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Discrete-and-continuum analysis of plane elastic girder orthogonal structures

Mishustin I.V.

#### Abstract:

We pay main attention to a linear discrete-and-continuum method for analysis of a plane regular orthogonal girder structure with rectangular cells. Each cell includes two diagonal rods that do not influence each other at the point of their intersection. Rods of the structure may undergo spatial deformations. The rods are rigidly connected to each other at nodes and their elastic axes and one of the principal axes of transversal cross section are in the plane of the girder structure. Introducing the assumptions mentioned, we may split out the problem into two independent ones: the problem on deformation of the girder structure in its plane and the problem on bending of the structure out off this plane. Using the method of gluing and the method of initial parameters, we reduce each of these problems to pure discrete theory describing by finite difference equations. Governing relationships of these theories are as follows: geometrical equations, physical equations, and static equations. All these relationships are stated in terms of the values of displacements of nodes and angles of rotation at these nodes, total deformations of the rods, initial stresses and moments acting in the rods. The equations of compatibility of total deformations are also stated. The theories developed may be considered as a discrete analogue for plane stress state and the theory of bending for plates that follows from the moment theory of elasticity. The theories constructed are illustrated by numerical examples.

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