Solving the problems of structural mechanics in determining the maximum deflection of rhombic plates with combined boundary conditions in agro-industrial engineering

At the present stage of the development of agro-industrial engineering, the design of parts and individual units is inextricably linked with comprehensive studies of the strength, rigidity and stability of structures under the influence of both static and dynamic loads. The design schemes of many elements can be presented in the form of rod, plate, shell and combined (plate-rod, shell-plate, etc.) systems. Such methods do not require the development of sophisticated account programs, relieve the designer at the initial stage of design from using powerful computers to obtain an operational result, they help to explain the results of refined verification calculations quite simply and correctly. Despite the presence of a large number of different software products, currently in construction mechanics and in accounting practice great importance is attached to the development and improvement of simple analytical methods for solving specific problems for typical elements of structures of buildings, structures and machines that have maximum simplicity, reasonable accuracy and the possibility of obtaining bilateral evaluations. In the article, the example shows that using the method of interpolation by the shape factor, it is possible to determine simply the maximum deflection of the plates in the form of a diamond with combined boundary conditions loaded with a uniformly distributed load. The interpolation method based on the shape factor is based on the isoperimetric method. The main argument in the obtained analytical dependencies is the ratio of the form factor to the area of the region. All bounded subsets of domains have boundary (support) solutions.