Bearing Capacity Of Corroded Steel Structure With Stochastic Finite Element Method

There are a certain amount of random factors which affect structural behavior inapplication of engineering structures，traditional deterministic analysis method does notconsider the impact of these factors accurately which leading to the results of theanalysis unscientific. To develop stochastic finite element method which combinesstochastic theory with deterministic finite element to analyze the responses of structurewith stochastic factors can improve the accuracy of analysis. Steel structure whichpersist in the ocean air, industrial air and other corrosive environment appearedcorrosion which is difficult to avoid by constructing and protective measures, andmaintenance system. Its cross-sectional thickness is no longer a constant value whichchanged with rust pits distribution and corrosion depth after corroded. For the factorsthat based on cross-sectional thickness with random variation，in this paper stochasticfinite element method based on thickness with random variation are developed forbearing capacity of corroded steel structure. The main work of the thesis is mainlyconcerned with the following three aspects.1. Use the random field theory to test the surface characterization data of thecorrosion steel member which proofed that corrosion pit distribution and depthstochastic field was stationary and ergodic，so that the information of the wholestochastic field of corrosion depth can be used numerical characteristics of a samplefunction to represent. Using the exponential and the trigonometric function model tosimulate the autocorrelation function of corrosion depth random field，the corrosion depth random field is established，then the corrosion residual thickness random field isproposed.2. The stochastic field of corrosion residual thickness is introduced into thedeterministic finite element，the cross-sectional thickness is expressed as the sum of theresidual average thickness and the random variation；The geometry matrix of thedeterministic finite element is decomposed into the form of the sum of constant matrixand polynomial multiplication， so that the stiffness matrix is decomposed intodeterministic stiffness matrix and deviatoric stiffness matrix，and then the stochasticfinite element theory for bending deflection and large deflection of four-noderectangular element for thin plates is established.3. Applied the corrosion of steel structure stochastic finite element theory to write acomputer program, the corrosion H-shape steel eccentric compression bearing capacityis analyzed according to the program, and then finite element analysis and experimentalresults were compared and analyzed.