随机有限元法在锈蚀钢结构承载性能中的应用

发布时间：2018-10-31 17:33

【摘要】：在工程实际中，存在着很多影响结构行为的随机因素，传统确定性分析方法未能精确考虑这些因素影响，分析结果很难全面反映结构真实性能。开展随机理论与确定性有限元相结合的随机有限元分析方法，研究随机因素对结构行为影响，可以提高分析精度。许多长期处于海洋、工业、大气等腐蚀环境下的钢结构工程，通常难以通过防护和构造措施以及维修制度避免结构发生锈蚀。结构锈蚀后其截面厚度不再是恒定值，而是与锈坑分布和锈蚀深度相关的随机过程。本文以锈蚀钢结构厚度随机为研究问题出发点，建立基于截面厚度随机锈蚀钢结构承载性能随机有限元分析方法。本文主要研究工作如下： 1.应用随机场理论，对锈蚀构件表面特征数据进行平稳性和各态历经性检验，，研究结果表明，锈坑分布和深度随机场是平稳的且具有各态历经性，钢结构锈蚀深度随机场可以用一个样本函数的数字特征表示。本文应用指数三角函数型模型模拟了锈蚀深度随机场自相关函数，推导出锈蚀深度随机场谱密度函数，建立了锈蚀深度随机场，并由此推导出锈蚀后残余厚度随机场模型。 2.将锈蚀后残余厚度随机场引入确定性有限元分析中，把截面厚度表示为残余平均厚度与随机变化部分之和；把确定性有限元中的几何矩阵分解为常数项矩阵与多项式乘积之和的形式，从而使单元刚度矩阵被分解为确定性刚度矩阵和偏刚度矩阵，并以此建立了四结点矩形薄板单元弯曲小挠度和大挠度问题随机有限元分析理论。 3.根据建立的锈蚀薄板弯曲随机有限元分析理论，编制了计算机程序，以此分析了锈蚀H型钢偏心受压承载性，并将有限元分析结果与试验结果进行了对比分析。
[Abstract]:In engineering practice, there are many random factors which affect the behavior of structure. The traditional deterministic analysis method can not accurately consider these factors, so it is difficult to fully reflect the real performance of the structure. A stochastic finite element analysis method combining stochastic theory with deterministic finite element method is developed to study the influence of random factors on structural behavior and the accuracy of the analysis can be improved. Many steel structures which have been in the environment of marine, industrial and atmospheric corrosion for a long time are usually difficult to avoid structural corrosion by means of protective and structural measures and maintenance systems. The thickness of the section after corrosion is not a constant value, but a stochastic process related to the distribution of rust pits and corrosion depth. Based on the random thickness of corroded steel structures, a stochastic finite element analysis method for bearing capacity of corroded steel structures based on section thickness is established in this paper. The main work of this paper is as follows: 1. The random field theory is used to test the stability and ergodic properties of surface characteristic data of corroded components. The results show that the distribution of rust pits and depth random fields are stable and ergodic. The corrosion depth random field of steel structures can be expressed as a numerical feature of a sample function. In this paper, the exponential trigonometric function is used to simulate the corrosion depth random field autocorrelation function, the corrosion depth random field spectrum density function is derived, and the corrosion depth random field is established, and the model of the corroded residual thickness random field is derived. 2. The residual thickness after corrosion is introduced into the deterministic finite element analysis, and the thickness of the section is expressed as the sum of the residual mean thickness and the random variation part. The geometric matrix in deterministic finite element is decomposed into the sum of constant term matrix and polynomial product, so that the element stiffness matrix is decomposed into deterministic stiffness matrix and partial stiffness matrix. The stochastic finite element analysis theory of four node rectangular thin plate element with small bending deflection and large deflection is established. 3. Based on the theory of stochastic finite element analysis of corroded thin plate bending, a computer program is developed to analyze the eccentric bearing capacity of corroded H-section steel, and the finite element analysis results are compared with the experimental results.
【学位授予单位】：西安建筑科技大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TU391

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