Influence of Using Discrete Cross-Section Variables for All Types of Truss Structural Optimization with Dynamic Constraints for Buckling

Abstract

The use of continuous variables for cross-sectional dimensions in truss structural optimization gives solutions with a large number of different cross sections with specific dimensions which in practice would be expensive, or impossible to create. Even slight variations from optimal sizes can result in unstable structures which do not meet constraint criteria. This paper shows the influence of the use of discrete cross section sizes in optimization and compares results to continuous variable counterparts. In order to achieve the most practically applicable design solutions, Euler buckling dynamic constraints are added to all models. A typical space truss model from literature, which use continuous variables, is compared to the discrete variable models under the same conditions. The example model is optimized for minimal weight using sizing and all possible combinations of shape and topology optimizations with sizing.

Comparing Truss Sizing and Shape Optimization Effects for 17 Bar Truss Problem

“…The implementation of all of these aspects is not always possible, or even in some cases favorable, so combinations of two are most frequently employed. Previous research [1] shows the difference in results comparing individual aspect optimization and combinations of optimization aspects. Aside from a complete simultaneous sizing, shape, and topology optimization, the next most favorable type in terms of mass decrease is sizing and shape combined.…”

“…In addition to these constraints, the minimal element length constraint is implemented due to the possibility of a global extreme value having a small length which could not be produced. The value assigned to this constraint is taken from engineer experience or design guidelines given in literature or corresponding standards [1]. This constraint is given as (Eg.…”

“…For sizing optimization discrete cross-section sets must be used to give results representative of available stock in a given material. This is best described in papers [1,8,9] where authors showed how continuous sizing variables lead to unusable solutions. Realistic and definable constraints are just as important, and they allow for the design of trusses which can hold up in practice.…”

Effects of Limiting the Number of Different Cross-Sections Used in Statically Loaded Truss Sizing and Shape Optimization

“…Dynamic buckling constraints were used by authors in [ 6 ] to demonstrate the improvement in achieving the minimal weight using their proposed algorithm and compared their results to [ 7 ], which used these constraints on various test examples. A sizing optimization comparison, for example, with the Euler buckling constraint turned on and off in [ 8 ], shows the drastic increase in optimal weight due to the increase in the cross-sections of the compressed bars. The authors presented a new algorithm called PO (political optimization) in [ 9 ] and successfully used it to find the optimal solutions in standard test examples with the addition of buckling constraints.…”

Sizing and shape optimization material use in 10 bar trusses

“…In recent years authors have been slowly moving towards using more practical variable setups and constraints to bring truss optimization closer to direct realworld application. Researchers in [4,5] showed the need for using discrete cross-section variable sets in order to match available, standard, dimensions of cross-section profiles. The implementation of Euler buckling constraints has increasingly started becoming part of the mathematical model in most research [6][7][8].…”