Frane Vlak

NPV-based decision support in multi-objective design using evolutionary algorithms

Optimum design problems are frequently formulated using a single excellence criterion (minimum mass or similar) with evolutionary algorithms engaged as decision-support tools. Alternatively, multi-objective formulations are used with a posteriori decision-making amongst the Pareto candidate solutions. The former typically introduces excessive simplification in the decision space and subjectivity, the latter leads to extensive numerical effort and postpones the compromise decision-making. In both cases, engineering excellence metrics such as minimum mass can be misleading in terms of performance of the respective design in the given operational environment. This paper presents an alternative approach to conceptual design where a compound objective function based on the Net Present Value (NPV) and Internal Rate of Return (IRR) aggregate performance metrics is developed. This formulation models the integral value delivered by the candidate designs over their respective life-cycles by applying value-based NPV discounting to all objectives. It can be incorporated as an a priori compromise and consequently viewed as a weighted sum of individual objectives corresponding to their economically faithful representation over the entire operational life-time of the designs. The multi-objective design optimization is consequently expanded from purely engineering terms to coupled engineering-financial decision support.

An analytic solution for bending of thin-walled laminated composite beams of symmetrical open sections with influence of shear

An approximate analytic solution for bending of thin-walled laminated composite beams of symmetrical open sections with influence of shear is presented. Symmetrically laminated beams that possess membrane orthotropy are considered. The classical Euler–Bernoulli’s and Timoshenko’s bending beam theories are augmented by terms which take into account the shear strain in beam mid-surface as well as the warping of the cross section due to shear. Consequently, the beam is subjected to bending with the influence of shear caused by transverse forces acting in the plane of symmetry and in addition to tension/compression due to shear in the case of cross sections with one axis of symmetry. The beam is subjected only to bending with the influence of shear in the case of transverse forces acting in the planes of symmetry. The expressions for the normal stresses and displacements are presented in the closed analytic form. The factor that depends on the fiber orientation is introduced in order to analyze the material influence on shear. Simply supported and clamped beams subjected to distributed transverse load are investigated. The solutions obtained for open sections are also valid for mono-symmetrical closed sections, taking into account the constraint that loads act in the beam longitudinal plane of symmetry/planes parallel to the longitudinal plane of symmetry. Illustrative examples are provided, and the analytic results show a very good agreement with the results obtained by the finite element analysis utilizing three-dimensional shell elements.