vault, arch, structure, building, raising, accretion, gravity, elasticity,  viscoelasticity, rate of process, prestressed elements, local support, strength, stability, bearing capacity.

We study the influence of gravity forces on objects gradually formed in their presence. We consider the cases of aging viscoelastic and purely elastic materials. Within the framework of  linear mechanics of accreted solids we solve the mathematically two-dimensional problem on the  erection of a heavy semicircular arch structure on a smooth rigid foundation by the method of  layer-by-layer thickening of an initially installed structure on the side of its internal surface.  We show that, to estimate the strength, stability and the bearing capacity of a heavy structure, it  is extremely important to take into account the gravity forces acting on this structure not only in  its final configuration but during the entire erection process. We also d monstrate certain  possibilities of a very efficient control of the stressed state of an accreted solid.

Manzhirov Alexander Vladimirovich e-mail: parshin@ipmnet.ru, M.Sc., Ph.D., Sc.D., Professor; Head of the Laboratory for Modeling in  Solid Mechanics, Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences,  Moscow; Professor, Head of a Branch of the Department of Applied Mathematics, Bauman Moscow State  Technical University, Moscow; Professor of the Department of Higher Mathematics, National Research  Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow. Parshin, Dmitry Alexandrovich e-mail: manzh@ipmnet.ru, M.Sc., Ph.D.; Scientific Researcher of the Laboratory for Modeling in  Solid Mechanics, Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences,  Moscow; Associate Professor of the Department of Applied Mathematics, Bauman Moscow State Technical University, Moscow.