Study On Boundary Element Method For Elastic Half-infinite Domain Problems

As a numerical method,the boundary element method has been developed due to its small amount of calculation and high precision.The boundary element method can automatically satisfy the boundary conditions at infinity,without manual truncation,without applying artificial boundaries,and has inherent advantages in dealing with infinite domain problems.The boundary element method of finite field and infinite domain has obtained relatively good research results.This dissertation aims to deal with many half-infinite domain problems in engineering.Based on the theory,calculation program of existing elastic statics and dynamic boundary element method,by the introduction of infinite boundary element,the corner point problem was processed,the corresponding Matlab program was programmed to deal with the static and dynamic fluctuations of the half-infinite domain,and the dynamic response of the slope under traffic load was calculated.In this dissertation,the theoretical derivation of the half-infinite domain boundary element method for elastic statics was carried out.The half-infinite domain problem was divided into finite field part and infinite domain part.The finite field part was based on the existing boundary element theory.The corner point problem was studied emphatically.It was proposed that the boundary slope corner points belong to the mixed corner point and should be geometrically respectively.The processing of corner points and physical corner points.The infinite boundary element was introduced in the infinite domain,and the coordinate interpolation function and the corresponding displacement attenuation function are derived.Since that Kelvin basic solution contains rigid body displacement,the modified Kelvin basic solution was used and nested into the boundary element theory for calculation.The example was selected for verification.The elastic static method provides a theoretical basis and support for the dynamics.The elastic dynamics half-infinite domain boundary element method of elastic dynamics was theoretically derived.Based on the more developed time domain boundary element method,the same solution as statics was used to divide the spatial dispersion into regular units and infinite boundary units.The third coordinate of the three-dimensional basic solution was integrated to obtain the two-dimensional time domain basic solution.After a series of integral operations,the two-dimensional semi-infinite domain elastic dynamic integral equation was obtained.Numerical calculation was performed to deal with the singularity of singular elements and tosolve the integral equation.The dynamic response of the slope under traffic load was calculated.The theory and program of the time domain boundary element method of the dynamic half-infinite domain problem was verified with the double-exponential explosion load and the sudden load as example.It can be seen from the results of the numerical example that the accuracy and computational efficiency are relatively reliable.Finally,the dynamic response of the slope under traffic load was calculated.