發(fā)布時間：2018-10-31 17:33

【摘要】：在工程實際中，存在著很多影響結(jié)構(gòu)行為的隨機因素，傳統(tǒng)確定性分析方法未能精確考慮這些因素影響，分析結(jié)果很難全面反映結(jié)構(gòu)真實性能。開展隨機理論與確定性有限元相結(jié)合的隨機有限元分析方法，研究隨機因素對結(jié)構(gòu)行為影響，可以提高分析精度。許多長期處于海洋、工業(yè)、大氣等腐蝕環(huán)境下的鋼結(jié)構(gòu)工程，通常難以通過防護和構(gòu)造措施以及維修制度避免結(jié)構(gòu)發(fā)生銹蝕。結(jié)構(gòu)銹蝕后其截面厚度不再是恒定值，而是與銹坑分布和銹蝕深度相關(guān)的隨機過程。本文以銹蝕鋼結(jié)構(gòu)厚度隨機為研究問題出發(fā)點，建立基于截面厚度隨機銹蝕鋼結(jié)構(gòu)承載性能隨機有限元分析方法。本文主要研究工作如下： 1.應(yīng)用隨機場理論，對銹蝕構(gòu)件表面特征數(shù)據(jù)進行平穩(wěn)性和各態(tài)歷經(jīng)性檢驗，，研究結(jié)果表明，銹坑分布和深度隨機場是平穩(wěn)的且具有各態(tài)歷經(jīng)性，鋼結(jié)構(gòu)銹蝕深度隨機場可以用一個樣本函數(shù)的數(shù)字特征表示。本文應(yīng)用指數(shù)三角函數(shù)型模型模擬了銹蝕深度隨機場自相關(guān)函數(shù)，推導(dǎo)出銹蝕深度隨機場譜密度函數(shù)，建立了銹蝕深度隨機場，并由此推導(dǎo)出銹蝕后殘余厚度隨機場模型。 2.將銹蝕后殘余厚度隨機場引入確定性有限元分析中，把截面厚度表示為殘余平均厚度與隨機變化部分之和；把確定性有限元中的幾何矩陣分解為常數(shù)項矩陣與多項式乘積之和的形式，從而使單元剛度矩陣被分解為確定性剛度矩陣和偏剛度矩陣，并以此建立了四結(jié)點矩形薄板單元彎曲小撓度和大撓度問題隨機有限元分析理論。 3.根據(jù)建立的銹蝕薄板彎曲隨機有限元分析理論，編制了計算機程序，以此分析了銹蝕H型鋼偏心受壓承載性，并將有限元分析結(jié)果與試驗結(jié)果進行了對比分析。
[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.
【學(xué)位授予單位】：西安建筑科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：TU391

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