Implementation of natural frequency analysis and optimality criterion design

Levy, R.; Chai, King

doi:10.1016/0045-7949(79)90096-8

Cited by 24 publications

(1 citation statement)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Over the last few decades, and many researchers have given considerable attention to develop efficient optimization algorithms to solve structural optimization problems with frequency constraints. Pioneering works in this field were carried out using gradient-based optimization techniques [5][6][7]. However, it has been recognized for many years that frequency constraints are highly nonlinear, non-convex, and implicit with respect to the design variables, and this makes dynamic sensitivity analysis difficult or even impossible [8,9].…”

Section: Introductionmentioning

confidence: 99%

Optimal Design of Large-scale Dome Truss Structures with Multiple Frequency Constraints Using Success-history Based Adaptive Differential Evolution Algorithm

Kaveh

Hamedani²,

Hamedani³

2022

Period. Polytech. Civil Eng.

View full text Add to dashboard Cite

The success-history based adaptive differential evolution (SHADE) algorithm is an efficient modified version of the differential evolution (DE) algorithm, and it has been successfully applied to solve some real-world optimization problems. However, to the best of our knowledge, it has been rarely applied in the field of structural optimization. The optimal design of structures with frequency constraints is well known as a highly nonlinear and non-convex optimization problem with many local optima. In this paper, the SHADE algorithm is examined in the context of size optimization of large-scale truss structures with multiple frequency constraints. In SHADE, a historical memory of successful control parameter settings is used to guide the generation of new control parameters. In order to demonstrate the effectiveness and efficiency of SHADE, three truss optimization problems with multiple frequency constraints are presented. The three examples considered in this paper include a 600-bar single-layer dome-shaped truss, a 1180-bar single-layer dome-shaped truss, and a 1410-bar double-layer dome-shaped truss. The results obtained by the SHADE algorithm are presented and compared with the best-known results reported in the literature. Numerical results indicate the effectiveness and superior performance of SHADE over other algorithms in terms of solution accuracy and robustness. It is worth mentioning that in all the three cases considered, the optimal designs obtained by SHADE are the best ones reported in the literature so far. However, SHADE often requires fewer structural analyses than those required by the other algorithms.

show abstract

Section: Introductionmentioning

confidence: 99%

Optimal Design of Large-scale Dome Truss Structures with Multiple Frequency Constraints Using Success-history Based Adaptive Differential Evolution Algorithm

Kaveh

Hamedani²,

Hamedani³

2022

Period. Polytech. Civil Eng.

View full text Add to dashboard Cite

show abstract

An adaptive procedure for stabilizing convergence quality in frequency‐constrained design optimization of bar structures supporting non‐structural mass

Phan

McGee

1991

Numerical Meth Engineering

View full text Add to dashboard Cite

This paper presents an improved optimality criteria (OC) method for minimum-weight design of bar structures supporting non-structural mass and subjected to multiple natural frequency constraints and minimum gauge restrictions. The convergence quality of the OC method hinges on both the number of active constraints retained and the choice of a proper step size. This being the case, a criterion, which uses previous scaled designs to 'adaptively' tune the step size, is established with the purpose of dissolving the (sometimes violent) oscillations of scaled design weights in the iteration history. As the step size is tuned, the convergence rate is decreased. Hence, a modified Aitken's accelerator, which extrapolates from previous scaled designs to obtain an improved one, is used. Its effect is to both increase the overall rate and reduce the net cost of convergence by reducing the number of repeat finite element analyses. The method presented here is used to qualitatively survey the convergence of several OC recursive schemes compositely used to resize and to evaluate the Lagrange multipliers. Design examples are presented to demonstrate the method. The method is adaptable, as it eliminates the need for adjustments of internal parameters during the redesign stage.

show abstract

The Integrated Approach of FEM-SLP for Solving Problems of Optimal Design

Pedersen¹

1981

Optimization of Distributed Parameter Structures — Volume I

View full text Add to dashboard Cite

Implementation of natural frequency analysis and optimality criterion design

Cited by 24 publications

References 4 publications

Optimal Design of Large-scale Dome Truss Structures with Multiple Frequency Constraints Using Success-history Based Adaptive Differential Evolution Algorithm

Optimal Design of Large-scale Dome Truss Structures with Multiple Frequency Constraints Using Success-history Based Adaptive Differential Evolution Algorithm

An adaptive procedure for stabilizing convergence quality in frequency‐constrained design optimization of bar structures supporting non‐structural mass

The Integrated Approach of FEM-SLP for Solving Problems of Optimal Design

Contact Info

Product

Resources

About