尺度效应  材料尺度参数  屈曲载荷
英文关键词:remodified couple stress theory  functionally graded materials  scale effects  material length parameter  degree of anisotropy ,buckling analysis
基金项目:国家自然科学基金项目(面上项目,重点项目,重大项目)
作者单位E-mail
贺丹 沈阳航空航天大学 danhe@sau.edu.cn 
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中文摘要:
      基于新修正偶应力理论建立了微尺度平面正交各向异性功能梯梁的屈曲分析模型。含有两个材料尺度参数的模型可描述不同方向上不同程度的尺度效应。基于最小势能原理推导了控制方程及边界条件并以简支梁的屈曲为例分析了屈曲载荷及尺度效应受材料尺度参数、几何尺寸、功能梯度变化指数的影响。算例结果表明:本文模型预测的梁屈曲载荷总是大于传统理论的结果,即反映了尺度效应。尺度效应会随着梁几何尺寸的减小而逐渐增大。当几何尺寸远大于尺度参数时尺度效应消失本文模型将自动退化为传统宏观模型。各向异性材料的尺度效应受材料不同方向的尺度参数影响的效果不同;功能梯度变化指数对屈曲和尺度效应的影响与材料组分分布有关。
英文摘要:
      A model for the buckling analysis of plane orthotropic functionally graded micro-beams was developed on the basis of remodified couple stress theory. The model contains two material length scale parameters, which enables it to separately represent the different scale effects in two orthogonal directions. The present model can be degenerated to classical macroscopic model when the geometrical size of the beam is much larger than the material length parameter. The governing equations and boundary conditions are derived through principle of minimum potential energy and Timoshenko theory. A simply supported micro-beam is taken as the illustrative example and solved. The influences of material length scale parameter ,geometrical size ,and power law index on the buckling critical load and scale effects are analyzed. Numerical results indicate that the buckling critical load of the micro-beam predicted by the present model are always greater than those predicted by the classical FG beam model, i.e. the scale effects were reflected. The scale effects will be gradually weaken with the increasing of the geometrical size of the beam, and diminish when the geometrical size is much larger than the material length parameter. The scale effects influenced by the material length scale parameters of two directions are different. In addition, theinfluence of power law index on scale effects and buckling is conncted with material component distribution.
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