边界温度对二维梯度材料板冷却瞬态应力场影响

发布时间：2018-06-24 11:01

本文选题：二维FGM + 热应力　；参考：《河北工程大学》2015年硕士论文

【摘要】：根据功能梯度材料的研究现状,本文提出采用有限单元法研究2D-FGM平面在边界温度影响下冷却过程中的瞬态热应力场问题。结合傅里叶定律和热力学第一定律,推导出了二维热传导的微分方程。按照有限单元法的一般求解过程,对结构进行网格划分,求解出二维热传导的有限元方程,最后结合二维热传导的边界条件,求出相应的温度场。为了确保有限元解的收敛性,引入了位移插值函数。当取一个单元分析时,可以求得对应的单元节点应力和节点位移的关系,将所有单元节点位移所产生的应变势能求和,结合单元体总势能的表达式,即可得到平面热应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平板结构,在空隙、组分、位移边界取固定值的前提下,根据Kerner细观力学模型得到其物性参数,使用FORTRAN语言编制冷却瞬态热应力的有限元程序,分析对比解析解和程序解的误差,检验程序的正确性。最后根据程序求解的结果,对冷却瞬态热应力的规律进行分析,研究边界温度对二维功能梯度材料板冷却瞬态应力场影响。仅在2D-FGM平板上侧设置不同的加热边界条件的结果表明:冷却过程中板内产生的是正应力,应力向板的温度高的区域集中,常函数温度函数对板内的应力影响大于其他三种温度函数,随着边界温度增大,应力增幅最大为150%,最小也达到了76.89%。在平板上侧设置不同的温度函数,下侧固定的温度值和上侧设置不同的温度函数,其他三边设置固定的温度值,可以得到类似上面的结果。所不同的是,内部应力集中的位置不同。因此,在实际应用中,本文对不同的温度边界条件下的2D-FGM设计具有重要的参考意义。
[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.
【学位授予单位】：河北工程大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB34

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