Engineering Transactions, 27, 4, pp. 517-527, 1979

A Direct Approach to Shape Optimisation of Structures

Z.K. Leśniak
Technical University of Białystok
Poland

Shape optimisation of structures constitutes - mathematically a non-standard problem of the calculus of variations consisting in searching for the conditional extremum of a functional which does not possess, as a rule, a "localization property". The solution of this problem using classical methods of the calculus of variations, as well as dynamic programing methods, creates some difficulties. The paper presents a direct method of solving such problems — analogous to the Ritz-method in the calculus of variations by assuming that the function constituting the solution is expressed in an analytical form (e.g. a polynomial) and by finding the coefficients of this expression using the methods of nonlinear programming.

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References

I. M. GELFAND and S. V. FOMIN, Calculus of variations, Prentice-Hall, Inc., Englewood Cliffs, New Yersey 1963.

Z. K. LEŚNIAK, Optymalizacja kształtu luku jako przekroju dźwigarów sklepieniowych, Mech. Teoret. i Stos., 6, 1, 79-91, 1968.

Z. K. LEŚNIAK, Methoden der Optimierung von Konstruktionen unter Benuntzung von Rechenautomaten, Wilbelm Ernst und Sohn, Berlin-München-Düsseldorf, 1970 [in German] and

Z. K. LEŚNIAK, Metody optymalizacji konstrukcji przy zastosowaniu maszyn matematycznych, Arkady, Warszawa 1970 [in Polish].

Z. K. LEŚNIAK, Some practical application of structural optimisation, IUTAM Symposium on Optimalisation in Structural Design, Warsaw, Poland, 1973, Springer-Verlag, Berlin-Heidelberg-New York, 563-569, 1975.




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