Complex Analysis And Weight Function Method Of Cracks Emanating From Cellular Beam Hole Angle

There is large stress concentration in the hole angle of the cellular beam.In previous experiments,the hole angle can crack,resulting to the rapid destruction of the cellular beam.There are few relevant researches on the cracking of cellular beam holes at present.In this paper,the crack propagation regularity of the cellular beam hole is studied and the complex analysis method and weight function method of stress intensity factor solution are studied.Firstly,the quasi static test and finite element simulation of cellular beam specimen are carried out.By the test of eightcellular beam with different high-thickness ratio,opening rate and stiffening rib,the propagation of the crack in the corner of honeycomb are recorded in detail and the influence of hole angle cracking on mechanical properties of cellular beam was analyzed.On the basis of experiment,the stress intensity factor was selected as the fracture mechanical parameter,and the stress intensity factor of crack in the hexaghon hole angle was analyzed.The conformal mapping function is constructed by using the Muskhelishvili complex analysis method and the conformal mapping principle.By expanding the conformal mapping function,the analytical solutions of stress intensity factor for the double crack of hexagonal hole under the remote tensile stress are derived.The examples are given to analyze the symmetry cracks and asymmetrical cracks of positive hexagonal holes.Compared with Abaqus finite element simulation results,the analytical solutions have high accuracy.Aiming at the crack of hexagonal hole in the finite plate,the method of weight function is used to solve the problem.On the basis of the closed-form solution of the Wu-Carlsson weight function,the universal weight function method is derived for solving the stress intensity factor of hexagon hole angle crack.Considering the stress concentration and the stress state of the plate are complicated,the load of uniform distribution to fifth distribution on the crack surface were selected as the reference load.The model of hexagon hole in the finite plate of pure tensile,pure bending and pure shear is analyzed.The calculation results of weight function method and finite element method agree well.Aiming at the oblique crack of hexagonal hole in the cellular beam,on the basis of the weight function method of hexagonal hole angle crack in the finite plate,take out a hole in the cellular beam as the basic mechanical unit and apply the appropriate boundary conditions,the crack stress intensity factor and geometric influence factor were obtained.The stress intensity factor of a basic mechanical unit under bending and shear is calculated by an example analysis.The stress intensity factor calculation method of the hexagonal hole cellular beam angular crack is provided.