OPTIMAL DESIGN OF TIMBER-FRAME BUILDINGS

17 - Optimum Performance-Based Seismic Design of Frames Using Metaheuristic Optimization Algorithms

The method of optimal design of structures by finite topology modification is presented in the paper. This approach is similar to growth models of biological structures, but in the present case, topology modification is described by the finite variation of a topological parameter. The conditions for introducing topology modification and the method for determining finite values of topological parameters characterizing the modified structure are specified. The present approach is applied to the optimal design of truss, beam, and frame structures. For trusses, the heuristic algorithm of bar exchange is proposed for minimizing the global compliance subject to a material volume constraint and it is extended to volume minimization with stress and buckling constraints. The optimal design problem for beam and frame structures with elastic or rigid supports, aimed at minimizing the structure cost for a specified global compliance, is also considered.

Non-parametric free-form optimal design of frame structures in natural frequency problem

The robust design of structures is essential to improve their stabilities in structural design optimization and has been studied based on a variety of optimization methods. In this study, we propose a non-parametric optimization method for the robust shape design of solid, shell, and frame structures subjected to uncertainty loadings. We adopt the concept of principal compliance to perform the robust shape design considering loading uncertainty and transform the principal compliance minimization problem into the fundamental eigenvalue maximization problem associated with the weighting coefficients of the unknown loadings. The proposed non-parametric shape optimization method for robust design consists of four main procedures: the eigenvalue analysis of structures, derivation of shape gradient functions considering repeated eigenvalues, velocity analysis based on the H1 gradient method, and shape updating. We perform several design examples to confirm the validity of the proposed non-parametric shape optimization method. The optimal results show that the proposed optimization method works efficiently to reduce the principal compliance and enhance the robust behavior of each design example. As a feature, by setting the weighting coefficients, we can enhance the robust of the structures subjected to the unknown loadings at different loading positions and with different magnitudes of the directions of the admissible loading space.

In this article, a harmony search algorithm is presented for optimum design of steel frame structures. Harmony search is a meta-heuristic search method which has been developed recently. It is based on the analogy between the performance process of natural music and searching for solutions of optimization problems. The design algorithms obtain minimum weight frames by selecting suitable sections from a standard set of steel sections such as American Institute of Steel Construction (AISC) wide-flange (W) shapes. Stress constraints of AISC Load and Resistance Factor Design (LRFD) and AISC Allowable Stress Design (ASD) specifications, maximum (lateral displacement) and interstorey drift constraints, and also size constraint for columns were imposed on frames. The results of harmony search algorithm were compared to those of the other optimization algorithms such as genetic algorithm, optimality criterion and simulated annealing for two planar and two space frame structures taken from the literature. The comparisons showed that the harmony search algorithm yielded lighter designs for the design examples presented.

In this article, an efficient hybrid optimization algorithm based on invasive weed optimization algorithm and shuffled frog-leaping algorithm is utilized for optimum design of skeletal frame structures. The shuffled frog-leaping algorithm is a population-based cooperative search metaphor inspired by natural memetic, and the invasive weed optimization algorithm is an optimization method based on dynamic growth of weeds colony. In the proposed algorithm, shuffled frog-leaping algorithm works to find optimal solution region rapidly, and invasive weed optimization performs the global search. Different benchmark frame structures are optimized using the new hybrid algorithm. Three design examples are tested using the new method. This algorithm converges to better or at least the same solutions compared the utilized methods with a smaller number of analyses. The outcomes are compared to those obtained previously using other recently developed meta-heuristic optimization methods.

CEPAO—an automatic program for rigid-plastic and elastic-plastic analysis and optimization of frame structures

Optimal shakedown design of metal structures under stiffness and stability constraints

Generative artificial intelligence offers a more efficient solution for the design of structures. However, an inverse generation of structures, which meet multiple design objectives, remains an open problem. This article thus focuses on the inverse design of frame structures and proposes Graph-based Diffusion-Generative Multiobjective design (GraphDGM), a graph-based generative data-driven surrogate model constrained by multiple targets. By integrating the finite element method (FEM), we construct datasets of frame structures subjected to various conditions. We then developed a conditional graph generation model based on the denoising diffusion probabilistic models (DDPM) and the attention mechanism. We show that our method can efficiently accomplish the inverse design of various frame structures, including a vehicle’s skeleton subjected to five simultaneous constraints. Furthermore, we present comparative experiments against baseline methods to demonstrate the effectiveness and superiority of the GraphDGM.

A modified objective function method for solving nonlinear multiobjective fractional programming problems

The performance‐based seismic design of steel special moment‐resisting frame (SMRF) structures is formulated as a multiobjective optimization problem, in which conflicting design criteria that respectively reflect the present capital investment and the future seismic risk are treated simultaneously as separate objectives other than stringent constraints. Specifically, the initial construction expenses are accounted for by the steel material weight as well as by the number of different standard steel section types, the latter roughly quantifying the degree of design complexity related additional construction cost; the seismic risk is considered in terms of maximum interstory drift demands at two hazard levels with exceedance probabilities being 50% and 2% in 50 years, respectively. The present formulation allows structural engineers to find an optimized design solution by explicitly striving for a desirable compromise between the initial investment and seismic performance. Member sizing for code‐compliant design of a planar five‐story four‐bay SMRF is presented as an application example using the proposed procedure that is automated by a multiobjective genetic algorithm. Copyright © 2004 John Wiley & Sons, Ltd.

This study covers the review of algorithms developed for the optimum design of steel skeletal structures from the first article published in 1960 until to date. The paper initially describes the mathematical formulation of a simple truss structural design problem. The early optimum design algorithms that were based on mathematical programming techniques where the design variables are assumed to be continuous are reviewed. The optimum design of steel framed structures necessitates the selection of steel profiles from the standard list of discrete steel sections and requires the satisfaction of design code provisions. Both mathematical programming and optimality criteria techniques need more capability to produce solution to this type of optimum design problems. Soft computing techniques emerged recently provide solution directly without needing any approximation. These techniques are classified and reviewed and their use in obtaining the optimum solution of actual industrial steel design applications is given.

Probabilistic optimal design of framed structures

In this paper, a nonlinear programming problem is considered where the functions involved are η-semi-differentiable. An equivalent η-approximated vector optimization problem is constructed by a modification of the objective and the constraint functions in the original multi-objective programming problem. The connection between (weak) efficient points in the original multi-objective programming problem and its equivalent η-approximated vector optimization is proved. Furthermore, a modified Lagrange function is introduced for a constructed vector optimization problem. By the help of the modified Lagrange function, saddle point results are presented for the original multi-objective programming problem.

Optimum sizing design of steel frame structures through maximum energy dissipation of friction dampers under seismic excitations