Response Boundary Calculation And Reliability Analysis Of The Structures Under Uncertain Time-varying Parameters

There are a lot of uncertainty in the practical engineering.Reliability and response boundary of structure are uncertain when the structure parameters or external load is uncertain and time-varying.Therefore,this paper uses interval process theory and stochastic process theory to calculate the response bounds and analyse reliability of structure under uncertain time-varying parameters.The main research contents are as follows:(1)By introducing the interval process theory into the random vibration analysis of the elastic beam,a non-random vibration analysis method of the elastic beam is proposed in this paper to efficiently solve the dynamic displacement response bounds for the elastic beam under uncertain excitations.Firstly,based on the interval process model,the conception of the spatial-time interval field and corresponding characteristic parameters are given to describe the uncertainty of excitations applied to the elastic beam in spatial and time domain.Secondly,the middle point function and radius function of the displacement response for the elastic beam are deduced based on the mode superposition method,hence the analytical formulation of the upper and lower displacement response bound function of the elastic beam is obtained.In addition,the displacement response bound functions of the simply supported beam structure under two forms of external excitations are given.Finally,several numerical examples are investigated to demonstrate the effectiveness of the proposed method.(2)To analyse the dynamic response of elastic beam displacement more accurately,the fractional derivative is used to describe the damping mechanism of the elastic beam.In this formulation,the modal superposition method is employed to convert the differential equations of fractional damping beam into a series of decoupling equations.A Laplace transform technique is used to obtain the fractional Green's function,the Duhamel's integral is used to obtain the displacement response of fractionally damped beam.For interval field description,it's same to the integer damped beam.Numerical example shows that the dynamic displacement response bounds of the fractionally damped beam in uncertain excitation are similar to the integral damped beam.The fractional derivative model can describe the physical properties of the elastic beam more accurately,the more accurate dynamic displacement response boundary of beam structure can be obtained in non-random vibration analysis.(3)To analyse the time-variant reliability of structure by Monte Carlo simulation,a great deal of performance function calls lead to the large computational cost.Therefore,the first-order approximate model of the time-variant performance function is proposed.The time-variant reliability of structure can be calculated by the Monte Carlo simulation based on the model,which provides an efficient tool for assessing reliability of a complex structure.Using time discretization,the design lifetime can be divided into a number of time quantum.The most probable point(MPP)of the time-variant performance function can be searched by the first-order reliability method(FORM)and interpolation method.Finally,the first-order approximation model is obtained with the Taylor expansion method in MPP.The efficiency and accuracy of the algorithm is verified by several examples.This algorithm can be utilized for reliability analysis of complex practical engineering problems.