Stress Analysis For Blunt-notch And Sharp-notch By Boundary Element Method

The notched elements are often used in engineering structures.The serious stress concentration and singular stress will affect the structure safety.There are great theoretical significance and high engineering application value to study the singular stress at the notch root.In this paper,the boundary element method was used to calculate the thermal-elastic stress field and stress concentration coefficients for the blunt notch,and singular stress field together with the stress intensity factor for the sharp notch.The relationships between the stress concentration,singular stress field and the notch depth,notch angle are studied.The main work is listed as follows:Firstly,the basic theory and implementation process of boundary element method for the elastic mechanics are summarized.The elastic stress fields near the blunt notch tip are calculated by the boundary element method.The blunt notch model with the notch angle of 30°,60°,90°,135° and hole radius of 0.05 mm,0.5mm,1.0mm and 2.5mm were selected.The stresses of inner points along the angular bisector of blunt notch are evaluated.It was found that the maximum circumferential stress was located on the circular boundary of the notch root,and it decreased with the increase of the distance away from the notch end and eventually tended to the average stress on angular bisector of the notch.The radial stress values on the angular bisector increase from zero to the extreme value and then gradually decrease.In addition,when the notch opening angle is an acute angle,the axial stress and radial stress slightly decreased along with the increase of opening angle,but the tangential stress decreased obviously along with the increase of opening angle.When the notch opening angle is an obtuse angle,the ratio of circumferential stress value and the extreme of the notch of circumferential stress of different round hole radius does not changeover the radius of circular aperture.Secondly,the natural thermal stress boundary element method was introduced to analyze the thermal stress fields near the single material and bi-material notch tip.It was found that the thermal stress field near the blunt notch tip was similar to the elastic stress field.The singularity order and thermal stress intensity factor for the sharp notch were also calculated.It was found that there was only Type-I thermal stress intensity factor K1 for the symmetric sharp notch and its value decreased with the increase of opening angle.There were Type-I and Type-II stress intensity factors at the sharp inclined notch,and the thermal stress intensity factor K1 decreased with the increase of inclining notch angle,while the thermal stress intensity factor K2 increased with the increase of inclining notch angle.At the same time,the finite element method was also used to analyze the structural model.The accuracy of the boundary element result was verified by comparison with the result from the finite element method.However,it is only needed to divide the element along the outer boundary in the boundary element method.The higher calculation accuracy can be obtained with fewer elements by the boundary element method,which greatly reduce the calculated amount of engineering structure analysis.