Modelling of momentless thin-walled shells of revolution by vector rational parametric curves of the second degree

Abstract

The completed scientific research proposed the use of vector rational parametric curves of the second degree for modelling of momentless thin-walled shells of revolution with the determination of meridian and hoop forces under axisymmetric loading. This approach represents the dissemination of progressive experience in design of complex technical objects in the domestic aviation industry. The appropriate mathematical apparatus was presented and its application was demonstrated. The obtained results were compared with the corresponding ones available in the literature. The greater flexibility and productivity of vector parametric geometric modelling tools compared to conventional algebraic ones has been substantiated. The generalizing nature of the developed methodology was demonstrated in relation to the existing development of individual models for spherical, conical, ellipsoidal, paraboloidal, hyperboloidal, toric and other middle surfaces of thin-walled shells. This further emphasizes the effectiveness of the presented mathematical apparatus and its suitability for implementation in the environment of computer information technologies. In addition to theoretical achievements, the proposed method also has important practical significance, illustrated by the example of the domes of Orthodox temples and chapels. The highlighted issue is relevant for the current historical stage of Ukraine's development, associated with military actions on its territory. The latter determines the destruction of these facilities, the need for their restoration and the construction of new ones. These circumstances are also caused by the growing number of people turning to higher powers for help. The presented approach successfully implements the desired variety of shapes and sizes of the analyzed architectural structures in accordance with the requirements of ensuring the individuality of Christian sacred buildings. The presented tools are appropriate at the stage of preliminary design, when a significant number of dome variants are considered for the purposes of comprehensive optimization, and detailed processing of each of them requires significant costs or is impossible due to the lack of necessary information. The discussed topic deserves further development by extending it to more complex operation cases, in particular under the action of non-axisymmetric loads.