A Temporally-piecewise Adaptive Scaled Boundary Finite Element Method For Solving The Fuzzy Uncertain Viscoelastic Problems

In recent years,as the rapid development of the transport systems,a large number of underground engineering construction are shaping increasingly,such as tunnel,slope,deep excavation engineering.A lot of geological disasters have occurred in the processes of engineering construction and operation,especially the fracture,hill-creep and large deformation,which caused by the rheological effect of concrete,rock and soil.These problems seriously affect the safety and normal operation of the construction,the accurate prediction of creep displacement and stress relaxation have become one of the main works of the current research.In addition,the creep and relaxation processes of geological materials are highly uncertain processes.In the past,most of the material parameters were considered as certainty problems,which often led to analysis errors.Fuzzy algorithm is one of the effective ways to solve uncertain problems.In view of the creep displacement and stress relaxation of geological materials under long-term sustaining load,the following aspects are mainly carried out:1 The viscoelastic temporally-piecewise adaptive scaled boundary finite element method theory is introduced,and its equations are derived.At first,the three parameter solid constitutive model is selected and its recursive constitutive equation is derived in the time domain.Based on the scaled boundary finite element method and the time domain adaptive technique,the adaptive scaled boundary element equations in time domain are derived,and the adaptive convergence condition is given.2 According to the transformation method of fuzzy theory,fuzzy processing of parameters is carried out,and fuzzy algorithm is verified by Monte-Carlo method.The program of the corresponing algorithm is compliled in Matlab language.3 Based on the temporally-piecewise adaptive scaled boundary finite element method,the viscoelastic creep model is constructed.Firstly,the creep displacement analysis model of the viscoelastic plate is built,and the influences of the variation of the parameters on the creep displacement are obtained.The fuzzy uncertainty analysis of creep displacement is carried out,and the influences of parameters,time step and tolerable error on fuzzy uncertainty of creep displacement are obtained.Then the fuzzy uncertainty analysis model of the creep displacement of the tunnel under the infinite domain is constructed,and the influences of the parameters,time step and the tolerable error on the fuzzy uncertainty of the creep displacement are obtained.4 Based on the scaled boundary finite element method,the stress singularity analysis model is constructed.Firstly,a relaxation stress analysis model of viscoelastic plate with a single edge crack is constructed,and the influences of the parameter variation on the relaxation stress of the singularity are obtained.The fuzzy uncertainty analysis of relaxation stress is carried out,and the influences of parameters,time step and tolerable error on fuzzy uncertainty of relaxation stress at singular point are obtained.Then,the fuzzy uncertainty analysis model of singularity heat conduction is constructed,and the fuzzy uncertain influences of thermodynamic parameters on the heat flux at singular point are obtained.The influences of the related parameters on the creep displacement and relaxation stress in the model are obtained by modeling and analyzing the viscoelastic creep displacement and singularity relaxation stress problems,which provide references for the further study of the geological materials' rheological problems.