Additive Manufacturing of a Cylindrical Arch of Viscoelastic Aging Material Under Gravity Action at various Modes of the Process

The engineering problem of successive construction of a heavy circular vault (a cylindrical arch) on a smooth rigid horizontal base is studied. The constructed vault manifests properties of creep and aging. The construction goes by layer-by-layer buildup of a prefabricated residual stress-free vaulted preform originally installed on the base. A buildup process in which a large number of thin layers of additional material are successively attached to the interior cylindrical surface of the arch is considered. The process is modeled as a continuous accretion process, that is, an infinitely thin material layer is added to the solid on every infinitesimal time interval. The added material is assumed not to be prestressed. The sliding mounting of the vault to the base is assumed. The case of plane strain of the vault is examined. The initial-boundary value problems describing deformation process of the structure in question before, during and after its accretion within the framework of the linear theory of viscoelasticity of accreted solids are stated and solved analytically in series and quadratures. Numerous numeral calculations for different time modes of the viscoelastic vault constructing process are performed. The influence of the temporal characteristics of the process on obtained stress state of the constructed vault is investigated. Some practically relevant phenomena are discovered. Requirement of taking into account the gravity forces in the course of the whole constructing process but not only in the terminal structure configuration is shown convincingly.