本文選題：二維FGM + 熱應(yīng)力��； 參考：《河北工程大學》2015年碩士論文

【摘要】：根據(jù)功能梯度材料的研究現(xiàn)狀,本文提出采用有限單元法研究2D-FGM平面在邊界溫度影響下冷卻過程中的瞬態(tài)熱應(yīng)力場問題。結(jié)合傅里葉定律和熱力學第一定律,推導出了二維熱傳導的微分方程。按照有限單元法的一般求解過程,對結(jié)構(gòu)進行網(wǎng)格劃分,求解出二維熱傳導的有限元方程,最后結(jié)合二維熱傳導的邊界條件,求出相應(yīng)的溫度場。為了確保有限元解的收斂性,引入了位移插值函數(shù)。當取一個單元分析時,可以求得對應(yīng)的單元節(jié)點應(yīng)力和節(jié)點位移的關(guān)系,將所有單元節(jié)點位移所產(chǎn)生的應(yīng)變勢能求和,結(jié)合單元體總勢能的表達式,即可得到平面熱應(yīng)力的有限元基本方程。本文研究的模型是常物性Al 1100/Ti-6Al-4V/Zr O2 FGM平板結(jié)構(gòu),在空隙、組分、位移邊界取固定值的前提下,根據(jù)Kerner細觀力學模型得到其物性參數(shù),使用FORTRAN語言編制冷卻瞬態(tài)熱應(yīng)力的有限元程序,分析對比解析解和程序解的誤差,檢驗程序的正確性。最后根據(jù)程序求解的結(jié)果,對冷卻瞬態(tài)熱應(yīng)力的規(guī)律進行分析,研究邊界溫度對二維功能梯度材料板冷卻瞬態(tài)應(yīng)力場影響。僅在2D-FGM平板上側(cè)設(shè)置不同的加熱邊界條件的結(jié)果表明:冷卻過程中板內(nèi)產(chǎn)生的是正應(yīng)力,應(yīng)力向板的溫度高的區(qū)域集中,常函數(shù)溫度函數(shù)對板內(nèi)的應(yīng)力影響大于其他三種溫度函數(shù),隨著邊界溫度增大,應(yīng)力增幅最大為150%,最小也達到了76.89%。在平板上側(cè)設(shè)置不同的溫度函數(shù),下側(cè)固定的溫度值和上側(cè)設(shè)置不同的溫度函數(shù),其他三邊設(shè)置固定的溫度值,可以得到類似上面的結(jié)果。所不同的是,內(nèi)部應(yīng)力集中的位置不同。因此,在實際應(yīng)用中,本文對不同的溫度邊界條件下的2D-FGM設(shè)計具有重要的參考意義。
[Abstract]:According to the research status of functionally graded materials, a finite element method is proposed to study the transient thermal stress field in the cooling process of 2D-FGM plane under the influence of boundary temperature. Combined with Fourier law and the first law of thermodynamics, the differential equation of two dimensional heat conduction is derived. According to the general solution process of finite element method, the finite element equation of two-dimensional heat conduction is solved by meshing the structure, and the corresponding temperature field is obtained by combining the boundary condition of two-dimensional heat conduction. In order to ensure the convergence of the finite element solution, the displacement interpolation function is introduced. When a element is analyzed, the relationship between the stress of the node and the displacement of the node can be obtained. The strain potential energy generated by the displacement of all the nodes of the element can be summed up, and the expression of the total potential energy of the element can be combined with the expression of the total potential energy of the element. The basic finite element equation of plane thermal stress can be obtained. The model studied in this paper is the constant physical properties Al 1100% Ti-6Al-4V / ZrO 2 FGM plate structure. The physical parameters are obtained according to the Kerner meso-mechanical model under the condition of the fixed values of the voids, components and displacement boundaries. The finite element program of cooling transient thermal stress is compiled by FORTRAN language. The error between the analytical solution and the program solution is analyzed and compared to verify the correctness of the program. Finally, according to the results of the program, the law of cooling transient thermal stress is analyzed, and the influence of boundary temperature on the cooling transient stress field of two-dimensional functionally graded material plate is studied. The results of setting different heating boundary conditions on the upper side of the 2D-FGM plate show that normal stress is produced in the plate during cooling, and the stress is concentrated in the high temperature area of the plate. The effect of the constant function temperature function on the stress in the plate is greater than that of the other three kinds of temperature functions. With the increase of the boundary temperature, the maximum stress increase is 150, and the minimum is 76.89. The same results can be obtained by setting different temperature functions on the upper side of the plate, fixed temperature values on the lower side and different temperature functions on the upper side, and fixed temperature values on the other three sides. The difference is that the internal stress concentration is different. Therefore, in practical application, this paper has important reference significance for 2D-FGM design under different temperature boundary conditions.
【學位授予單位】：河北工程大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TB34

【參考文獻】

相關(guān)碩士學位論文 前1條

1 張靖華;功能梯度材料梁、殼結(jié)構(gòu)的靜態(tài)力學響應(yīng)[D];蘭州理工大學;2004年

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本文編號：2061305