功能梯度多孔材料结构的非线性力学行为

发布时间：2018-05-15 19:30

本文选题：功能梯度多孔材料 + 物理中面　；参考：《兰州理工大学》2017年硕士论文

【摘要】：本文研究了两种密度梯度分布模式(对称结构Model I和非对称Model II)下,功能梯度多孔材料结构(梁和圆板)的非线性力学行为,并详细讨论了材料的密度梯度性质、边界条件和机械载荷等因素对结构弯曲、屈曲以及过屈曲等力学行为的影响。主要工作有:1)采用解析方法研究了功能梯度多孔材料梁的非线性力学行为。首先分别基于经典梁理论、一阶剪切变形梁理论以及物理中面的概念,利用能量法推导出热载荷或横向和轴向载荷作用下功能梯度多孔材料梁非线性静态响应的控制方程,然后直接求解该方程得到问题闭合形式的解析解。通过所得解析解,具体分析了加紧和简支两种边界条件下,孔隙率、密度分布模式、细长比和外载荷对梁弯曲、屈曲以及过屈曲行为的影响。结果表明:热载荷作用下,两端夹紧和两端简支功能梯度梁的变形行为完全不同;孔隙率以及密度分布模式均对梁的弯曲和过屈曲有显著的影响;细长比的的增加使得横向剪切变形的影响减弱,从而经典梁的无量纲临界屈曲载荷高于剪切变形梁,其挠度则小于剪切变形梁。2)采用打靶方法数值地研究了功能梯度多孔材料圆板的非线性力学行为。基于经典板理论,利用能量法推导出横向和径向均布载荷作用下功能梯度多孔材料圆板非线性静态响应的控制方程,然后通过打靶法数值地求解所得控制方程。具体分析了夹紧和简支两种边界条件下,孔隙率、密度分布模式、外载荷对轴对称圆板弯曲、屈曲行为的影响。结果表明:孔隙率和密度分布模式均对圆板的弯曲和过屈曲有显著的影响;合理的密度分布模式及恰当的孔隙率选取,能有效的提高梁和圆板的力学性能。
[Abstract]:In this paper, the nonlinear mechanical behaviors of functionally graded porous material structures (beams and circular plates) under two density gradient distribution modes (symmetric structure Model I and asymmetric Model II) are studied, and the density gradient properties of the materials are discussed in detail. The effects of boundary conditions and mechanical loads on the mechanical behavior of structures such as bending, buckling and post-buckling. The nonlinear mechanical behavior of functionally graded porous material beams is studied by analytical method. Firstly, based on the classical beam theory, the first order shear deformation beam theory and the concept of physical midplane, the governing equations of nonlinear static response of functionally graded porous material beams under thermal or transverse and axial loads are derived by using the energy method. Then the analytic solution of the closed form of the problem is obtained by solving the equation directly. The effects of porosity, density distribution model, slenderness ratio and external load on the bending, buckling and post-buckling behavior of beams under two boundary conditions, I. e. The results show that the deformation behavior of the clamped and simply supported functionally gradient beams is completely different under the thermal load, and the porosity and density distribution have significant effects on the bending and post-buckling of the beams. The increase of slenderness ratio weakens the influence of transverse shear deformation, so the dimensionless critical buckling load of classical beam is higher than that of shear deformation beam. The deflection is smaller than that of shear-deformed beam. (2) the nonlinear mechanical behavior of functionally graded porous circular plates is numerically studied by means of shooting method. Based on the classical plate theory, the governing equations of nonlinear static response of circular plates with functionally gradient porous materials under transverse and radial uniform loads are derived by using the energy method, and the control equations are solved numerically by the shooting method. The effects of porosity density distribution mode and external load on the bending and buckling behavior of axisymmetric circular plates under clamping and simply supported boundary conditions are analyzed in detail. The results show that both porosity and density distribution model have significant influence on bending and overbuckling of circular plates, and reasonable density distribution mode and proper porosity selection can effectively improve the mechanical properties of beams and circular plates.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB34;O341

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