Shape optimization of continua using NURBS as basis functions

Azegami, Hideyuki; Fukumoto, Shota; Aoyama, Taiki

doi:10.1007/s00158-012-0822-4

Cited by 47 publications

(23 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The algorithm for solving Problem 2 based on the sequential quadratic programming is shown in previous papers [5,6]. In this algorithm, the H 1 gradient method is used for reshaping with shape derivatives g 0 and g 1 in (12) and (8), respectively.…”

Section: Solutionmentioning

confidence: 99%

“…The method for computing the shape derivative of the cost function is given as an adjoint variable method considering the rule for p. A solution to this new problem is presented based on the algorithm of sequential quadratic programming using the H 1 gradient method for reshaping in order to maintain the smoothness of the boundary [3][4][5][6]. The effectiveness of the rule for p is confirmed based on a numerical solution to a cantilever problem.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Construction method of the cost function for the minimax shape optimization problem

Shintani

Azegami

2013

JSIAM Letters

Self Cite

View full text Add to dashboard Cite

The present paper describes a method by which to formulate a shape optimization problem of a linear elastic continuum for minimizing the maximum value of a strength measure, such as the von Mises stress. In order to avoid the irregularity of the shape derivative of the maximum value, the Kreisselmeier-Steinhauser function of the strength measure is used as the cost function. In the cost function, a parameter is used to control the regularity of the shape derivative. In the present paper, we propose a rule by which to appropriately determine the parameter. The effectiveness of the proposed rule is confirmed through a numerical example of a cantilever problem.

show abstract

Section: Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Construction method of the cost function for the minimax shape optimization problem

Shintani

Azegami

2013

JSIAM Letters

Self Cite

View full text Add to dashboard Cite

show abstract

“…Isogeometric analysis (IGA) [16,33] combines the variational framework of the finite element method (FEM) [34] with the basis functions used in computer-aided design B David J. Benson dbenson@ucsd.edu 1 Department of Structural Engineering, University of California, San Diego, La Jolla, USA 2 Livermore Software Technology Corporation, Livermore, USA (CAD), e.g., nonuniform rational B-splines (NURBSs) [56]. This methodology has been successfully applied to a variety of domains, e.g., structural vibration [17], electromagnetics [15], fluids [1,7], fluid-structure interaction [6,8,32], phase field analysis [13,43], contact [48,72], fracture [18], shape optimization [2,57], topology optimization [19,67], cables and shells [10][11][12]58].…”

Section: Introductionmentioning

confidence: 99%

A multi-patch nonsingular isogeometric boundary element method using trimmed elements

2015

View full text Add to dashboard Cite

One of the major goals of isogeometric analysis is direct design-to-analysis, i.e., using computer-aided design (CAD) files for analysis without the need for mesh generation. One of the primary obstacles to achieving this goal is CAD models are based on surfaces, and not volumes. The boundary element method (BEM) circumvents this difficulty by directly working with the surfaces. The standard basis functions in CAD are trimmed nonuniform rational Bspline (NURBS). NURBS patches are the tensor product of one-dimensional NURBS, making the construction of arbitrary surfaces difficult. Trimmed NURBS use curves to trim away regions of the patch to obtain the desired shape. By coupling trimmed NURBS with a nonsingular BEM, the formulation proposed here comes close achieving the goal of direct design to analysis. Example calculations demonstrate its efficiency and accuracy.

show abstract

“…Azegami et al (1997) discussed the irregularity issue in shape optimization due to the ill-posedness that occurred when the gradient method in Hilbert space was directly applied. Azegami et al also proposed a gradient method which is recently applied to the shape optimization using the IGA (Azegami et al 2013). The design velocity field is an important component in computing shape sensitivities and updating the FE mesh during the shape optimization.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric configuration design optimization of built-up structures

Lee

Cho

2014

Struct Multidisc Optim

View full text Add to dashboard Cite

We derive the isogeometric configuration sensitivity of the Mindlin plates by using the material derivative and adjoint approaches. This is utilized in the shape design optimization that includes a variation of design components in its shape and orientation. By the isogeometric approach, the NURBS basis function in CAD system is directly utilized in the response analysis, which enables the seamless incorporation of higher continuity and exact geometry such as curvature and normal vector into the computational framework. The impact of exact curvature in the bending problem of Mindlin plates on the configuration design sensitivity is demonstrated through numerical examples. The obtained design sensitivity is further utilized in the shape design optimization of built-up structures. Due to the non-interpolatory property of the NURBS basis functions, a mismatch of patches in the built-up structures could occur during the isogeometric design optimization, which can be easily resolved using transformed basis functions.

show abstract

Shape optimization of continua using NURBS as basis functions

Cited by 47 publications

References 39 publications

Construction method of the cost function for the minimax shape optimization problem

Construction method of the cost function for the minimax shape optimization problem

A multi-patch nonsingular isogeometric boundary element method using trimmed elements

Isogeometric configuration design optimization of built-up structures

Contact Info

Product

Resources

About