Research On Theoretical Calculation Method Of Damage Degree Of The Mode Ⅰ Cracked Beam

Beam structures are common load-bearing structures and have a very wide range of applications in aerospace,mechanical and civil engineering fields.Cracking is one of the most common forms of damage in beam structures,which has an important impact on the load-carrying capacity and remaining life of the structure.The modeling methods,damage identification methods,and repair means of cracked beam structures have always been popular research topics.After years of development,numerous results have been achieved in modeling and damage identification methods for cracked beam structures,but there are still some problems that have not yet been solved.In this thesis,based on the cracked beam model under static loading,the calculation method of the theoretical damage degree of the element containing transverse cracked beam structure is derived,and the following studies are mainly carried out.1.Based on the stress intensity factor,the theoretical damage degree calculation methods for rectangular beam elements containing tension-type transverse cracks and slotted damage rectangular beam elements are derived.For the rectangular beam containing transverse cracks subjected to static load,based on the tandem spring model,the stiffness of the cracked tandem spring is calculated by the crack stress intensity factor,and the theoretical damage degree calculation formula of the rectangular beam element containing open type cracks is derived based on the damage degree calculation method of the element linear stiffness,and the explicit expression of the crack height and the damage degree of the element is established.A static load model of a cracked beam is established,the damage degree of the model is calculated by the static deflection curvature damage quantification method,and the problems of the crack modeling method and crack damage influence area are discussed,it is concluded that the crack singularity can make the model calculation converge quickly,and the influence area of the crack on the length direction is 0.5 times the height of the beam on each side when it is subjected to static load,the accuracy of the formula for calculating the crack damage degree under different stress states is also verified by the calculation example.The theoretical damage degree calculation formula of rectangular beam slotted element is derived from cracked beam theory,and verify the accuracy of the formula by slotted damage beam calculation example.2.In the calculation example,it was found that the error in calculating the damage degree of isosceles trapezoidal beam cells containing transverse cracks was large when using the damage degree calculation method of the rectangular beam crack element.Based on the theoretical damage calculation method for rectangular beam elements containing transverse cracks,a crack stress diffusion model is established by equating the crack damage element linear stiffness model,calculating the crack stress diffusion angle,and deriving the damage degree calculation formula for isosceles trapezoidal beam crack elements.Four crack stress diffusion models are proposed,and through the isosceles trapezoidal beam case,the linear stress diffusion model is selected to calculate the theoretical damage degree of trapezoidal beam elements with transverse cracks,and the accuracy of the crack stress diffusion model damage calculation method is verified through the case.The accuracy of the calculation formula was further improved by fitting a correction to the equation for calculating the theoretical damage degree of crack stress diffusion in trapezoidal beam,based on the damage data of the cracked beam model,and the calculation was verified by the example.3.Based on the linear crack stress diffusion model,the theoretical damage degree calculation method is derived for T-beam elements containing transverse cracks in the flange and web,and the cracked solid finite element model is established by Ansys to verify the accuracy of the calculation formula for the damage degree of web cracks,and it is found that the flange crack damage has different influence laws on the T-beam.By establishing flange crack and web crack models of T-beam with different parameters,the two calculation formulas are modified by fitting with structural dimensional correlation respectively,and the modified calculation formulas have good accuracy for the theoretical damage degree of T-beam elements containing cracks.