Multiobjective Evolutionary Structural Optimization Using Combined Static/Dynamic Control Parameters

Woo-Young, Kim; Grandhi, Ramana V.; Haney, Mark

doi:10.2514/1.16971

Cited by 25 publications

(19 citation statements)

References 11 publications

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“…"#$ , and are functions of the design variables, and gradients of the structural compliance with respect to are easily computed with the adjoint method [25]. Optimal topologies are found with the method of moving asymptotes [26]; the process is terminated when the difference in objective function between consecutive iterations is less than 1•10 - 5 . The details of the aforementioned filter are as follows.…”

Section: A Aeroelastic Compliancementioning

confidence: 99%

“…The resulting optimization problem is typically solved with SIMP-based methods (solid isotropic material with penalization), or level set methods. This parameterization is utilized in the work of Kim et al [5] (at a single panel level, rather than a complete wing), James and Martins [6], and Dunning et al [7]. The resulting structure typically bears no resemblance to traditional rib/spar networks, which may indicate one of two things.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Topology of Aircraft Rib and Spar Structures Under Aeroelastic Loads

Stanford

Dunning

2015

Journal of Aircraft

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Several topology optimization problems are conducted within the ribs and spars of a wing box. It is desired to locate the best position of lightening holes, truss/cross-bracing, etc. A variety of aeroelastic metrics are isolated for each of these problems: elastic wing compliance under trim loads and taxi loads, stress distribution, and crushing loads. Aileron effectiveness under a constant roll rate is considered, as are dynamic metrics: natural vibration frequency and flutter. This approach helps uncover the relationship between topology and aeroelasticity in subsonic transport wings, and can therefore aid in understanding the complex aircraft design process which must eventually consider all these metrics and load cases simultaneously.

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Section: A Aeroelastic Compliancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Topology of Aircraft Rib and Spar Structures Under Aeroelastic Loads

Stanford

Dunning

2015

Journal of Aircraft

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“…17 Xia and Wang applied the level set method to circumvent the formation of gray intermediate material areas that commonly occur in compliance minimization of thermoelastic structures. 18 Finally, practical examples of thermoelastic topology optimization can be found in works by Penmetsa et al 19 and Kim et al 20 where topology optimization was utilized in the design of thermal protection systems (TPS) that are subjected to both intense thermal and vibro-acoustic loads during atmospheric reentry. …”

Section: Topology Optimizationmentioning

confidence: 98%

Stiffening of Thermally Restrained Structures via Thermoelastic Topology Optimization

Deaton¹,

Grandhi²

2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

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In the past, the majority of work in the thermal structures field has focused on design problems whereby thermal expansion can be accommodated as a means to reduce or eliminate thermal stresses. In the modern day, several new applications, including engine exhaust-washed structures for embedded engine aircraft, are posing new design scenarios where this prescription is not possible. Thus it becomes necessary to utilize new design techniques to solve the problem of stiffening and stress reduction in thermal structures with restrained expansion. In this work, a design scenario is presented to demonstrate the challenges associated with design of thin shell structures in a thermal environment and the breakdown of common design methodologies. These challenges include a fundamental nonintuitiveness in the design space and the design dependency that occurs with thermal loading. Three different topology optimization formulations are presented and applied to solve this problem. The effectiveness of these methods are benchmarked against one another and general recommendations are made regarding effective design solutions for restrained thermal structures. NomenclatureA = cross section area c = compliance e = element index for topology optimization E = elastic modulus E e = elemental elastic modulus E o = base elastic modulus F = reaction force F o = reaction force at reference thickness F L = limit on reaction force in optimization F me = mechanical load vector in FEA F th = thermal load vector in FEA k = stiffness ratio parameter K s = spring stiffness K = stiffness matrix in FEA L = length M = reaction moment M o = reaction moment at reference thickness N = total number of topology design elements p = penalization factor ρ e = pseudo-density design variable ρ min = minimum allowable pseudo-density t = thickness t o = nominal baseline thickness ΔT = elevated temperature change U = displacement vector in FEA v e = element volume V f = allowable volume fraction for optimization w = width

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“…The same authors have also applied this method to two different objectives (Proos et al (2001b)), namely, minimum compliance and maximum specific inertia. Kim et al (2006) developed a multiobjective structural optimization method for a three-dimensional (3D) thermal protection system de-sign using an ESO algorithm. They again used a weighted sums method with the objective of minimizing maximum thermal stress and maximizing the fundamental frequency.…”

Section: A Quick History Of Topology Optimizationmentioning
confidence: 99%

Multiobjective and multi-physics topology optimization using an updated smart normal constraint bi-directional evolutionary structural optimization method
Munk
¹
,
Kipouros
²
,
Vio
³

et al. 2017
Struct Multidisc Optim
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To date the design of structures using topology optimization methods has mainly focused on single-objective problems. Since real-world design problems typically involve several different objectives, most of which counteract each other, it is desirable to present the designer with a set of Pareto optimal solutions that capture the trade-off between these objectives, known as a smart Pareto set. Thus far only the weighted sums and global criterion methods have been incorporated into topology optimization problems. Such methods are unable to produce evenly distributed smart Pareto sets. However, recently the smart normal constraint method has been shown to be capable of directly generating smart Pareto sets. Therefore, in the present work, an updated smart Normal Constraint Method is combined with a Bi-directional Evolutionary Structural Optimization (SNC-BESO) algorithm to produce smart Pareto sets for multiobjective topology optimization problems. Two examples are presented, showing that the Pareto solutions found by the SNC-BESO method make up a smart Pareto set. The first example, taken from the literature, shows the benefits of the SNC-BESO method. The second example is an industrial design problem for a micro fluidic mixer. Thus, the problem is multi-physics as well as multiobjective, highlighting the applicability of such methods to real-world problems. The results indicate that the method is capable of producing smart Pareto sets to industrial problems in an effective and efficient manner.

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Multiobjective Evolutionary Structural Optimization Using Combined Static/Dynamic Control Parameters

Cited by 25 publications

References 11 publications

Optimal Topology of Aircraft Rib and Spar Structures Under Aeroelastic Loads

Optimal Topology of Aircraft Rib and Spar Structures Under Aeroelastic Loads

Stiffening of Thermally Restrained Structures via Thermoelastic Topology Optimization

Multiobjective and multi-physics topology optimization using an updated smart normal constraint bi-directional evolutionary structural optimization method

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