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  本文選題：功能梯度多孔材料 + 物理中面��； 參考：《蘭州理工大學(xué)》2017年碩士論文

【摘要】：本文研究了兩種密度梯度分布模式(對稱結(jié)構(gòu)Model I和非對稱Model II)下,功能梯度多孔材料結(jié)構(gòu)(梁和圓板)的非線性力學(xué)行為,并詳細(xì)討論了材料的密度梯度性質(zhì)、邊界條件和機(jī)械載荷等因素對結(jié)構(gòu)彎曲、屈曲以及過屈曲等力學(xué)行為的影響。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線性力學(xué)行為。首先分別基于經(jīng)典梁理論、一階剪切變形梁理論以及物理中面的概念,利用能量法推導(dǎo)出熱載荷或橫向和軸向載荷作用下功能梯度多孔材料梁非線性靜態(tài)響應(yīng)的控制方程,然后直接求解該方程得到問題閉合形式的解析解。通過所得解析解,具體分析了加緊和簡支兩種邊界條件下,孔隙率、密度分布模式、細(xì)長比和外載荷對梁彎曲、屈曲以及過屈曲行為的影響。結(jié)果表明:熱載荷作用下,兩端夾緊和兩端簡支功能梯度梁的變形行為完全不同;孔隙率以及密度分布模式均對梁的彎曲和過屈曲有顯著的影響;細(xì)長比的的增加使得橫向剪切變形的影響減弱,從而經(jīng)典梁的無量綱臨界屈曲載荷高于剪切變形梁,其撓度則小于剪切變形梁。2)采用打靶方法數(shù)值地研究了功能梯度多孔材料圓板的非線性力學(xué)行為�；诮�(jīng)典板理論,利用能量法推導(dǎo)出橫向和徑向均布載荷作用下功能梯度多孔材料圓板非線性靜態(tài)響應(yīng)的控制方程,然后通過打靶法數(shù)值地求解所得控制方程。具體分析了夾緊和簡支兩種邊界條件下,孔隙率、密度分布模式、外載荷對軸對稱圓板彎曲、屈曲行為的影響。結(jié)果表明:孔隙率和密度分布模式均對圓板的彎曲和過屈曲有顯著的影響;合理的密度分布模式及恰當(dāng)?shù)目紫堵蔬x取,能有效的提高梁和圓板的力學(xué)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.
【學(xué)位授予單位】：蘭州理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TB34;O341

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本文編號：1893619