âComputational Civil Engineering - "Intersections" International Journal

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“Computational Civil Engineering 2005”, International SymposiumIaşi, România, May 27, 2005Considerations concerning the optimization of reinforcedconcrete bridge designConstantin Ionescu 11 Technical University "Gheorghe Asachi" Iasi, RomaniaSummaryThe paper suggests a procedure for optimal design of a bridge using computationsoftware, which exists in the literature, and a special subroutine added in order tobe applicable for reinforced concrete bridges.The optimal solution results from combination of three main processes: bridgedesign going through classical stages according to present regulations;application of optimal design by automated computation software, based on finiteelement method; and finally selection of the optimal structure from more partiallyoptimal structures, each in I own class, through multicriterial decision.KEYWORDS: bridge, design, optimization, computer aided design, optimalsolutions, objective function, restrictions and optimization variables, structuralmodel and mathematical model.1. INTRODUCTIONThe optimization process, meaning the identification of the optimal solution, mightbe found equivalent with a research activity in the domain of admissible solutions.Reviewing the literature, one might find that different typical optimization methodsdiffer mainly in the way of processing the succession of steps in admissible domainand by procedures to accelerate the convergence of the desired solution.Development of the mathematical procedures (through selection of the directionsand initial solution) represents the highest difficulty in application of mathematicalprogramming methods to optimal design of structures. Hence, optimality criteriabecome more important because they imply, essentially, derivation of the necessaryand sufficient conditions to apply for obtaining the optimum with regard to specificrequirements of design. So far, discrete optimization criteria for a number of designcondition was described implying resistance, static stiffness, dynamic stiffness,static stability etc. Several software like OPTSTAR, OPCOM, OPTIM, SESATETC. were developed to use discrete optimality criteria as basis of structuresoptimization. All these programs are based on finite element method.
258 C. Ionescu2. CONSIDERATIONS ON OPTIMIZATION OF STRUCTURES USINGCOMPUTATION SOFTWARE - OPTSTARThe COSMOS/M software includes an optimization procedure named OPTSTAR.This software is based on finite element method. The method consists indeveloping a structural model using three types of elements: one-dimensional(rods), bi-dimensional (slabs) and three-dimensional (solids). The software worksmainly on PC compatible computers, integration also Fast Finite Element, anequation systems solving procedure developed by Structural Research and AnalysisCorporation.Structural optimization reached with this procedure (OPTSTAR) offers thepossibility to define a structure which is optimal in geometry as well as in section,considering the conditions imposed while defining the specific elements of anyoptimization process: objective function, restrictions, and optimization variables.Operation s steps into a structural analysis process are:• Construction of the geometrical model. Classical entities are used:points, lines, curves (conics, splines etc.), surfaces (planes, curved,generated by rotation), volumes, regions.• Physical modeling. This step consists in introducing the physical constantswhich define the material we are working with and, in the case of uni andbi-dimensional structures the geometric-inertial characteristics of thebeams and slabs are introduced. Data on material enclose: elasticity moduli(E and G), density, linear dilatation coefficients etc.• Structure discretization. It is the most complex operation necessitating acertain efficiency related to: knowledge about the finite element libraryexperience concerning discretization to obtain the balance between thedesired precision and rapidity in solving the problem.• Modeling the bearing and actions. Bearings cancel a number of degreesof liberty of the elements. Actions might be imposed displacements, forces,pressure, torsions, linear or centrifugal accelerations, etc.• Analysis of the structure. This stage consists in: obtaining, representationand verification of the results.Computation software relies on an iterative process of transforming the physicalmodel of the structure until the assessment criteria are fulfilled. The acceptedcriteria are selected by the designer. The two versions of the software(COSMOS/M and COSMOS/FFE) will modify the dimensions and the shapes inorder to find the optimal model of the structure (feasible model). The software canoptimize simple (plane) or tri-dimensional structures.
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A viscoelastic-plastic prediction o
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