Algorithm, implementation, data preparation, calculation of statics and dynamics of beam lattice structures in SSKA KIDYM

Abstract

The problem of developing a universal analytical description and an algorithm for automatic computer calculations of dynamics, statics and kinetostatics of mechanical models of structures, which include beam lattices, is considered. These can be calculations of transient processes, steady-state free and forced vibrations, determination of equilibrium positions and stress-strain state under static and dynamic loads, etc. The structure itself can be flat or spatial, fixed or movable on a plane or in space. Various equipment can be attached to it. It is shown how it is possible to analytically describe a part of the structure, which is a beam lattice, in a language for preparing computer data of a special computer algebra system KiDyM (SCAS KiDyM). 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 allows us to introduce a new element into the accepted language for describing mechanical models - a “Beam”, for which the positions of coordinate systems associated with its extreme sections, its geometric and physical parameters are indicated. The position of these sections is determined by the lattice nodes, as by solid bodies. Thus, the generalized coordinates of the mechanical model are determined. An algorithm for the formation of elements of mechanical models of SCAS KiDyM has been developed. This gives the elastic structure of the mechanical model. The tools available in this program automatically build the equations of dynamics and statics, i.e. form a mathematical model, according to which dynamic and static calculations are carried out. The article demonstrates the proposed method in detail on the example of calculating the deformation of a window frame. A comparison of the results with calculations based on an independent program was made. Key words: lattice beam structures, Bernoulli-Euler beams, a special system of computer algebra, calculations of the dynamics of spatial mechanical models.