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This paper is devoted to the optimal design of laminated composite structures. The goal of the study is to assess the quality and the performance of an algorithm based on the directional derivative method. Particular attention is paid to the one-dimensional search, a critical step of the process, performed by cubic splines approximation. The optimization problem is formulated as weight minimization, under constraints on the mechanical behavior of the structure. The assumed design variables are the ply thicknesses, treated as continuous design variables, constrained by technological requirements. The structural analysis is performed making use of quadrilateral four-node composite elements, based on the first order shear deformation theory. The algorithm is applied to the optimization of a rectangular laminated plate. The results obtained are compared with those obtained by other similar studies and show the effectiveness and accuracy of the proposed approach.

Approaches the shakedown optimal design of reinforced concrete (RC) structures, subjected to variable and repeated external quasi‐static actions which may generate the well‐known shakedown or adaptation phenomenon, when constraints are imposed on deflection and/or deformation parameters, in order to simulate the limited flexural ductility of the material, in the presence of combined axial stress and bending. Within this context, the classical shakedown optimal design problem is revisited, using a weak upper bound theorem on the effective plastic deformations. For this problem a new computational algorithm, termed evolution strategy, is herein presented. This algorithm, derived from analogy with the biological evolution, is based on random operators which allow one to treat the areas of steel reinforcements at each RC cross‐section of the structure as design variables of discrete type, and to use refined non‐linear approximations of the effective bending moment – axial force M‐N interaction diagrams of each RC cross‐section. The results obtained from case studies available in the literature show the advantages of the method and its effectiveness.