Abstract
A procedure is proposed for the automated construction of the bending moments influence matrix in the frame based on the graph of its discrete model. Forming the incidence matrix of the graph characterizing the topological structure of the design scheme of the frame, through matrix transformations of the displacement vectors, at the transition from local coordinate systems to a global system, it is possible to establish the relationship between the nodal displacements and the displacement increments of individual sections in the direction of the axis of the segment and perpendicular to it. The composition of only three initial matrices of the frame structure, the incidence matrix of the graph, the node coordinate matrix and the matrix of the frame model internal rigidity, solves the problem of automatic formation of the bending moments influence matrix with the help of a PC. The procedure proposed for the construction of the influence matrix, makes it possible to find the forces in the frame structure caused by external load, in the matrix form.
Highlights
During the intensive development of the finite element method in the second half of the 20th century, a number of Russian scientists in the field of structural theory attempted to create alternative numerical methods to calculate frame structures with the help of computers [1] [4]
In accordance with the duality principle, the stress state of the system in this case is determined by the equilibrium matrix, which is found by transposing the geometric matrix
To create a fully automated method for the formation of a geometric matrix, it was sufficient to provide it with a description of the frame structure, its geometric parameters, as well as physical and mechanical properties, in matrix form
Summary
During the intensive development of the finite element method in the second half of the 20th century, a number of Russian scientists in the field of structural theory attempted to create alternative numerical methods to calculate frame structures with the help of computers [1] [4]. The point at issue is the development of an automated method for frame structure calculation, which is an alternative to the finite element method.
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