| Uncertainties are inevitable in realistic engineering applications,practical demand of quantitative analysis for uncertain problems has made new methods for treating uncertainties become important in virtually all branches of mechanics.In this thesis,three issues(i.e.viscoelasticity,transient nonlinear heat transfer and bimodular problems)are treated as research objects to explore numerical modelling methods of related forward /inverse problems with fuzzy uncertainties.The common characteristics of these issues are as follows: The solution of deterministic problem is complex,time-consuming and its computing accuracy and efficiency are affected by many factors.The deterministic problem generally needs to be solved repeatedly in the process of uncertainty analysis,which makes it more difficult to solve related uncertain problems and also poses new challenges solution methods in terms of computational accuracy and efficiency.As one of the non-probabilistic uncertainty methods which only need a small amount of prior knowledge,fuzzy method is becoming increasingly popular for the analysis of numerical models that incorporate uncertainty in their description in recent years.Although several investigations on fuzzy problems have been involved in many engineering fields and disciplines,and various inspiring achievements have been made,there are few reports directly related to the studied three issues,particularly to the inverse fuzzy analysis.This thesis mainly focuses on the following aspects:(1)Computational accuracy and efficiency of the deterministic forward problem;(2)Numerical modelling of fuzzy forward problem based on α-cut strategy,and the computational accuracy and efficiency of interval estimation required for each α-cut level;(3)Numerical modelling of fuzzy inverse problem based on α-cut strategy,and computational accuracy and efficiency of solving the inverse fuzzy problem.With the above consideration,the following work has been carried out:(1)Combining a temporally piecewise adaptive algorithm with scaled boundary finite element method or finite element method,a new method has been proposed to solve the time-dependent deterministic viscoelasticity and transient nonlinear heat transfer problem,which renders a stable temporal computing accuracy when the time step changes and needs no iteration,and makes it convenient for the adaptive computing of derivatives.For deterministic bi-modular problem,a nonlinear finite element algorithm based on smoothed constitutive model and sensitivity analysis is adopted to improve the computational efficiency of solving nonlinear problem;(2)For the studied three issues,α-cut strategy based numerical models for fuzzy forward problems have been proposed.The optimization method is applied to solve interval problem at each α-cut level.It can avoid the interval overestimation by interval arithmetic,and the restriction of small interval scale by perturbation/Taylor expansion algorithm.It can also ensure the accuracy of interval estimation.Meanwhile,sparse grid interpolation based surrogate models have been constructed for the studied three issues and combined with parallel computing strategy to improve the efficiency of optimization method.Additionally,a hybrid interval estimation method based on Taylor expansion and optimization method has been proposed,which can take into account the computing accuracy and efficiency.It can not only be used to solve the transient nonlinear heat transfer problem with full-scale interval,but also is expected to be combined with the α-cut strategy to further improve the computational efficiency of fuzzy analysis;(3)For the studied three issues,α-cut strategy based numerical models for fuzzy inverse problems have been established.Numerical methods with sparse grid interpolation based surrogate model and particle swarm optimization algorithm have been proposed,which are combined with parallel computing technology to improve the computational efficiency of interval inverse problem at each α-cut level.Additionally,for the fuzzy viscoelastic inverse problem,a two-stage inverse strategy has been proposed to reduce the scale of inverse problem;(4)All the proposed methods have been numerically verified,and the impacts of several related factors on computing accuracy and efficiency are investigated.Numerical results show that for the studied three issues:the proposed methods of forward fuzzy problems can successfully predict membership functions of the output responses(e.g.displacement and temperature)when physical parameters are fuzzy-uncertain;the proposed methods of inverse fuzzy problems can effectively identify membership functions of the input parameters in a single/combined manner when the measurement information is fuzzy-uncertain.This thesis not only provides effective numerical methods for the forward and inverse fuzzy analysis of the studied three issues,but also gives a valuable reference for other time-dependent or nonlinear problems with fuzzy uncertainties.Additionally,as the numerical methods for forward/inverse fuzzy problems proposed in this thesis are all α-cut strategy based interval analysis,so these methods can also be applied to solve the related forward/inverse problems with interval uncertainties. |
