PSI - Issue 50

2

Dmitry Parshin et al. / Procedia Structural Integrity 50 (2023) 320–326 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

321

Nomenclature t

time variable

z , ,   polar cylindrical coordinates: radial, circular (angular), and axial r radius-vector ( ) 0 r  moment when the point r is added to the growing body in question u v , displacement and velocity vectors E D , small strain and strain rate tensors T stress tensor I identity tensor m Poisson number  age of the material element, at which its stress state is considered ( , )  C t shear creep strain developing by the time moment t from the unit shear stress applied at the age of   C specific (per unit load) creep resource of the material at its very large age C  overall change of the material specific creep resource due to aging ( )  G value of elastic modulus of the second kind at the material age of   G elastic modulus of the second kind of the material at its very large age G  overall change of the material elastic modulus of the second kind due to aging ( ) a t variable (decreasing) internal wall radius of the arched structure being constructed 0 t time moment of the arched workpiece installation on the foundation start/stop t time moments of starting/stopping the addition of new material to the constructed structure 0 stop , a a initial and final values of the structure internal wall radius, ( ) ( ) start 0 0 a a t a t   , ( ) stop stop a a t  b constant external wall radius of the structure being constructed  mass density of the structure material g acceleration of gravity   hoop stress in the constructed structure ,0   initial hoop stress in the material being added to the structure in its constructing process 1. Introduction When calculating structures, it is often impossible to refuse to take into account the forces of gravity acting on them. Traditionally, these forces are taken into account by applying the appropriate mass loading to the entire calculated structure. However, real structures, as a rule, do not arise in their ready-made form simultaneously, but are built gradually, and gravity forces act on their elements from the very first moment of the construction process. In such cases, the traditional account of gravity forces in principle cannot give correct ideas about the stress-strain state of the structure under consideration. Indeed, every arbitrarily small element added beyond the others to the structure during the construction process begins to exert an additional force effect by its own weight on the structure being constructed, which will cause the appearance of additional stresses and, consequently, strains in the entire structure. And the aggregate effect of all elements consecutively included in the structure is by no means identical to the effect of the simulta neous “application of gravity” to all these elements already located in the finished structure. So, it is obvious that adequate mathematical descriptions of the evolvement processes in the stress-strain state of consecutively constructed large-sized structures should be carried out on the basis of mathematical models in solid mechanics that would take into account the features of a particular additive process of the calculated structure construction, but not only the final geometry of this structure. Such models are not classical in mechanics: they belong to the field of mechanics of growing bodies (Arutyunyan et al, 1991; Arutyunyan and Manzhirov, 1999).