Stress-Based Topology Optimization of Steel-Frame Structures Using Members with Standard Cross Sections: Gradient-Based Approach

Changizi, Navid; Jalalpour, Mehdi

doi:10.1061/(asce)st.1943-541x.0001807

Cited by 28 publications

(22 citation statements)

References 39 publications

(37 reference statements)

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“…The lower limit

ρ_{\min}

avoids singularity during optimization whereas the upper limit is based on the maximum cross‐sectional area available for I‐shaped sections in American Institute of Steel Construction 38 . An approach for relating the cross‐sectional area to other geometric properties for I‐shaped cross‐sections suggested by Changizi and Jalalpour 39 is adopted in this study and the regression curves for the median range are used for the numerical examples.…”

Section: Methodsmentioning

confidence: 99%

Topology optimization employing a condensation method for nonlinear structural frames with supplemental mass

Changizi

Warn

2021

Numerical Meth Engineering

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A topology optimization schema employing a condensation method for nonlinear frame structures with supplemental mass subjected to time‐varying excitation is presented. In the context of the design of structural frames, in certain applications, the supplemental mass can be order(s) of magnitude larger than the mass of the system itself. Thus, condensing the system of governing equations to only those associated with the supplemental mass, reduces the complexity and computational cost of the dynamic analysis and thus the optimization process. In addition to considering material nonlinearity, distributed plasticity, and multiaxial interactions, the hysteretic beam finite element (FE) model employed in this study has constant elastic stiffness and hysteretic matrices facilitating a Guyan‐type condensation of the nonlinear dynamic equations. Furthermore, the nonlinear dynamic equations and element evolution equations of hysteretic FE modeling are concisely presented as a system of first‐order nonlinear ordinary differential equations (ODEs) that can be solved using general ODE solvers. The schema is demonstrated on various design problems considering different arrangements of supplemental mass, where the objective is to minimize the volume of the structure subject to maximum displacement constraint using a single p‐norm.

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“…The lower limit

ρ_{\min}

Section: Methodsmentioning

confidence: 99%

Topology optimization employing a condensation method for nonlinear structural frames with supplemental mass

Changizi

Warn

2021

Numerical Meth Engineering

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“…Concerning structural systems and trusses optimisation, recent improvements include multi-objective optimisation techniques [395], Differential Evolution Algorithms [267], quantile regression for fostering the use of (discontinuous) I-beam cross-sections as design variables [396], and developments with the Interior Point method for non-linear and non-convex truss optimisation problems [397]. However, one of the most impressive developments can be found by Larsen et al [398], a near-optimal truss design based on the homogenisation-based continuum TO.…”

Section: Steel Elements Designmentioning

confidence: 99%

Topology Optimisation in Structural Steel Design for Additive Manufacturing

2021

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Topology Optimisation is a broad concept deemed to encapsulate different processes for computationally determining structural materials optimal layouts. Among such techniques, Discrete Optimisation has a consistent record in Civil and Structural Engineering. In contrast, the Optimisation of Continua recently emerged as a critical asset for fostering the employment of Additive Manufacturing, as one can observe in several other industrial fields. With the purpose of filling the need for a systematic review both on the Topology Optimisation recent applications in structural steel design and on its emerging advances that can be brought from other industrial fields, this article critically analyses scientific publications from the year 2015 to 2020. Over six hundred documents, including Research, Review and Conference articles, added to Research Projects and Patents, attained from different sources were found significant after eligibility verifications and therefore, herein depicted. The discussion focused on Topology Optimisation recent approaches, methods, and fields of application and deepened the analysis of structural steel design and design for Additive Manufacturing. Significant findings can be found in summarising the state-of-the-art in profuse tables, identifying the recent developments and research trends, as well as discussing the path for disseminating Topology Optimisation in steel construction.

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“…To investigate the properties of the design space, the sections are plotted in Figure 1. The line in the figure represents the quantile regression model for the 90th percentile (Changizi and Jalalpour, 2017b). As can be seen that the sections are sparsely distributed over the plane and a given Area could potentially correspond to several sections.…”

Section: Discrete Optimization Algorithmmentioning

confidence: 99%

“…To compare the differences brought by various selections of design variables, namely using both Area and Ix or using Area only , an algorithm using the cross-sectional area only is also proposed. The cross-sectional area is updated using equation (11), and other sectional properties can be determined using the quantile regression model (Changizi and Jalalpour, 2017b) shown in Figure 1. The plastic section modulus is not included in the regression model, and it is calculated when other sectional dimensions are derived using the regression model.…”

Section: Discrete Optimization Algorithmmentioning

confidence: 99%

“…A section is controlled by several sectional properties, and if the Area or Ix is selected as the design variable, regression models representing relationships between the design variables and other sectional properties are needed. Such a practice is frequently used (Adeli and Sarma, 2000;Changizi and Jalalpour, 2017b;Gong et al, 2012;Xu et al, 2006) because discrete problems are made continuous and therefore much easier to solve. If Area is selected as the design variable, it seems possible to arrive at a certain section through a given Area.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An efficient discrete optimization algorithm for performance-based design optimization of steel frames

Wang

Zhang

Qin

et al. 2019

Advances in Structural Engineering

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Performance-based design optimization of steel frames, with element sections selected from standard sections, is a computationally intensive task. In this article, an efficient discrete optimization algorithm is proposed for performance-based design optimization of steel frames. The computational efficiency is improved by searching in a sensible manner, guided by the deformation information of structural elements. To include all standard sections in the design space, the cross-sectional area ( Area) and moment of inertia ( Ix) are selected as the design variables. Based on different relationships between Area and Ix, a twofold strategy is put forward, which includes a quick exploration and an elaborate exploitation. For comparison, a similar algorithm is also proposed, using Area as the only design variable. A fixed relationship between Area and other sectional properties is used. Two numerical examples are presented to minimize the structural weight while satisfying performance constraints. The results indicate that the proposed discrete algorithm can achieve lighter structural designs than the area-only algorithm. Furthermore, the convergence history proves that a high computational efficiency can be realized by using the proposed algorithm.

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Stress-Based Topology Optimization of Steel-Frame Structures Using Members with Standard Cross Sections: Gradient-Based Approach

Cited by 28 publications

References 39 publications

Topology optimization employing a condensation method for nonlinear structural frames with supplemental mass

Topology optimization employing a condensation method for nonlinear structural frames with supplemental mass

Topology Optimisation in Structural Steel Design for Additive Manufacturing

An efficient discrete optimization algorithm for performance-based design optimization of steel frames

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