### Abstract

The general problem of concern is to find the optimum shape of an elastic body, which requires minimizing an objective function subject to stress, displacement, frequency, and manufacturing constraints. The basic approach so far has been to choose a set of geometric design variables that define the shape of the structure. Typically the design variables have been chosen as coefficients of splines and polynomials, coordinates of 'control' nodes, and other geometric parameters. An automatic finite element discretization scheme that uses geometric entities such as lines, arcs, splines, and blending functions, is then used to relate changes in position of interior grid points in the finite element mesh to changes in the design variables. In this paper, a set of natural design variables is chosen as the design variables defining the shape. Specifically, the design variables are the magnitudes of a set of fictitious loads applied on the structure. The displacements produced by these fictitious loads, or natural shape functions, are added onto the initial mesh to obtain the new shape. Consequently, a linear relationship is established between changes in grid point locations and design variables through a finite element analysis. Plane elasticity problems are solved using the new approach. The quality of the finite element meshes produced and other salient features of the shape optimal design problem are discussed.

Original language | English (US) |
---|---|

Pages (from-to) | 87-106 |

Number of pages | 20 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 66 |

Issue number | 1 |

DOIs | |

State | Published - 1988 |

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### ASJC Scopus subject areas

- Computer Science Applications
- Computational Mechanics

### Cite this

**A shape optimization approach based on natural design variables and shape functions.** / Belegundu, A. D.; Rajan, Subramaniam.

Research output: Contribution to journal › Article

*Computer Methods in Applied Mechanics and Engineering*, vol. 66, no. 1, pp. 87-106. https://doi.org/10.1016/0045-7825(88)90061-8

}

TY - JOUR

T1 - A shape optimization approach based on natural design variables and shape functions

AU - Belegundu, A. D.

AU - Rajan, Subramaniam

PY - 1988

Y1 - 1988

N2 - The general problem of concern is to find the optimum shape of an elastic body, which requires minimizing an objective function subject to stress, displacement, frequency, and manufacturing constraints. The basic approach so far has been to choose a set of geometric design variables that define the shape of the structure. Typically the design variables have been chosen as coefficients of splines and polynomials, coordinates of 'control' nodes, and other geometric parameters. An automatic finite element discretization scheme that uses geometric entities such as lines, arcs, splines, and blending functions, is then used to relate changes in position of interior grid points in the finite element mesh to changes in the design variables. In this paper, a set of natural design variables is chosen as the design variables defining the shape. Specifically, the design variables are the magnitudes of a set of fictitious loads applied on the structure. The displacements produced by these fictitious loads, or natural shape functions, are added onto the initial mesh to obtain the new shape. Consequently, a linear relationship is established between changes in grid point locations and design variables through a finite element analysis. Plane elasticity problems are solved using the new approach. The quality of the finite element meshes produced and other salient features of the shape optimal design problem are discussed.

AB - The general problem of concern is to find the optimum shape of an elastic body, which requires minimizing an objective function subject to stress, displacement, frequency, and manufacturing constraints. The basic approach so far has been to choose a set of geometric design variables that define the shape of the structure. Typically the design variables have been chosen as coefficients of splines and polynomials, coordinates of 'control' nodes, and other geometric parameters. An automatic finite element discretization scheme that uses geometric entities such as lines, arcs, splines, and blending functions, is then used to relate changes in position of interior grid points in the finite element mesh to changes in the design variables. In this paper, a set of natural design variables is chosen as the design variables defining the shape. Specifically, the design variables are the magnitudes of a set of fictitious loads applied on the structure. The displacements produced by these fictitious loads, or natural shape functions, are added onto the initial mesh to obtain the new shape. Consequently, a linear relationship is established between changes in grid point locations and design variables through a finite element analysis. Plane elasticity problems are solved using the new approach. The quality of the finite element meshes produced and other salient features of the shape optimal design problem are discussed.

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U2 - 10.1016/0045-7825(88)90061-8

DO - 10.1016/0045-7825(88)90061-8

M3 - Article

VL - 66

SP - 87

EP - 106

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

IS - 1

ER -