A Direct Approach to Shape Optimisation of Structures

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.