基于Mori-Tanaka等效特性模型,研究了功能梯度材料变截面立柱在均布载荷作用下的过屈曲行为.考虑几何方程、本构方程及平衡方程,建立了功能梯度材料变截面立柱在均布载荷作用下的过屈曲控制微分方程,其中假设材料性质沿厚度方向按幂率变化.采用打靶法获得了由陶瓷氧化锆和金属钛合金两相材料组成的FGM变截面立柱的屈曲和过屈曲行为数值解.给出了不同变截面系数和不同梯度指数下立柱的过屈曲平衡路径和平衡构形.讨论了截面变化系数、材料梯度指数对立柱屈曲和过屈曲行为的影响.
Base on Mori-Tanaka scheme of equivalent properties, the post-buckling behaviors of a functionally graded material (FGM) column with variable cross sections under distributed load is considered in this paper.Considering of the geometric equation, physical equation and equilibrium equation of the deformed column, the governing differential equations of post-buckling of a FGM column with variable cross-section subjected to distributed load are established.It is assumed that the properties of the materials along the direction of the column thickness vary in a simple power law.The buckling and buckled behaviors of FGM variable cross-section column made of zirconia and Ti-6Al-4V are obtained by employing the numerical shooting technique.The equilibrium paths as well as the post-buckling configurations of the deformed column with different variable cross-section coefficient and different gradient index are presented.The effects of variable section coefficient and power law index of FGM on the buckling and post-buckling are discussed in details.
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