STUDY OF THE INFLUENCE OF GEOMETRY ON INTERNAL FORCES IN THIN-WALLED MOMENTLESS DOMES OF REVOLUTION UNDER DEAD LOAD

Abstract

Domes have been quite popular in the construction of important architectural objects, such as temples, palaces, various public buildings, etc., for many centuries. This is also true for modern times. The presented facts are caused by the beauty and solemnity of the domes, their technical ability to cover long distances without the use of internal supports. Accentuated information is the main advantage of these structures. The particular interest in thin-walled varieties is explained by the desire to reduce the consumption of materials required for construction, which reduces its cost. The disadvantages of domes include the complexity of design, manufacture and operation. Their weight is converted into meridional compressive forces, which are satisfactorily perceived by concrete, stone, brick during operation. Circumferential internal forces act along the tangents to the parallels. The upper parts of the domes are compressed, while the lower parts can be significantly stretched. In this case, the base of the dome is additionally reinforced or a support ring is installed. The finite element method, which is successfully implemented by computer means for calculating the strength of structures, is now widely used. His idea for shells is to divide them into a significant number of interacting components. The described approach allows obtaining sufficiently accurate results. Membrane theory, which is based on Laplace’s formula, remains the mathematical basis for the corresponding modelling. This refers to the simplicity and productivity of its application at the conceptual design stage for defining preliminary approximate acting forces. This, in particular, helps to exclude unpromising options from further detailed processing. Another good example is the verification of computer calculations, where errors can be caused by people incorrectly entering certain information. The theory allows us to more correctly understand and predict the behaviour of the objects under study. However, the membrane methodology also has disadvantages associated with the occurrence of bending moments at the junction of the dome with the support ring. The article analyses specific cases of determining meridional and circumferential forces in thin-walled momentless domes of revolution loaded with their own weight, depending on variable geometry. Vector rational parametric curves of the second degree were used as generators to ensure flexible computer shaping. Prospects for further relevant scientific research are outlined.