Interval Sensitivity Of Structural Static Displacement With Uncertain Parameters

In actual engineering situations, the structural parameters are often uncertain, such as inaccuracy of the measurement, error in the manufacturing process, invalidity of some components, etc. Although in most instances, error or uncertainties are likely to be small. But these errors or uncertainties may combine to make structural response have large deviations or unpredictability, especially in the multi-components system. Therefore, this paper presents a new method to estimate static structural displacements reanalysis with interval parameters.In this paper presents several method of static structural displacements reanalysis. When the structural parameters are small changes, that matrix perturbation method and Neumann series method, are both shown that the excellent results. But matrix perturbation method and Neumann series method are failure with the structural parameters more and more large. At this point, apply the Epsilon algorithm for static structural displacements reanalysis. Firstly, the Epsilon algorithm is introduced and expanded to vector series. Two methods, the Neumann series and the perturbation are used to construct the vector basis. The solution step is straight ward and it is easy to implement with the general finite element analysis system. The computational effort is much smaller than that of the full analysis of the modified structures.In a typical optimization process it is necessary to evaluate the response for numerous modified designs. For some of these designs, it is also necessary to evaluate the response derivatives. So, effective solution techniques for structural analysis and sensitivity are essential in the optimization of large-scale structures.In this paper, a unified approach for accurate approximations of displacements and displacement derivatives at various modified designs was presented. It was based on static displacement perturbation theory and Neumann Series. With the initial and modified stiffness, the explicit expression was constructed by Neumann expansion of the nodal displacements we needs. Unlike common approximations of the structural response, the approach presented is not based on calculation of derivatives. Rather, approximations of modified displacements are used to evaluate the modified displacement derivatives. Similar computational procedures were employed for evaluating displacements, first- and second-order derivatives of displacements. Numerical results show that accurate approximations of derivatives can be achieved with a small the approximations are based on results of a single exact analysis of initial design. The procedure is easy to implement, suitable for different types of design variables and structures and can be used with a general finite element system.Structural optimization and sensitivity analysis with FEM is based on accurate finite element model of structures and reasonable mathematical model of optimization problems. Modern commercial FEM software always involve sensitivity analysis module, which is used to find out the concerned variables quickly in the case of great number of variables. It is suitable to measure the weight of the variables to different estimation standard. However, the software usually calculates only the first-order derivatives which could not satisfy practical applications. The first-and second-order matrix computedby modified structures (10~7m) in static analysis are used to replaced thefirst- and second-order derivatives in Taylor series in this paper. When the structural parameters are parameters of interval of uncertainty, sensitive first-order Taylor expand and interval expansion, accordingly compute interval sensitive of static structural displacements. In paper presents the difference method for interval sensitive of static structural displacements. By comparing with the exact solutions and the difference method solutions, it is show that interval Taylor expansion more effective than difference method.For without the tedious iterative and inverse process, it can be used in general software to fill the gas of interval sensitivity.