ANALYTICAL DESCRIPTION AND ALGORITHM OF CALCULATIONS OF MECHANICS OF STRUCTURES WITH BERNOULLI – EULER BEAMS USING SCAS KIDY

Abstract

The problems of developing a universal analytical description and algorithm for automatic computer calculations of dynamics, statics and kinetostatics of mechanical models of structures including a beam lattice are considered. This can be calculations of transient processes, steady-state free and forced oscillations, determination of equilibrium positions and stress-strain states under static and dynamic loads, etc. The structure itself can be flat or spa- tial, stationary or moving on a plane or in space. Various instruments and devices can be attached to it. Arbitrary connections can be taken into ac- count. It is shown how it is possible to succinctly, using a special language for preparing computer data, analytically describe a part of a structure rep- resenting a beam lattice. Based on the theory of elasticity of Bernoulli-Euler beams, 2 forms of the canonical representation of the potential energy of an elastic beam are obtained. This makes it possible to introduce into the language of description of mechanical models of the special computer algebra system KiDyM (SCAS KiDyM) a new beam element, for which the position of the coordinate systems associated with the extreme sections is indi- cated. The positions of these sections are determined by lattice nodes, like solid bodies. Angular and linear coordinates of such solid bodies give gen- eralized coordinates of the mechanical model. An algorithm has been developed for the formation of elements adopted to describe mechanical models in SCAS KiDyM. Thus, the elastic structure of the mechanical model is formed. Using the available tools in this program, equations of dynamics and statics are automatically constructed, that is, a mathematical model is formed, and dynamic and static calculations can be carried out. The proposed method is demonstrated in detail on the example of calculating the deformation of an elastic lattice, with is the basis of a UAV (unmanned aerial vehi- cle). The results are compared with calculations using the ANSYS program