Study On Mixed Constraint Modal Synthesis Method For Local Nonlinear Of Soil-structure Interaction

In recent years, the study of soil-structure interaction has been progressively extended and deeply. As the problem models are bigger and wider, the degree of element nodes is so much that it needs highly computing device and a long time to calculate. Moreover different working cases will take multiple workload. A feasible calculation method which meets the calculation accuracy and saves the calculation cost is extraordinary needed. Dynamic substructure method divides the soil-structure interaction system into several subsystems. Firstly the monomer reaction of each subsystem is respectively solved, and then the response of each monomer is assembled to make it comply with the conditions of interaction. The reaction of the whole system is addressed. Dynamic substructure method reduces greatly the amount of calculation. It is just an ideal calculation method, but this method can only solve the linear problem.Depending on the research of local nonlinear problem, the linear and nonlinear mixed constraint modal synthesis method was proposed. The specific implementation of the method was investigated. For making the full advantage of the existing commercial software, the method implementation was combined with ANSYS software. By the thorough analysis and research on the structure stiffness matrix extraction method during the whole process, the equivalent elasticity modulus of elastic-plastic model; the uniform viscoelastic boundary and nonlinear contact problem, the mixed constraint modal synthesis method can solve the complex conditions of soil- structure interaction system It opened up a research area of dynamic substructure method.In this paper, the main achievements and innovation work are as follows:1. Implementation of mixed constraint modal synthesis method modal in ANSYS was studied firstly to solve the seat number problem of stiffness matrix extraction. Founded on the four methods of ANSYS secondary development. The secondary development tools UPFs was used to extract matrix by the FORTRAN language. The matrix was extracted by self-programming in accordance with the order of the node number from small to large.2. The nonlinear stiffness matrix extraction of substructure in the plastic phase is one of the difficult work in this paper. In order to generate the elastic-plastic stiffness matrix at a certain moment in the nonlinear time history analysis, the nonlinear plastic area was put forward to the equivalent linear elastic region. Using piecewise equivalent linearization method in a small period of time in the plastic stage, each plastic unit was equivalent to elastic. The formula of equivalent elastic modulus was deduced. Using ANSYS multipoint restart, the structure can continue to the next moment analysis. The operation and control method between ANSYS and MATLAB was proposed. General analysis by an example model, including nonlinear static Pushover analysis and simple harmonic dynamic time history analysis, the time history response curves were obtained. Those curves matched good with the ANSYS direct calculation method. It is verified that the matrix extraction method in elastic-plastic stage by the secondary development program files was feasible.3. Local nonlinear foundation soil- shear wall structure interaction model was established. Based on local nonlinear characteristics, the area which not entered nonlinear phase was divided into several linear substructure, and the other was divided into several nonlinear substructures. A detailed analysis process and the development program of mixed constraint modal synthesis method were written. The implementation process between ANSYS and MATLAB were emphasized.4. In the soil- structure interaction analysis model, the uniform viscoelastic boundary conditions were brought into the soil boundary to simulate the soil semi-infinite domain. The equation of substructure with uniform viscoelastic boundary was derived.The potential energy criterion of truncation criterion was demonstrated to apply on linear substructure with uniform viscoelastic boundary. It is shown that the method also can deal with complex boundary issues.5. By choosing reasonable target elements and contact elements, iterative calculating contact stiffness and setting up the friction coefficient, the highly nonlinear contact problem was brought in the dynamic substructure method. The processing method of contact relations between box foundation and soil was proposed. The analysis method for the contact element was divided in two. The target surface was delimited into the linear box foundation substructure of the highly stiffness, and the contact surface was delimited into the nonlinear soil around substructure of the low stiffness. The linear and nonlinear modal synthesis equations of the contact relationship between the box foundation and soil around was derived. It broadened the application fields of mixed constraint modal synthesis method.6. Through some examples calculation, the linear and nonlinear soil area was given a recommended range. When setting the uniform viscoelastic boundary, the nonlinear substructure area is two times the base width, and the linear substructure areas of both sides were 1.5 times the base width. The overall model freedom degree was less than using a general model. The computational efficiency was improved.7. The mixed constraint modal synthesis method was extended to three dimensional soil-structure interaction analysis. The research is primarily focused on the difference with two dimensional modal problems. The substructure equation with uniform viscoelastic boundary condition was deduced afresh for the three dimensional problem. The linear and nonlinear modal synthesis equations of the contact relationship between the box foundation and soil around of three dimensional model was derived afresh. The formula of equivalent elasticity modulus was deduced afresh. The results showed that the mixed constraint modal synthesis method can solve the problem of three dimensional complex soil- structure interaction.8. In implementation of the mixed constraint modal synthesis method, due to gradually extract the elastic-plastic stiffness matrix and the eigenvalue equation calculation in the whole stage analysis, the change rule of the first n order main frequency and vibration model was known. So the structural stiffness change rule in elastic-plastic stages was also understood. It provided support for analyzing the structural system research.