Research On The Calculation Model And Method For The Dynamic Interaction Of Structure With Complex Layered Soil

The interaction of the complex layered unbounded domain with structure is an important part of the dynamic and static structure analysis.Accuratly modelling the radiation damping of unbounded domain is the important foundation to solve the interaction analysis.A number of research results show that the influence of complex layered unbounded domain on superstructure can not be ignored,expressly for the anisotropic medium.The unbounded foundation is mostly layered in practical engineering.However,in order to simplify calculation many researchers select the homogeneous foundation as study object.Hence,it is more practical significance to study the static and dynamic problems of the layered unbounded domain.Many experimental and numerical methods have been devoted to anayze the layered unbounded domain problems.However,there are few researches on the complex layered soil.Based on the research situation of the interaction action of the unbounded soil and structure,the present numerical methods are complex and the corresponding compute efficiency is not high for the large scale problems.This makes that many research results can not be widely promoted.Therefore,there is important practical significance and scientific research value to propose a new efficient method to model the complex layered unbounded medium.Based on the modified scaled boundary finite element method,a new numerical method is proposed to solve the complex layered unbounded domain problem.The continued fraction solution and the new transfer boundary for the layered medium are built.And the equation of motion for the modified scaled boundary finite element method is proposed.Then,the static and dyanamic characteristics of the complex layered medium are extensively studified and discussed.Only the computational domain surface needs to be discretized,so the geometric dimension is reduced by one and the calculated work is reduced.The prposed method need not the fundamental solution as the the boundary finite method,threrfore,the proposed method is more suitable for modeling the model with complex geometry.The definition of a scaling line which replaces the original scaling center makes the modified SBFEM be more suitable for analyzing the layered model.This avoids the approximate solution causing by seting the scaling center in infinity.Meanwhile,the substructure method for the modified scaled boundary finite element method is developed to delal with the inclined layered unbounded medium.The main contents in this paper are as follows:1.Based on the modified scaled boundary finite element method,the time domain model for the complex layered unbounded domain is established.The dynamic response for the complex layered medium is solved by the proposed method.In the proposed method,only the boundary needs to be discretized and no fundamental solution is needed,and the radiation boundary condition of unbounded domain can be satified automatically.The proposed method can directly model the layered medium by using the scaling line definition.By applying the weighted residual technique and the Hamilton variational principle,the modified scaled boundary finite element governing equation with isotropic and anisotropic medium are given respectively.A new continued fraction solution of the dynamic stiffness for the modified scaled boundary finite element is derived.By introducing the auxiliary variable,the second order differential governing equation is transformed into the first order differential equation.Therefore,it greatly simplifies the calculation.In order to eliminate the instabilities casing by the spurious modes in the system,the shift spectrum method is applied in this paper.The stability of numerical results has been improved and the computing scale is also reduced.In this paper,the precise integration method and the modified scaled boundary finite element method are coupled to solve the global motion equation for the anisotropic medium.The compute efficiency is improved by using the coupled method.The substructure method for the modified scaled boundary finite element is proposed to deal with the inclined layered model,and this technology extends the application range of the modified scaled boundary finite element method.The isotropic and anisotropic layered unbounded domain models are solved by using the proposed method.The accuracy of the proposed method is proved by comparing with the reference solution.The influences of anisotropic parameter,soft layer,tunnel and inclined layer on the results are discussed.2.The static bounded and unbounded domains models of the modified scaled boundary finite element are built.The static solutions for the side face load and side face displacement constraint are derived.And the new expressions of the side face force and side face restraint displacement are given.They are expressed in the exponential form of the radial coordinates.It is suitable for the satic analysis of the layered medium.The substructure method is applied to solve the bounded domain problem with hole.The proposed method can deal with the complexed bounded domain problem by using substructure method.The accuracy of the proposed method is present by analyzing the static response of numerical examples.The influences of anisotropic parameter,the form of side face force,load combination form and the model with hole on numerical results are dicussed in detail.It provides technical basis for the practical engineering design.3.A new wave propagation transfer boundary for the layered medium is built based on the acceleration unit impulse response.This method is suitable for the scalar and vector wave propagation problems of unbounded domain.It extends the application range of the modified scaled boundary finite element method.The solution process is only in the time domain in this method which avoids the error bringing by the time domain and frequency domain conversion.The acceleration unit impulse response is computed by using piecewise linear hypothesis and extrapolation parameter method.When the action time is bigger than the linear cut off time,the acceleration unit impulse response keeps linearly change.The convolution integral in time domain is avoided and the computational effect is improved.Meanwhile,the ne integral discrete scheme for the interaction force between the structure and unbounded domain is given.Then,the equation of motion for the layered unbounded domain is buit.The dynamic response of the layered unbounded domain can be solved.The accuracy of proposed method is proved by computing the scalar and vector unbounded domain problems.Then,the influences of cut off time and extrapolation parameter on the acceleration unit impulse response are discussed.The vibrational isolation effect of the groove in the complex unbouded domain with tunnel is analyzed.The proposed method can be used to analyze the complex problems.It illustrates that the proposed method has wide applicability range.4.The decoupled wave equation of the three dimensional layered half space is derived.By using Fourier-Bessel transform,the complex partial differention equation for the transversely isotropic layered half space is transformed into two ordinary differential equations.The wave equations are solved by applying the precise integration method.According to the relationship between displacement and stress,the adjacent layers can be assembled.The dynamic stiffness or dynamic compliance of layered half space with differed boundary conditions is solved by inverse transformation.The dynamic characteristics of layered half space soil are analyzed.The proposed method can directly model three dimensional layered unbounded domain problems by introducing the scaling line definition.According to the results of isotropic and anisotropic models,it can be seen that the proposed method has high precision.At last,the influences of anisotropic parameter on the dynamic results are analyzed.