Research On Crack Propagation And Ultrasonic Scattering Of Cracked Solids Based On The Method Of Finite Spheres

Crack defects exist in various materials and can seriously weaken the performance of the material,and there are numerous accidents caused by cracks.Therefore,it is of great significance to study crack defects.In this paper,a high-efficiency and highprecision meshless method-the method of finite sphere(MFS)is used.Because its shape function and integration method select flexible characteristics,it has higher computational efficiency in solving fracture problems.In this paper,MFS is used to study the stress and strain of static cracks,the dynamic propagation of cracks and the scattering of ultrasonic waves in cracked solids.The basic theory of MFS is described,the discrete method of the solution domain,the selection of the shape function,the application method of the boundary conditions,the choice of the numerical integration method,and the one-dimensional heat conduction problem are calculated using MFS.The program of MATLAB to write the finite sphere program and the steps of computer automatically generating nodes are proposed.Under the condition of linear elasticity,the stress and strain of the static crack in the rectangular plate are calculated by MFS.Using the quadratic polynomial-based shape function term solves the problem of low calculation accuracy in the singular value region of the crack tip.The stress value of the singular value field at the crack tip is compared with the analytical solution to verify the effectiveness of this method.On this basis,the crack propagation criterion is used to calculate the crack propagation angle.The level set method was used to locate the crack location,and the propagation of the mixed crack was numerically simulated.In the analysis and simulation of ultrasonic scattering,MFS is used to calculate the wave equation to avoid the dispersion error problem caused by the finite element method.The trigonometric function is selected as the basis of the shape function,and the time integration of the displacement adopts the improved Bathe time integration method.Through the numerical simulation of the scattering of ultrasonic cracks encountered by the cracks,the simulation results observed the reflection and transmission of ultrasonic cracks and the wall of the specimen.