复合材料圆筒形薄壳热屈曲问题研究

发布时间：2018-01-03 22:36

本文关键词：复合材料圆筒形薄壳热屈曲问题研究　出处：《大连理工大学》2015年硕士论文　论文类型：学位论文

【摘要】：新型材料的出现给航空航天、汽车、医学等行业向着更高端产业发展带来了契机,但伴随着它的广泛应用也带来了诸多问题,比如力学问题就是大家所关注的一个重要方面,其中热屈曲力学行为成为当前研究的热点也是难点。为此本文借助Donnell薄壳理论推导了圆筒形薄壳热屈曲临界温升的理论解,研究了金属材料、功能梯度材料(FGM)和纤维树脂复合材料圆筒形薄壳的热屈曲行为,并结合有限元数值解验证和对比分析,对理论解进行修正。主要工作和结论如下：(1)根据Donnell简化准则,利用Timoshenko推导方法,通过联立几何方程、物理方程、平衡方程和边界条件,推导出金属材料圆筒形薄壳在均匀温升下的热屈曲理论解。然后利用有限元数值方法,得到金属圆筒形薄壳在均匀温升下的特征值,即临界温升。最后通过对比分析,进而提出修正系数,完善金属材料圆筒形薄壳在均匀温升下的热屈曲理论解。(2)分别根据Timoshenko推导方法和von Mises推导方法,推导出FGM圆筒形薄壳在均匀温升下的两种热屈曲理论解,结果显示两种理论推导结果误差小于1%,表明理论计算结果的一致性。同时利用有限元数值计算方法,求得FGM圆筒形薄壳在均匀温升下的特征值。通过比较理论解和数值解,进而提出修正系数,完善FGM圆筒形薄壳在均匀温升下的热屈曲理论解。(3)根据Donnell简化准则,利用von Mises方法,推导出纤维树脂材料圆筒形薄壳在均匀温升下的热屈曲理论解,并利用有限元数值方法,求得到纤维树脂材料圆筒形薄壳在均匀温升下的特征值,结果显示理论解与数值解最大误差低于16%,这是由于纤维材料各向异性及层间应力引起的误差所致。(4)综合理论推导和数值计算,结果均表明：金属材料圆筒形薄壳热屈曲临界温升与其弹性模量无关；FGM圆筒形薄壳临界温升值随着幂指数k的增加而增大;三种材料圆筒形薄壳热屈曲临界温升值与其几何长度无关,与其半径成反比。
[Abstract]:The emergence of new materials to aerospace, automotive, medical and other industries to the more high-end industry development opportunities, but with its wide application has also brought a lot of problems. Mechanics, for example, is an important aspect of concern. The thermal buckling mechanical behavior has become a hot topic and a difficult point in recent years. In this paper, the theoretical solution of the critical temperature rise of thermal buckling of cylindrical thin shells is derived by Donnell thin shell theory, and the metal materials are studied. The thermal buckling behavior of functionally graded material (FGM) and fiber resin composite cylindrical thin shell is verified and compared with finite element method. The main work and conclusions are as follows: 1) according to the Donnell simplification criterion, by using the Timoshenko derivation method, the simultaneous geometric equation and the physical equation are adopted. The equilibrium equation and boundary conditions are used to deduce the theoretical solution of thermal buckling of cylindrical thin shells with metallic materials under uniform temperature rise, and then the eigenvalues of thin cylindrical shells under uniform temperature rise are obtained by using finite element numerical method. That is, critical temperature rise. Finally, through comparative analysis, the correction coefficient is put forward. The theoretical solution of thermal buckling of cylindrical thin shell with metal material under uniform temperature rise is improved. (2) according to Timoshenko derivation method and von Mises derivation method, respectively. Two theoretical solutions for thermal buckling of FGM cylindrical thin shells under uniform temperature rise are derived. The results show that the errors of the two theories are less than 1%. It is shown that the theoretical results are consistent and the eigenvalues of FGM cylindrical thin shells under uniform temperature rise are obtained by using finite element numerical method. By comparing the theoretical and numerical solutions, the correction coefficients are proposed. The theoretical solution of thermal buckling of FGM cylindrical thin shell under uniform temperature rise is improved. (3) according to the Donnell simplified criterion, the von Mises method is used. The theoretical solution of thermal buckling of cylindrical thin shell with fiber resin under uniform temperature rise is derived, and the characteristic value of cylindrical thin shell of fiber resin material under uniform temperature rise is obtained by using finite element numerical method. The results show that the maximum error between the theoretical solution and the numerical solution is less than 16, which is caused by the anisotropy of fiber material and the error caused by interlaminar stress. The results show that the critical temperature rise of thermal buckling of cylindrical thin shell is independent of its elastic modulus. The critical temperature rise of FGM cylindrical shell increases with the increase of power exponent k. The critical temperature rise of thermal buckling of cylindrical thin shell of three kinds of materials is independent of its geometric length and inversely proportional to its radius.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB33

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