Structural optimization based on topology optimization techniques using frame elements considering cross-sectional properties

Takezawa, Akihiro; Nishiwaki, Shinji; Izui, Kazuhiro; Yoshimura, Masataka

doi:10.1007/s00158-006-0059-1

Cited by 26 publications

(11 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Due to the large dimensionality of the design space, this discrete problem is often relaxed to nonlinear optimization problems with continuous design variables instead of the binary design variables. Several methods have been proposed for topology optimization based on the physical or geometric values such as the variable element thickness [43,44], crosssectional area [45], or pseudodensity as the design variables, that is,…”

Section: Independent-continuous-mapping (Icm) Methodsmentioning

confidence: 99%

Topology Optimization Using Parabolic Aggregation Function with Independent-Continuous-Mapping Method

Tie

Sui

2013

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This paper concentrates on finding the optimal distribution for continuum structure such that the structural weight with stress constraints is minimized where the physical design domain is discretized by finite elements. A novel Independent-Continuous-Mapping (ICM) method is proposed to convert equivalently the binary design variables which is used to indicate material or void in the various elements to independent continuous design variables. Moreover, three smooth mappings about weight, stiffness, and stress of the structural elements are introduced to formulate the objective function based on the so-called concepts of polish function and weighting filter function. A new general continuous approach for topology optimization is given which can eliminate the stress singularity phenomena more efficiently than the traditionalε-relaxation method, and an alternative strain energy method for the stress constraints is proposed to overcome the difficulty in stress sensitivity analyses. Mathematically, by means of a generalized aggregation KS-like function defined as the parabolic aggregation function, a topology optimization model is formulated with the weight objective and single parabolic global strain energy constraints. The numerical examples demonstrate that the proposed methods effectively remove the stress concentrations and generate black-and-white designs for practically sized problems.

show abstract

Section: Independent-continuous-mapping (Icm) Methodsmentioning

confidence: 99%

Topology Optimization Using Parabolic Aggregation Function with Independent-Continuous-Mapping Method

Tie

Sui

2013

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…However, for frequency‐constrained topology optimization problems, local modes associated with the unnecessary elements may occasionally appear . One way to solve this problem is to keep the local modes from being observed during the optimization process, and a similar approach was used in the works of Tcherniak and Takezawa et al by letting the mass value of the unnecessary elements equal zero. Likewise, in the present work, the material density values of the unnecessary elements are assigned with an extremely small value, whereas the densities for the retained elements keep their original value.…”

Section: Problem Formulationmentioning

confidence: 99%

An engineering method for complex structural optimization involving both size and topology design variables

Chen

2018

Numerical Meth Engineering

View full text Add to dashboard Cite

This work presents an engineering method for optimizing structures made of bars, beams, plates, or a combination of those components. Corresponding problems involve both continuous (size) and discrete (topology) variables. Using a branched multipoint approximate function, which involves such mixed variables, a series of sequential approximate problems are constructed to make the primal problem explicit. To solve the approximate problems, genetic algorithm (GA) is utilized to optimize discrete variables, and when calculating individual fitness values in GA, a second-level approximate problem only involving retained continuous variables is built to optimize continuous variables. The solution to the second-level approximate problem can be easily obtained with dual methods. Structural analyses are only needed before improving the branched approximate functions in the iteration cycles. The method aims at optimal design of discrete structures consisting of bars, beams, plates, or other components. Numerical examples are given to illustrate its effectiveness, including frame topology optimization, layout optimization of stiffeners modeled with beams or shells, concurrent layout optimization of beam and shell components, and an application in a microsatellite structure. Optimization results show that the number of structural analyses is dramatically decreased when compared with pure GA while even comparable to pure sizing optimization.

show abstract

“…For simple cross-sectional shapes, such as circular or rectangular sections, an analytical equation can be derived for relating cross-sectional area to moment of in ertia. Structures using these cross-sectional shapes for members were used for design under local and global instability constraints (Achtziger 1999;Ohsaki and Katoh 2005;Richardson et al 2012;Torii et al 2015), optimizing vehicle bodies (Fredricson et al 2003;Pedersen 2003Pedersen , 2004, material selection and cross-section design (Fredricson 2005; Takezawa et al 2007), and reliabilitybased design (Mogami et al 2006), using displacement-based objectives. However, actual structures are usually designed from an available library of standard sections (for example, factorybuilt I-beams).…”

Section: Introductionmentioning

confidence: 99%

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

Changizi

Jalalpour

2017

J. Struct. Eng.

View full text Add to dashboard Cite

Structural optimization based on topology optimization techniques using frame elements considering cross-sectional properties

Cited by 26 publications

References 37 publications

Topology Optimization Using Parabolic Aggregation Function with Independent-Continuous-Mapping Method

Topology Optimization Using Parabolic Aggregation Function with Independent-Continuous-Mapping Method

An engineering method for complex structural optimization involving both size and topology design variables

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

Contact Info

Product

Resources

About