About Determination Optimal--Weight Statically Indeterminate Bar Structures of Complex Stress by Using Explicit Forms of the Conditions,
COLLEGE OF TRANSPORT AND TELECOMMUNICATIONS GYOER (HUNGARY)
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Designing minimum-weight bar structures are usually made only by implicit functions of the conditions. In this essay we formulate the conditions as an explicit functions of the cross-sectional characteristics in order to have better applicability of mathematical programming algorithms. For this purpose we decompose the large-sized structure of optional geometry into substructures. With the help of this decomposition we can substitute the dimensioning of the whole structure for dimensionings of several small and easy handling structures. Then we move back the dimensioned large structure within the appropriate degree of tolerance used in practice. The form of the stress vector of a bar we trace back to algebraic summing of some displacement vector components. So we get a formula which is suitable to produce the functions of the conditions both at the structures having rigid connections at the nodes and at some special cases as the trusses.