基于有限体积法的结构随机分析及结构系统疲劳可靠性分析

发布时间：2018-06-27 19:51

本文选题：结构系统 + 有限体积法　；参考：《哈尔滨工程大学》2015年博士论文

【摘要】：在结构的分析和设计中,考虑各种随机因素影响的观点逐步被学者们接受。开展结构随机分析与结构系统可靠性分析具有十分重要的意义。目前,结构元件的可靠性理论的发展已经比较成熟,但是结构系统可靠性理论的发展相对而言比较迟缓。如何给出结构响应量与随机变量之间的显式表达式是结构随机分析与结构系统可靠性分析的难点之一,这一问题尚未得到很好的解决。因此,本文针对该问题提出了采用有限体积法研究结构的随机分析及结构系统可靠性分析,该方法能够很好的解决这一难点问题。有限体积法在计算流体力学领域应用广泛。该方法思想简单、容易实施,且得到的方程具有明确的物理意义,其因变量在控制体上满足积分守恒。在解决结构动力学随机分析问题时,有限体积法采用显式算法,能够给出结构响应量与随机变量之间的显式表达式,使得结构动力学的随机分析问题容易实现,为结构系统可靠性分析奠定了理论基础。根据有限体积法的基本理论,建立了有限体积法的基本控制方程,采用非结构化网格推导了有限体积法控制方程的数值离散计算格式,并给出了求解结构静力学与结构动力学问题的基本过程。并通过算例分析,将有限体积法的计算结果分别与解析解和有限单元法的计算结果进行了对比,验证了该方法的正确性,也证明了该方法具有较好的计算精度和较高的计算效率。开展了基于有限体积法的实体结构静力学随机分析。将摄动法与有限体积法结合,建立了实体结构的静力学随机分析的基本模型,推导了结构的静力学随机分析的基本方程,并通过自编的计算机程序计算了实体结构的静力学随机分析问题,并用蒙特卡罗法验证了该方法的正确性,也证明了该方法具有较高的计算效率,可为结构可靠性分析提供理论基础。研究了基于有限体积法的实体结构的动力学随机分析问题,结合摄动法与有限体积法建立了实体结构随机分析的基本方程,推导了结构响应量与随机变量之间的显式表达式,并给出了实体结构动力学随机分析问题的基本求解过程。考虑载荷与结构具有随机性,计算了实体结构动力学随机分析问题,并与蒙特卡罗法的计算结果进行对比,证明了该方法的正确性和可行性,解决了结构随机分析及可靠性分析的一个难点问题。最后,基于有限体积法研究了实体结构系统的疲劳可靠性分析问题。建立了实体结构系统的疲劳可靠性分析模型,提出了基于有限体积法的结构系统疲劳失效的判别准则,给出了搜索结构系统主要失效模式的基本过程,计算了实体结构系统的疲劳失效概率和可靠度,得到的结果是符合实际的,为进一步在工程中的应用提供了理论参考。
[Abstract]:In structural analysis and design, the idea of considering the influence of various random factors has gradually been accepted by scholars. It is very important to carry out random structural analysis and structural system reliability analysis. At present, the reliability theory of structural components has been developed more mature, but the reliability theory of structural systems is relatively slow. How to give the explicit expression between structural response and random variables is one of the difficulties in structural stochastic analysis and structural system reliability analysis, which has not been solved well. Therefore, in this paper, the finite volume method is used to study the stochastic analysis of structures and the reliability analysis of structural systems. This method can solve this difficult problem very well. Finite volume method is widely used in computational fluid dynamics. The method is simple and easy to implement, and the equations obtained have clear physical significance, and the dependent variables satisfy the conservation of integrals on the control body. In solving the stochastic analysis problem of structural dynamics, the explicit algorithm is used in the finite volume method, and the explicit expression between the structural response quantity and the random variables can be given, which makes the stochastic analysis problem of structural dynamics easy to realize. It lays a theoretical foundation for reliability analysis of structural system. According to the basic theory of the finite volume method, the basic governing equation of the finite volume method is established, and the numerical discrete calculation scheme of the control equation of the finite volume method is derived by using the unstructured grid. The basic process of solving structural statics and structural dynamics problems is also given. The results of finite volume method are compared with those of analytical solution and finite element method, and the correctness of the method is verified. It is also proved that this method has better calculation accuracy and higher calculation efficiency. The statics random analysis of solid structures based on finite volume method is carried out. By combining perturbation method with finite volume method, the basic model of statics random analysis of solid structure is established, and the basic equation of statics random analysis of structure is derived. The static random analysis problem of solid structure is calculated by computer program, the correctness of the method is verified by Monte Carlo method, and the efficiency of this method is proved. It can provide a theoretical basis for structural reliability analysis. The dynamic stochastic analysis of solid structures based on finite volume method is studied. The basic equations of stochastic analysis of solid structures are established by means of perturbation method and finite volume method. The explicit expressions between structural responses and random variables are derived. The basic process of solving the stochastic analysis problem of solid structure dynamics is also given. Considering the randomness of load and structure, the stochastic analysis problem of solid structure dynamics is calculated, and compared with the result of Monte Carlo method, the correctness and feasibility of the method are proved. A difficult problem of stochastic analysis and reliability analysis is solved. Finally, the fatigue reliability analysis of solid structure system is studied based on finite volume method. The fatigue reliability analysis model of solid structure system is established, and the criterion of fatigue failure based on finite volume method is proposed, and the basic process of searching the main failure modes of structure system is given. The fatigue failure probability and reliability of the solid structure system are calculated, and the results are in line with the reality, which provides a theoretical reference for further application in engineering.
【学位授予单位】：哈尔滨工程大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TB114.3

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