Deal With Fluctuations By Time Domain Boundary Element Method For Dual Inner Boundaries

The time domain boundary element method is an efficient and convenient numerical processing method.In recent years,it has attracted more and more researchers' attention,and it has developed rapidly with the rapid development of computers and other technologies.It is also very effective to deal with real-world engineering problems by time-domain boundary element method.Firstly,the relevant control equations of the actual problem are given,then the control equations are transformed to obtain the corresponding integral equations on the boundary,and then the integral equations are divided into Conditions or boundary elements of known conditions,so that the boundary integral equation can be discretized.Finally,the discretized boundary integral equations are assembled and solved by certain mathematical methods.This treatment greatly reduces the workload and requires calculation.It is only the unknowns on the boundary,which effectively reduces the difficulty of the original problem.In addition,because the time domain boundary element method introduces the basic solution,the time domain boundary element method has the characteristics of combining analysis and numerical values,so the obtained result has higher precision.In this dissertation,based on the classical single connected domain time domain boundary integral equation,the time domain boundary integral equation of the two connected domains is derived through the fictitious "channel",and the established double connected domain time domain boundary integral equation is numerically processed,including Re-discrete,assemble,and jointly solve.Compared with the classical single-connected domain time-domain boundary integral equation,the new boundary added in the double-connected domain time-domain boundary integral equation has no singularity in the integration process,and can be directly integrated.The non-singular integral part of the two-connected domain time domain boundary integral equation after discretization is processed by the combination of numerical method and finite integral method.For the integral part with singularity,Hadamard finite integral method is strictly used for processing.Moreover,the integration order of time and space is changed in the calculation process,so that the calculation amount is reduced a lot,and the obtained integration result becomes relatively simple.Therefore,the finite integral method with the singular integral Hadamard principal value can be used to improve the computational efficiency,which improves the ability of the boundary element method to solve practical problems.Finally,the dual connectivity domain time domain boundary element method is successfully applied.Solve the elastic dynamic double connected domain plane problem.After completing the theoretical derivation of the boundary equations of the two-connected domain,the Matlab software is used to program the time-domain integral equations of the two-connected domain to form a complete set of general procedures,and then the dual connected domain instances are selected for verification,thus verifying the dual connectivity.The correctness of the theoretical derivation of the domain time domain boundary integral equation and the effectiveness of programming.Finally,the two-connected domain time domain boundary integral equation is applied to the subway load problem,which embodies the practicability of the boundary element method in the dual connected domain period.