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In this paper, the direct one-dimensional beam model introduced by one of the authors is refined to take into account nonsymmetrical beam cross-sections. Two different beam axes are considered, and the strain is described with respect to both. Two inner constraints are assumed: a vanishing shearing strain between the cross-section and one of the two axes, and a linear relationship between the warping and twisting of the cross-section. Considering a grade one mechanical theory and nonlinear hyperelastic constitutive relations, the balance of power, and standard localization and static perturbation procedures lead to field equations suitable to describe the flexural-torsional buckling. Some examples are given to determine the critical load for initially compressed beams and to evaluate their post-buckling behavior.

We present two applications of a direct one-dimensional beam model suitable for describing the buckling of thin-walled structures. The first application considers the buckling of a compressed beam with an intermediate stiffener under various warping constraints. The second describes the buckling of a two-bar frame, known as a Roorda frame, loaded by a dead force at the joint. Various warping constraints at the bar ends are considered and the relevant buckling modes and loads are numerically evaluated. Numerical results are presented for both cases; some of these appear to be new.

The objective of this paper was solving the optimization problem of lightweight stiffened structures modelled as a two-dimensional domain in an efficient computational way. The underlying premise was that mass should be distributed in an efficient way, so as to use a minimum amount of material to accomplish the mechanical function. This premise was expressed as a global, multi-objective optimization problem in which stiffness and mass were conflicting objectives. Alternative local evolution rules were implemented to update mass density or Young's modulus at each step of the iterative procedure. The solution of the structural optimization problem was accomplished by a novel automatic procedure consisting of two consecutive stages of control and optimization. In the first stage of Proportional Integral Derivative (PID) control gains were manually selected whereas in the second stage the finding of optimal values of control gains, target, and cost indices was allowed. In this study a bone-like material was adopted and a thin slab was analysed as a sample problem. © 2010 Springer-Verlag