Arch Structure Erection by an Additive Manufacturing Technology under the Action of the Gravity Force

The paper studies the influence of the gravity forces on gradually constructed objects in the field of gravity. The cases of viscoelastic aging and pure elastic materials are considered. A model of erection of a circular (semicircular) arch structure on a smooth rigid horizontal basement by the method of layered thickening of a previously mounted blank structure from inside is developed in the framework of the linear mechanics of accreted bodies. The model takes into account the influence of gravity forces on the erected structure during the entire process of its erection. In addition, the model allows creating prestresses in the accreted structure elements in the process of erection and admits arbitrary time-variable loads on the outer surface of the erected arch. The corresponding essentially two-dimensional problems of mechanics of quasistatic deformation of the considered structure before its accretion, at the stages of continuous accretion, in the pauses between these stages, and after the accretion are posed in the plane strain state approximation. The analytic solutions of these problems are constructed as series and by quadratures, which permits tracing the evolution of the structure stress-strain states at all stages listed above. These studies can be used to analyze objects produced by additive manufacturing technologies.