Luis Simões

Optimization of Frames with semi-rigid connections

This work describes a computer-based method for the optimum design of steel frameworks accounting for the behaviour of semi-rigid connections. The procedure explicitly accounts for both connections and members by taking connection stiffnesses and member sizes as continuous-valued and discrete-valued design variables, respectively. The optimization algorithm minimizes the cost of the connections and members of the structure subjected to constraints on stresses and displacements under specified design loads. Two examples are presented to illustrate the features of the optimization method.

Optimization of cable-stayed bridges with box-girder decks

Abstract Box-girder decks are very effective solutions for long span cable-stayed bridges, due to their high torsional stiffness and streamlined profile, which usually lead to a good aerodynamic behaviour. A study on the optimization of such structural system is presented in this paper. The deck is modelled through the assembly of planes of plate-membrane elements. A multicriteria approach is considered for the optimization itself, with constraints on maximum stresses, minimum stresses in stays and deflections under dead load condition. Two illustrative examples are shown.

OPTIMIZATION OF CABLE-STAYED BRIDGES WITH THREE-DIMENSIONAL MODELLING

Abstract This paper describes an analytical sensitivity analysis and optimization implementation for cable-stayed bridge design. The finite element software is based on the Vax/VMS version of the Modulef code [1 MODULEF Reference Guide. INRIA (1992).] and was adapted to an IBM-PC compatible. The main focus of this research concerns the analytical sensitivity analysis developed on this platform. The cable-stayed bridge optimization is posed as a multiobjective optimization with goals of minimum cost of material, stresses and displacements. Cable anchor positions on the main girder and pylon and cross-sectional sizes of the structural members are dealt with as design variables. By using the maximum entropy formalism it is shown that a Pareto solution may be found indirectly by the unconstrained optimization of a scalar function. The validity and effectiveness of the proposed technique is examined by means of a three-span steel cable-stayed bridge.

Sizing and Geometry Optimization of Cable-stayed bridges

This paper describes a method which sets steel cable-stayed bridge design in a multi-objective optimization context with goals of minimum cost and stress. The cable anchor positions on the main girder and pylon and the cross-sectional sizes of the structural members are dealt with as design variables. A Pareto solution is found by means of an entropy-based optimization algorithm. Illustrative examples for both the fixed and variable geometry problems show the significance of dealing with cable anchor positions as design variables. The influence of the stresses arising during the erection procedure on the optimum solutions is also emphasized.

OPTIMIZATION OF CABLE-STAYED BRIDGES SUBJECTED TO EARTHQUAKES WITH NON-LINEAR BEHAVIOUR

Earthquake-resistant provisions are essential features of the design of cable-stayed bridges built on seismic prone areas. Optimization can be employed to reduce cost and enhance geometrical and/or mechanical properties of the structure, The structural analysis programme developed here allows for a three-dimensional representation of cable-stayed bridges. Sensitivity analysis is carried out by analytic means both for the combined modal analysis/response spectra and the time-history methods. This enables the prediction of the variation of the structural response to earthquakes with respect to changes in the design variables. The optimization consists of a problem of multiple goals seeking to improve objectives such as cost, stresses, code of practice and erection requirements. This optimization problem turns out to be equivalent to the minimization of an unconstrained convex scalar function, which can be done by conventional quasi-Newton methods. Illustrative examples are given describing the features and ...

Fuzzy optimization of structures by the two-phase method

Abstract This work presents the two-phase method for fuzzy optimization of structures. In the first phase the fuzzy solution is obtained by using the level cuts method and in the second phase the crisp solution, which maximizes the membership function of fuzzy decision making, is found by using the bound search method. Illustrative numerical examples involving skeletal structures and reinforced concrete slabs are solved.

SEARCH FOR THE GLOBAL OPTIMUM OF LEAST VOLUME TRUSSES

Abstract This paper describes two types of strategies that find the global optimum of structures designed for minimum volume consumption. This bilinearly constrained problem may present multiple optima and some examples of this nonconvex behaviour are given. In the first method two branch and bound ( B & B) based approaches are presented associated with suitable convex underestimating functions. The second is a cutting plane method and is derived as a generalization of Benders algorithm; although the relaxed problems yielded are still nonconvex, they are amenable by standard codes for 0-1 mixed LP. Frequently structural engineers are confronted with only a limited set of discrete alternatives; both solution techniques presented here are combinatorial in nature and suitable to be cast into a discrete variable model, for which the algorithms converge to the global optimum in a much smaller number of steps.

Optimum design of concrete cable-stayed bridges

The design of cable-stayed bridges involves a significant number of design variables and design objectives. The concrete cable-stayed bridge optimization is formulated here as a multi-objective optimization problem with objectives of minimum cost, minimum deflections and minimum stresses. A numerical method is developed to obtain the optimum design of such structures. This numerical method includes: structural analysis, sensitivity analysis and optimization. The structural analysis accounts for all the relevant effects (concrete time-dependent effects, construction stages and geometrical nonlinear effects). The structural response to changes in the design variables is achieved by a discrete direct sensitivity analysis procedure, and an entropy-based approach was used for structural optimization. The features and applicability of the proposed method are demonstrated by numerical examples concerning the optimization of a real-sized concrete cable-stayed bridge.

Reliability-based plastic synthesis of portal frames

Abstract A mathematical programming technique is described which minimizes the total average volume of steel reinforcement of a reinforced concrete frame for a specified failure probability. The structural material is assumed to exhibit a perfectly-plastic behaviour so that plastic collapse is the only possible failure mode. It consists of solving alternatively a reliability assessment problem, which incorporates recent developments in large-scale constrained concave quadratic programming and an optimal sizing problem (convex minimization) until the best reliability-based design against collapse is found.

1.4 – Optimization of an Orthogonally Stiffened Plate Considering Fatigue Constraints

The aim of this work is the optimization of a uniaxially compressed stiffened plate subjected to static and fatigue loading. The design variables are the thickness of the base plate, the number and stiffeners of the orthogonally stiffened plate. The constraints deal with the static overall plate buckling, the stiffener failure and the fatigue strength of the welded connections between the stiffeners and the interaction of the two types of failure. The cost function includes the cost of material, assembly, welding and painting. Randomness is considered both in loading and material properties. A level II reliability method (FORM) is employed. The overall structural reliability is obtained by using Ditlevsen method of conditional bounding. The costs of the plate designed to ensure a stipulated probability of failure will be compared with the solutions obtained for a code based method, which employs partial safety factors.