Research On Analytical Solution Of Ultimate Load For Elastic-plastic Instability Of Thin-walled Cylindrical Shells With Cracks

The thin-walled cylindrical shell structure not only has the advantages of light weight,large rigidity,good seismic performance and other mechanical properties,but also has the multiple advantages of simple manufacturing and installation,short construction period,low cost and construction and economy,which makes the thin-walled cylindrical shell widely used in practical engineering.The thin-walled cylindrical shell is prone to buckling under axial pressure and bending moment,which makes the thin-walled cylindrical shell unstable without reaching the material yield strength.In the process of rolling or welding,the component will cause physical defects such as cracks,and the influence of cracks on thin-walled cylindrical shell is uncertain.Therefore,it is necessary to study the stability of the cracked thin-walled cylindrical shell.In this paper,the analytical solution of the elastic-plastic limit load of the cracked thin-walled cylindrical shell is studied,which provides the theoretical basis for the application of the thin-walled cylindrical shell in the actual engineering structure.The normal stress distribution of the cracked cross section of thin-walled cylindrical shell is studied.Based on the equilibrium of internal and external forces and the condition of strain coordination continuity,the expression of normal stress distribution is established.The accuracy of the normal stress distribution of the crack cross section is verified by the finite element method.The ultimate load formula of elastic-plastic instability of thin-walled cylindrical shell with cracks is derived.Based on the Je?ek analytical method for solving theproblem of elastoplastic instability,the relationship between the axial force of thin-walled cylindrical shell and the deflection at the crack section is obtained by using the balance equation,the geometric relation of deformation and the physical equation of the crack section.Then,the analytical expression of the ultimate load of the thin-walled cylindrical shell with cracks is derived by using the extreme condition.The ultimate load of elastic-plastic instability of thin-walled cylindrical shell with circumferential cracks under axial compression is studied.The influence of crack length and slenderness ratio on ultimate load is calculated and analyzed.When slenderness ratio increases,the ultimate load of thin-walled cylindrical shell with cracks decreases,and with the increase of slenderness ratio,the influence on the ultimate load value decreases.The ultimate load of elastic-plastic instability of thin-walled cylindrical shell with circumferential cracks under the combined action of axial pressure and bending moment is studied.Under the combined action of axial pressure and bending moment,the effects of crack length,slenderness ratio,bending moment at both ends of cylindrical shell on the ultimate load,deflection at the crack cross section and elastic height are analyzed.When the crack length,slenderness ratio and bending moment at both ends of the cylindrical shell increase,the ultimate load will decrease to some extent,and the bending moment has the most obvious influence on the ultimate load;compared with the perfect component without crack,the ultimate load of the thin-walled cylindrical shell with crack is smaller;when the bending moment increases,the height of the elastic zone of the component decreases gradually,and the deflection at the crack surface increases nonlinearly.The accuracy of the analytical solution of the ultimate load for the elastic-plastic instability of thin-walled cylindrical shells with cracks is verified.Under the action of axial load and bending load,the relationship curve between the numerical solution and the analytical solution of the ultimate load of thin-walled cylindrical shell is basically the same.