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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.
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.
The fire resistance of concrete members is controlled by the temperature distribution of the considered cross section. The thermal analysis can be performed with the advanced temperature dependent physical properties provided by 5EN6 1992-1-2. But the recalculation of laboratory tests on columns from 5TU6 Braunschweig shows, that there are deviations between the calculated and measured temperatures. Therefore it can be assumed, that the mathematical formulation of these thermal properties could be improved. A sensitivity analysis is performed to identify the governing parameters of the temperature calculation and a nonlinear optimization method is used to enhance the formulation of the thermal properties. The proposed simplified properties are partly validated by the recalculation of measured temperatures of concrete columns. These first results show, that the scatter of the differences from the calculated to the measured temperatures can be reduced by the proposed simple model for the thermal analysis of concrete.
A categorical perspective towards aerodynamic models for aeroelastic analyses of bridge decks
(2019)
Reliable modelling in structural engineering is crucial for the serviceability and safety of structures. A huge variety of aerodynamic models for aeroelastic analyses of bridges poses natural questions on their complexity and thus, quality. Moreover, a direct comparison of aerodynamic models is typically either not possible or senseless, as the models can be based on very different physical assumptions. Therefore, to address the question of principal comparability and complexity of models, a more abstract approach, accounting for the effect of basic physical assumptions, is necessary.
This paper presents an application of a recently introduced category theory-based modelling approach to a diverse set of models from bridge aerodynamics. Initially, the categorical approach is extended to allow an adequate description of aerodynamic models. Complexity of the selected aerodynamic models is evaluated, based on which model comparability is established. Finally, the utility of the approach for model comparison and characterisation is demonstrated on an illustrative example from bridge aeroelasticity. The outcome of this study is intended to serve as an alternative framework for model comparison and impact future model assessment studies of mathematical models for engineering applications.