“Computational Civil Engineering - "Intersections" International Journal

“Computational Civil Engineering 2005”, International Symposium 259In modeling process the following sets of entities are defined: objective function(target, performance), variables and restrictions. These entities lead to formulationof the mathematical model.The variables represent those independent parameters which describe certainspecific aspects of the problem, such as: structural configuration and dimensionsused to define the model of the structure.There is a clear hierarchy between different classes of variables. As an example,for the bridge resistance structures the simplest class consists from the variablesdefining the geometric and technical characteristics of the elements.The higher category encloses the variables which refer to the configuration of thestructure (number and measure of the apertures, proportion between height andopening etc.).Objective function is a mathematical function with real values that express a linearor non-linear relation between the chosen variables. It describes the criterion fromquantitative point of view and it provides a modality of decision between theexistent solutions.Objective functions might be defined through the following factors: volume,weight, stress, tension, displacement, specific deformation, cross-section, velocity,acceleration, characteristic frequencies, temperature variations, and energy flowsetc.Admissible solutions, from which the optimal variant is selected identifying thevariables that lead to the extreme value of the objective function, must satisfycertain conditions. Analytically they are expressed by mathematical equalities andinequalities imposing limits to variables or groups of variables. These are theconstraints of the problem. The constraints are set according to operation behavioranalysis of a bridge structure and they refer to: volume, weight, tress, tension,displacement, specific deformation, cross-section area, velocity, acceleration,proper (natural) frequency, temperature variation, energy flows etc.Other restrictions refer to geometric configuration of the elements, i.e. height of thetransversal section might fluctuate within a range (superior and inferior limit) orthey are imposed directly to the variables: to be non-negative or integer numbers;to respect some condition of standardization etc.3. THE CONCEPT OF OPTIMAL DESIGN OF A BRIDGEThe inconveniences of an optimal structural computation software are highlightedby the ways to determine the working stages of the reinforced concrete and limitstates of bridge calculation or verification: normal and ultimate operation.