Random Excitation, Optimal Design, Based On The Structure Of Power Reliability

During the period of their serves, many engineering structures are inevitable to endure time-dependent random loads, and dynamic damage or failure will be the main failure modes. Therefore, it is important both on theory and practical application to perform the dynamic reliability analysis for the structure existing and optimize the design variables based on the reliability for those to be built. The main purpose of this dissertation is to establish the deterministic and the stochastic model of minimum weight of the structure, and the optimization is based on the structural dynamic response reliability. The dynamic response of the structure under stationary or non-stationary excitations is investigated, then the dynamic reliability is calculated and the design variables of the structures are optimized. The main work and achievements are summarized as follows:According to the spectrum analysis theory, the simple formula of the power spectrum between the excitation and the response is obtained. Then the time-domain statistical properties of the structural response are acquired through Fourier inverse transform, and Cauchy's residue theorem is applied to solving the integral of Fourier inverse transform, the structural dynamic reliability is calculated in terms of Possion hypothesis based on first passage failure. At last the structural design variables are optimized, and the basis of deterministic model is established.Based on Priestley's evolutionary spectrum theory, an evolutionary process modulated by decline composite exponential function, is investigated as one kind of non-stationary excitation commonly encountered in engineering, the analytical solution of the response properties is gained due to proper simplification. Then, according to two-state Markov hypothesis and the structural system reliability theory, the structural reliability is computed, and the optimization is achieved. This method can improve efficiency greatly compared with the popular algorithm.The minimum-weight model of stochastic structures under time-dependent random excitations is established based on the structural dynamic reliability. Pseudo Excitation Method (PEM) is used, thus one random process excitation can be transformed into a deterministic transient excitation, so the joint-random problem is turned into a single-random problem accurately, it can be solved easily by meansof perturbation method and sequence orthogonal decomposition theory respectively.The probabilistic approach is used to transform stochastic optimization into deterministic optimization, therefore the optimization can be achieved through multiple objective decision making theory. Optimal objectives is extended from single to multiple, this method is more appropriate to practical application.In conclusion, the structural optimization method based on the dynamic reliability is successfully established, and the research in this paper lays a foundation for further theoretical investigation and practical application.