Study On Time Domain Boundary Element Method For Elastoplastic Dynamic Problems Based On Strain-Softening Constitutive Model

As a numerical method,the boundary element method has got rapid growth due to its small amount of calculation and high accuracy.There are three methods of BEM to solve elastoplastic problems.They are methods which is based on fundamental solution of statics,dual reciprocity boundary element method(DR-BEM)and time domain boundary element method(TD-BEM)which is used to establish the boundary integral equation on the basis of dynamic fundamental solution.However,the study on dealing with the elastoplastic dynamics plane problem through the TD-BEM has just started.This study is faced with the following problems.The first problem is the establishment of the time domain boundary integral equation.There will be integral terms within the domain,especially when the elastoplastic problem is taken into consideration,which makes the equations underdetermined.The second one is the processing of singularity.Singularity is the most difficult problem to hinder the development of boundary element because it causes the instability of the calculation results.For the above problems,the content of this paper is as follows:When the TD-BEM is adopted to deal with the strain-softening problem,the coefficients in the integral equation should be recalculated.Meanwhile,the emergence of equivalent stress fundamental solution marks that the TD-BEM will be able to applied to solve the plane strain dynamics problems.To reduce the running time of the program,the compiling of parallel computing program in this paper is completed in the Matlab program.Restricting the development of boundary element,the processing of singularity has always been researched by numerous boundary element scholars.The researcher Li Hongjun originally adopts the Hadamard principal value integrals to process singularity,which has been so far the most effective and efficient method to process singularity.This paper continues to apply this method to process singularity and compile the corresponding Matlab program.To consider the traditional metal materials,after the discrete value,unit solving and matrix assembly of the boundary integral equation,the underdetermined algebraic equations is obtained.It is necessary to introduce elastoplastic constitutive relation to eliminate the indeterminateness of the equation.When the elastoplastic constitutive relation is given,how to introduce the algebraic equations is the difficulty to realize the numerical computation.Because in the stress space,it's hard to judge it's loading or unloading,when processing the strain softening problem based on the Mises yield criterion,this paper adopts the equivalent strain method in the strain space.In this way,the application of classic strain-softening constitutive model in the application of the time-domain boundary element is perfectly solved.To verify the correctness,the cantilever slab and infinite domain hole problems are chose to calculate.For geotechnical materials,when processing the strain softening problem based on the D-P yield criterion,it's necessary to consider the effect of mean stress on yield condition.To apply the constitutive model in the time-domain boundary element,it also needs to process the model in the strain space.After the theoretical part is completed,infinite domain hole problem is used for the geotechnical materials to prove the validity of the program.