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A continuum topology optimization methodology suitable for finding optimal forms of large-scale sparse structures is presented. Since the need to avoid long compressive spans can be critical in determining the optimal form of such structures, a formulation is used wherein the structure is modeled as a linear elastic continuum subjected to design loads, and optimized in form to maximize the minimum critical buckling load. Numerical issues pertinent to accurate solution of the linearized buckling eigenvalue problem and accurate design sensitivity analysis are discussed. The performance of the proposed design formulation is demonstrated on a few problems designed to find optimal forms of a canyon bridge, long-span bridges, and an electrical transmission tower. In all cases, very credible structural forms are obtained with the proposed design formulation. The results of the design examples solved are typically superior structural forms with regard to buckling stability than those obtained to minimize the mean structural compliance. CE Database subject headings: Optimization; Buckling; Sensitivity analysis; Eigenvalues.

The objective of this study is to describe a problem formulation and an optimization procedure for the design of elevated reinforced concrete foundations for vibrating machines. Special emphasis is placed on structures composed of footings, beams, and columns. The dimensions of the structure and its reinforcement are the design variables for the optimization problem. The objective function consists of costs of the concrete, the steel, the form, and the propping form. Constraints related to material and soil failure, as well as geometrical limits and human comfort are imposed. A new failure surface for columns and beams subjected to biaxial bending and axial loads is defined and used in the formulation. The main motivation of using the new failure surface is to save a large amount of computational effort in the solution of this dynamic response optimization problem. The problem of minimizing the structural cost while satisfying the operating and safety requirements is solved using an augmented Lagrangian method. A large number of constraints (time dependent and time independent) is treated without any difficulty in the method. The numerical methods used in the solution process are described. Optimal solutions for an example problem are obtained and discussed. DOI: 10.1061/(ASCE)0733-9445(2002)128:11(1470) CE Database keywords: Optimization; Design; Concrete structures; Dynamic loads; Soil-structure interaction.

Discrete ground structure topology optimization design methods have to date received considerable attention in structural engineering. An alternative class of structural topology optimization methods, which have not yet received much attention in structural engineering, but which have undergone considerable development in the past decade, are the so-called continuum formulations. In this work, a continuum structural topology optimization formulation is presented and applied to the concept design optimization of structural bracing systems that are needed to stiffen tall structures against sidesway under lateral-wind and seismic-type loading. Although demonstrated here in the context of these specific design examples, continuum structural topology optimization methods are believed to hold potential as a design tool for a wide range of civil engineering type structures. A variety of continuum topology design formulations, including static compliance minimization and eigenvalue optimization, are explored, and solution parameters are varied to show that a number of design possibilities can be realized as solutions.

A new failure surface and criterion are developed for prismatic reinforced concrete structural elements subjected to biaxial bending and axial load. The failure criterion is a smooth surface in 3D space (two moments and axial load). It is governed by eight parameters, four of which are strengths that can be computed directly from strain-based failure criteria. The remaining four are exponential coefficients whose values are calculated using optimization techniques. Since the failure criterion is intended for use in automated design-optimization procedures, methods for parameter estimation based on design of the RC structural element are developed and tested. The parameters of the proposed surface are calculated first by simply minimizing approximation errors and then by allowing only conservative approximation errors. A conclusion of this work is that the proposed methods are reliable and can be used to rapidly check allowable capacity constraints in load space during design optimization of reinforced concrete structures undergoing dynamic loading.