Computation of pareto optima in structural design

Carmichael, David G.

doi:10.1002/nme.1620150610

Cited by 64 publications

(31 citation statements)

References 11 publications

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“…The Pareto front of optimal designs will be investigated using the -constraint method. [20][21][22] In this method the power is constrained to be less than some value while the thrust is the objective for which the design is optimized. The constraint power is then slowly relaxed to calculate the Pareto front.…”

Section: Optimizationmentioning

confidence: 99%

Aeroelastic Shape Optimization of a Pluging Plate

Stewart¹,

Patil²,

Canfield³

et al. 2012

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

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In this paper, aeroelastic shape optimization is performed on flapping micro air vehicle (MAV) wings in forward flight. The aeroelastic model tightly couples the structural plate finite element model with an unsteady vortex lattice method aerodynamic model. A gradient-based optimizer is used to maximize the cycle-average thrust generated by the wing while minimizing the power requirements. The multiobjective optimization is performed using the -constraint method. The optimizer creates wings that maximize the span while the chord is limited by the power constraint. Nomenclatureα instantaneous angle of attack ∆t time step size η, ξ area coordinates of the DKT element Γ b vector of bound vorticies Γ w vector of wake vorticies ρ fluid density A b matrix of influence coefficients from the bound vorticity A e area of the e th finite element A w matrix of influence coefficients from the wake B DKT strain-displacement relationship matrix C s proportional structural damping D b DKT stress-strain relationship matrix F aero vecotr of aerodynamic forces acting on the wing F inertia vecotr of inertial forces acting on the wing g gravitational constant h rigid body motion at the nodes h CP vector of rigid-body velocity at the control points K s structural stiffness matrix for the DKT elements L lift m number of triangular elements in the structure M s structural mass matrix for the DKT elements m wing mass of the wing P in input power q vector of the global nodal degrees of freedom T thrust t h thickness of the plate T α,qmatrix that converts nodal deformation to control point rotations T a,cp matrix that converts pressure at the control points to nodal forces T V,q matrix that converts the nodal velocities to velocities at the control points V s velocity of the air acting on the wing due to the rate of the deformation V kin velocity of the air acting on the wing due to the prescribed kinematic motion

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Section: Optimizationmentioning
confidence: 99%

Aeroelastic Shape Optimization of a Pluging Plate
Stewart¹,
Patil²,
Canfield³
et al. 2012
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
2
0
1
0
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“…Using Eqs. (1) and (8), von Mises stresses of each element are obtained from the i th natural mode to the n th natural mode. Each natural mode is used as a displacement vector, and the stress components for each natural mode are obtained by using the strain-displacement and stress-strain relations.…”

Section: Control Parameter For Dynamic Analysismentioning
confidence: 99%

“…That is, multi-objective optimization is the generation of a design that achieves the optimum performance of the structure while consideration is given to various criteria. 7,8 The solution to the multi-objective problem is known as a Pareto optimum. 8,9 Pareto optima are not unique solutions, but rather they consist of a series of solutions.…”

Section: Introductionmentioning
confidence: 99%

See 1 more Smart Citation
Multi-Objective Evolutionary Structural Optimization Using Combined Static/Dynamic Control Parameters. Delivery Order 0007
Grandhi¹,
Woo-Young²,
Haney³
2007
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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information SPONSORING/MONITORING AGENCY REPORT NUMBER(S) AFRL-RB-WP-TR-2008-3090 DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution unlimited. SUPPLEMENTARY NOTESPAO Case Number: WPAFB 08-1717, 27 Mar 2008. Report contains color. ABSTRACTA thermal protection system (TPS) is responsible for protecting a spacecraft's components from melting due to high reentry temperatures. In the design of TPS, both maximum thermal stress and minimum natural frequency must be considered due to the combined thermoacoustic environment inherent in high-speed vehicle applications. A multiobjective structural optimization method for the three-dimensional acreage TPS design is developed using an evolutionary structural optimization (ESO) algorithm. The static control parameter used to find the optimum in minimum thermal stress design is modified to address an irregular mode-switching phenomenon, as well as to improve the modal stiffness in dynamic analysis. Two objectives are optimized simultaneously, namely, the maximization of fundamental natural frequency and the minimization of maximum thermal stress. The proposed modified control parameter is demonstrated in the design of a metallic TPS using the method of weighted objectives. The results are then compared with the conventional ESO sensitivity approach. This work concludes by applying the methodology which makes use of both topology and shape optimization in the design of an acreage TPS.
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“…Koski 1979Koski , 1982Carmichael 1980;Koski and Silvennoinen 1982;Adali 1983) do not encompass the bi-criteria problem discussed herein.…”

Section: Introductionmentioning
confidence: 95%

Bi-criteria optimization of structures liable to instability
Pietrzak
¹

1994
Structural Optimization
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The paper deals with the optimization of the geometry of structures prone to bifurcation instability. The optimization problem is treated as a bi-criteria one, with the aims of minimizing the volume of the structure and maximizing the safety factor against buckling. Since the two aims are conflicting, the solutions to the problem are taken to be of Pareto type. Two numerical examples are presented; the first one refers to a simple pin-jointed truss and the second one to a portal frame.

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Computation of pareto optima in structural design

Cited by 64 publications

References 11 publications

Aeroelastic Shape Optimization of a Pluging Plate

Aeroelastic Shape Optimization of a Pluging Plate

Multi-Objective Evolutionary Structural Optimization Using Combined Static/Dynamic Control Parameters. Delivery Order 0007

Bi-criteria optimization of structures liable to instability

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