Field Theory Of Deformation Superposed On Stressed Configuration And Stability And Vibration Of Arch

Generally speaking, engineering structures and components can be always looked on as working under invariable original loads and additional variable loads. As a rule, the state of working stress and strain of engineering structures and components can thought of as making additional deformation movement on referenced configuration with static pre-stress. There are different control equations of deformation movement on between configurations with pre-stress and without pre-stress, so it is definite to take the influence of pre-stress into account when seeking configuration or the parameter of it, and seeking structure or the disfigurement of it through the mechanical behavior of additional deformation. Elastic buckling analysis is just through the mechanic action of additional deformation to discuss buckling state, so elastic buckling and critical condition can be studied through the methods of additional deformation on pre-stressed configuration. That is to say, controlling equations displaying the relationship between the displacement of structural nodes and initial loads can be achieved from variation principle, they must have zero answers, if they have non-zero answers (presuming component's configuration alters and starts to lose stability , the conditions of initial loads can be gotten. and initial loads can be calculated correspondingly.In this article, using secondary load model, the theories of additional deformation on pre-stressed configuration are established by this method. As for arch structures which are widely used in bridges and building domes, their critical load are to be calculated when they are restrained differently and loaded in different ways, and calculate the influence of initial loads on inherent frequency.In the first character of this article, the thought's output of the research of field theory of additional deformation on pre-stressed configuration, the history of its' researches, the status in quo in domestic and oversea, and the history and status in quo of the researches on arch's stability.In the secondary character, using secondary load model, suppose the first load is static constant load, and call it initial load, the stress field of which are called static initial stress field; call the secondary load additional load, the stress and deformation of which are called additional stress and deformation. Call the configuration containing static initial stress field initial stress configuration and treat it as referenced configuration, and establish field theory of additional deformation on initial stress configuration. If initial stress field is known, the controlling equations, boundary conditions , corresponding virtual work and variation equation of additional stress, displacement and strain can be deduced.According to this system of theory, variation principle of displacement of elastic and static stability and variation equations of displacement of later buckling are described and demonstrated.In the third character, field theory of additional deformation of elastic buckling is studied, and it is transformed to be described in curve coordinate system from Descartes coordinate system, then variation equations of bending bar can be described in natural coordinate system.In the fourth character, using displacement variation equations of stability established on the base of linear theory of small deformation on pre-stressed configuration, introducing the method of lowering dimension, and then usual equations of critical equilibrium of arch are deduced. Three eigenvalues of initial stress are calculated when arch is under different restrictions and loading methods, then each variation equation of displacement are achieved to perform finite element calculation ulteriorly.Compared with the method of geometry of small deformation to deduce displacement controlling equations of critical equilibrium, this character begins with universal theory of additional deformation, using lowering dimension to deduce displacement controlling equations correctly, it shows the sup...