Application Of Wavelet Method For Solving Reliability Of Structure With Cracks

Based on the unique characteristic, aluminum alloys are widely used in the fields of aviation, marine platforms and so on. With the aggravation of environment, the structure’s service environment becomes more and more complex, so the structure’s damage accidents occurred more frequently than ever, and the process of structure destruction is complex, which is including from structural damage in micro-scale to structural failure in macro-scale. We have investigated this destruction process by using the wavelet multi-scale method which is widely used in other fields. Based on the theory of wavelet multi-scale methods and random model of fatigue multi-crack propagation, the CAS wavelet and Legendre wavelet were choosed as wavelet basis, then the wavelet basis was used to disperse random propagation equations, so the problem to solve differential equation of random propagation is transformed into solve algebraic equation. Then we could observe the propagation of fatigue crack in the scale from micro-scale to macro-scale.The main works of this paper are as follows:(1) Some of the relevant theories of wavelet multi-scale method such as Mallat arithmetic, integral operator matrix, CAS wavelets and Legendre wavelets are introduced in this paper.(2) The reliability of structures with cracks were solved under the general environment. In this thesis, Legendre wavelet and CAS wavelet combined with MATLAB programming are used to solve numerical solution of cracks propagation life respectively and provide the cracks propagation graphics, the crack growth rate will be increased when the time and lognormal random variables increased. Then use the complete integral reliability model to solve the reliability of structure with cracks, eventually it can got the trend of reliability versus life. With the time cumulating, the structure’s security reliability will be let down.(3) Based on solving reliability of structures which contain cracks under the general environment and combined with the environmental impact coefficient, the reliability of structure with cracks under the corrosive environment was solved.At last, the results of this paper have compared with the results of experiment and we have found that both results are very consistent, which indicates that solving the fatigue crack propagation by using the wavelet multi-scale method is feasible, and realize a smooth transition from short crack propagation to long crack propagation. The theoretical basis and calculation methods of structure with cracks which is in complex environments were provided.