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With the advances of the computer technology, structural optimization has become a prominent field in structural engineering. In this study an unconventional approach of structural optimization is presented which utilize the Energy method with Integral Material behaviour (EIM), based on the Lagrange’s principle of minimum potential energy. The equilibrium condition with the EIM, as an alternative method for nonlinear analysis, is secured through minimization of the potential energy as an optimization problem. Imposing this problem as an additional constraint on a higher cost function of a structural property, a bilevel programming problem is formulated. The nested strategy of solution of the bilevel problem is used, treating the energy and the upper objective function as separate optimization problems. Utilizing the convexity of the potential energy, gradient based algorithms are employed for its minimization and the upper cost function is minimized using the gradient free algorithms, due to its unknown properties. Two practical examples are considered in order to prove the efficiency of the method. The first one presents a sizing problem of I steel section within encased composite cross section, utilizing the material nonlinearity. The second one is a discrete shape optimization of a steel truss bridge, which is compared to a previous study based on the Finite Element Method.

Long-span cable supported bridges are prone to aerodynamic instabilities caused by wind and this phenomenon is usually a major design criterion. If the wind speed exceeds the critical flutter speed of the bridge, this constitutes an Ultimate Limit State. The prediction of the flutter boundary therefore requires accurate and robust models. This paper aims at studying various combinations of models to predict the flutter phenomenon.
Since flutter is a coupling of aerodynamic forcing with a structural dynamics problem, different types and classes of models can be combined to study the interaction. Here, both numerical approaches and analytical models are utilised and coupled in different ways to assess the prediction quality of the hybrid model. Models for aerodynamic forces employed are the analytical Theodorsen expressions for the motion-enduced aerodynamic forces of a flat plate and Scanlan derivatives as a Meta model. Further, Computational Fluid Dynamics (CFD) simulations using the Vortex Particle Method (VPM) were used to cover numerical models.
The structural representations were dimensionally reduced to two degree of freedom section models calibrated from global models as well as a fully three-dimensional Finite Element (FE) model. A two degree of freedom system was analysed analytically as well as numerically.
Generally, all models were able to predict the flutter phenomenon and relatively close agreement was found for the particular bridge. In conclusion, the model choice for a given practical analysis scenario will be discussed in the context of the analysis findings.

Numerical simulations in the general field of civil engineering are common for the design process of structures and/or the assessment of existing buildings. The behaviour of these structures is analytically unknown and is approximated with numerical simulation methods like the Finite Element Method (FEM). Therefore the real structure is transferred into a global model (GM, e.g. concrete bridge) with a wide range of sub models (partial models PM, e.g. material modelling, creep). These partial models are coupled together to predict the behaviour of the observed structure (GM) under different conditions. The engineer needs to decide which models are suitable for computing realistically and efficiently the physical processes determining the structural behaviour. Theoretical knowledge along with the experience from prior design processes will influence this model selection decision. It is thus often a qualitative selection of different models. The goal of this paper is to present a quantitative evaluation of the global model quality according to the simulation of a bridge subject to direct loading (dead load, traffic) and indirect loading (temperature), which induce restraint effects. The model quality can be separately investigated for each partial model and also for the coupled partial models in a global structural model. Probabilistic simulations are necessary for the evaluation of these model qualities by using Uncertainty and Sensitivity Analysis. The method is applied to the simulation of a semi-integral concrete bridge with a monolithic connection between the superstructure and the piers, and elastomeric bearings at the abutments. The results show that the evaluation of global model quality is strongly dependent on the sensitivity of the considered partial models and their related quantitative prediction quality. This method is not only a relative comparison between different models, but also a quantitative representation of model quality using probabilistic simulation methods, which can support the process of model selection for numerical simulations in research and practice.