Recent Investigations of Structural Optimization by Analytic Methods

In this paper, we discuss two analytic methods suggested by the author for solving structural optimization problems, viz. the “stepped reduction method [1, 3–5] and a method based on the principle of complementary energy [2]. In the former, we discretize first the Young’s modulus E(x) and the thickness of h(x) of structural elements. We use the initial parameter method and the Heaviside function for descriving results in analytic form and then we use a combination of homogeneous solutions to eliminate discontinuities of bending moment and shearing force at element boundaries. This means that we need to solve only simultaneous algebraic linear equations with a finite number of unknowns. The above methods will be illustrated on the following problems: 1.Optimal design of thin elastic solid annular plate under an arbitrary load (stepped reduction method) [6]; and2.Uniform strength for statically indeterminate beams [2,7].