Study On Elastodynamics By Time Domain Boundary Element Method For Cylindrical Cavity

At present,in view of engineering practical problems,due to the complexity of geometric shapes,physical properties and boundary conditions,numerical analysis methods are often used to solve it.Among them,compared with the finite element method,boundary element method(BEM)is also one kind of numerical analysis methods which only needs to discrete on the boundary.So,it can cut down one dimension so that the calculation amount can be effectively reduced.This is a significant highlight of BEM.The load of the dynamic problem changes with time,and the boundary integral equation contains time parameters.At this time,the time domain boundary element method becomes an efficient numerical analysis method to deal with the problem.This numerical analysis methods has been studied for plane problem and smooth boundary.In this dissertation,the three-dimensional problem of elastic dynamics of cylindrical cavity is studied by using time domain boundary element.Firstly,the traditional three-dimensional dynamic fundamental solution is transformed into a new form that is easy to integrate.The coefficient generated by the form in the process of integration is highly targeted and it is easy to distinguish its singularity type.Then,for the problem of discontinuity of surface force generated by the outer normal line at the geometrically unsmooth corners on the boundary,this dissertation establishes an additional equation based on the uniqueness of the strain tensor and the invariance of the stress tensor state.In the displacement field,this indicates a wider application in nonlinear and dynamic problems.In the process of solving the formed matrix equations after numerical processing of the boundary integral equation,the singularity generated in the time domain and the spatial domain are processed separately: the finite integration method is adopted for the singularity in the spatial domain,and the integration process is relatively simple.At the same time,the computational efficiency is also greatly improved.For the wavefront singularity in the time domain,the nature of the step function and the Dirac function is eliminated.For non-empty,singularity is calculated by Gaussian numerical integration method.Finally,for the cylindrical cavity model,this dissertation uses MATLAB program to compile a set of pre-processing meshing program,and refines the midpoint in the custom initial triangle mesh to effectively refine the cylindrical space model.Divided into grids to meet accuracy requirements.After the boundary integral equation been established and the singularity been resulted,the discontinuity problem of the spatial surface-force could be solved.After the pretreatment of the discontinuous faces,the model can be calculated.In this dissertation,based the conditions of different lengths,the problems of cylindrical cavity are calculated,then go to analyze the results between the 3-D problem and 2-D plane problem.