Shape optimization using adaptive shape refinement

Kohli, Himani; Carey, G. F.

doi:10.1002/nme.1620361408

Cited by 16 publications

(6 citation statements)

References 11 publications

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“…In recent literature, a commonly explored avenue for improving the efficiency of shape optimization algorithms is the use of an adaptive or refinement-based parametrization. Kohli and Carey 9 proposed a shape optimization algorithm with adaptive refinement, citing the increased likelihood of finding global optima and the reduced cost of evaluating gradients with finite-difference schemes in early iterations. Desideri et al 10 applied a nested, adaptive Bezier parametrization to a 2-D aerodynamic shape optimization problem and found improved convergence rates and solution quality with respect to the objective function.…”

Section: Introductionmentioning

confidence: 99%

A Dynamic Parametrization Scheme for Shape Optimization Using Quasi-Newton Methods

Hwang

Martins

2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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A variable parametrization scheme is developed and demonstrated for shape optimization using quasi-Newton methods. The scheme performs adaptive parametrization refinement while preserving the approximate Hessian of the shape optimization problem and enables free-form shape design using quasi-Newton optimization methods. Using a Bspline parametrization, the scheme is validated using a 1-D shape approximation problem and is shown to improve efficiency and optimal solution quality compared to the traditional quasi-Newton method. The scheme is also applied to a 3-D test problem, demonstrating the feasibility of free-form shape optimization using parametrization refinement and a method for partially constraining the degrees of freedom.

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Section: Introductionmentioning

confidence: 99%

A Dynamic Parametrization Scheme for Shape Optimization Using Quasi-Newton Methods

Hwang

Martins

2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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“…Recently, adaptive or refinement-based parametrization have been developed to improve the efficiency of shape optimization algorithms [30,31,32,33]. Zingg et al [34] show that gradient-based optimization is more efficient than gradient-free optimization in aerodynamics.…”

Section: Sole Design Frameworkmentioning

confidence: 99%

Design of optimized soft soles for humanoid robots

Magistris

Miossec

Escande

et al. 2017

Robotics and Autonomous Systems

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We describe a methodology to design foot soles for a humanoid robot given walking gait parameters (i.e. given centerof-mass and zero-moment-point trajectories). In order to obtain an optimized compliant sole, we devised a shape optimization framework which takes -among other inputs, an initial rough (simplified) shape of the sole and refines it through successive optimization steps under additional constraints and a cost function. The shape is optimized based on the simulation of the sole deformation during an entire walking step, taking time dependent input of the walking pattern generator into account. Our shape optimization framework is able to minimize the impact of the foot with the ground during the heel-strike phase and to limit foot rotation in case of perturbations. Indeed, low foot rotation enforces a vertical posture and secures the balance of the humanoid robot. Moreover, weight restriction (formulated as a constraint on the sole volume) is added to our optimization problem.

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“…Other examples of the applications of the gradient method inc1ude the optimization of a radar cross section [Bondeson et al (2004)], and the optimization of a shaft cross-section using an adaptive shape refinement technique akin to an automatic adjustment of the number of control points on a spline [Kohli and Carey (1993)]. An adaptive shape refinement technique, based on the gradient and the finite element methods, has been used by Schleupen et al (2000) to optimize sorne mechanical objects subjected to applied stresses.…”

Section: Optimization Techniquesmentioning

confidence: 99%