Study On The Elastoplastic Dynamic Plane Problems By Radial Integration Time Domain Boundary Element Method

The time domain boundary element method is a numerical method that converts the differential equation into an integral equation based on the fundamental solution of the transient,then performs numerical processing,transforms the integral equation into a series of algebraic equations and combines the initial and boundary value conditions.For the simple problem,the time domain boundary element method can transform the differential equations of the analysis problem into the domain-free integral boundary integral equations,and then only need to perform numerical dispersion and solution on the boundary in space,which has the dimension of research problem and the boundary dispersion only.advantage.However,the elastic dynamic plane problem with domain force and the differential equation corresponding to the elastoplastic dynamic plane problem cannot be completely transformed into a domain-free integral boundary integral equation,that is,the integral equation becomes a boundary-domain integral equation.For the case of regional integral,the time domain boundary element method not only performs numerical discretization on the boundary in the process of numerical processing,but also performs numerical dispersion on the region.At this time,the advantage of the time domain boundary element method to reduce the dimensionality of the computational problem and the need to perform numerical dispersion on the boundary no longer exists.This dissertation intends to use the radial integration method to transform the traditional boundary-domain integral equation into a domain-free integral boundary integral equation.When the integrand in the integral term in the domain is a known function,the region integral can be directly converted into the boundary integral by the radial integration method.When the integrand in the integral term in the domain is an unknown function,this dissertation uses the radial basis function as an interpolation function to approximate the unknown integrand function to adapt to the needs of subsequent radial integration.The solution after numerical processing is to solve a series of radial integrals,time integrals and boundary integral terms.It is observed that the time domain basic solution has vertical and horizontal wave subtraction forms,and the spatial singularity encountered in the radial integration process can be eliminated by the vertical and horizontal wave subtraction.Since the partial derivative of an integral path vector to the outer normal vector of the integral unit exists in the integrand in the process of domain integral transformation,the value on the singular unit is always zero,so the spatial singular performance encountered in the boundary integral process Automatically eliminated.The time singularity encountered during the time integration process is processed by the Hadamard principal value of the integral.For the elastoplastic dynamics problem,it is necessary to supplement the elastoplastic constitutive equation to solve the problem.Finally,this dissertation uses examples to verify the method.From the calculation results of the example,the proposed method has a greater advantage than the traditional time domain boundary element method.