Research Of Initial Stresses In Bars

The small deformation dynamics on the initial stress configuration is the field theory on small-deformation of solid with static initial stress field existing in the reference configuration. The purpose is to determine the small deformation under additional loading under the given initial static stress field in the reference configuration,and the corresponding reverse question,to determine the initial stress distribution in a structure subjected to additional deformation under the external load.Since the deformation of an engineering structure or component can usually be considered as the additional deformation superimposed on its initial stress configuration,this study is of great theoretical and engineering significance. Many scientists and mechanists,such as Euler,Prager,Green,Ericksen,Hill,Truesdell,Eringen,made great contribution in this field and developed a general theoretical system. However,there still remain a lot that should be further investigated.This thesis discusses the linear theory of field of elastic solids subjected to additional deformation,and the corresponding virtual work equations and the displacement-based variational principle. The governing equations,the corresponding variational equations and equivalent constitutive equations with the numerical expressions of initial stress were developed and applied to the analysis of the deformation of a bar. The conclusions related to the influences of initial stress on the additional deformation,especially to the natural frequency and were obtained. The effect of inner pressure on the static and dynamic stiffness of a bar with an elliptical thin-walled section was discussed. The feasibility of evaluating the pre-stress with the measured frequencies of a structure under external excitation,and the influence of the mean normal stress on the mechanical properties of a column was also discussed. The method for the additional deformation of the bar with initial stress was modified,by using a second-order deformation theory.