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Optimal design of cantilevered elastica for minimum tip deflection under self-weight

Publication ,  Journal Article
Plaut, RH; Virgin, LN
Published in: Structural and Multidisciplinary Optimization
May 1, 2011

The optimal distribution of material to minimize the vertical deflection of the free end of a horizontal cantilever is determined. The beam is only subjected to its own weight. Large deflections are considered, and the structure is modeled as an inextensible elastica. A minimum-area constraint is included, and is active in a region near the tip. After the problem is formulated, numerical results are obtained with the use of a shooting method. The moment of inertia is assumed to be proportional to the area or its square or cube. The results depend on this relationship, the minimum-area constraint, and a nondimensional parameter depending on the beam's density, length, and modulus of elasticity. In the numerical results presented, if the minimum area is 1/20 of the area of the uniform beam, the tip deflection for the optimal design is 78-89% smaller than that for the uniform beam. An experiment is conducted and the data are in close agreement with the numerical results. © 2010 Springer-Verlag.

Duke Scholars

Published In

Structural and Multidisciplinary Optimization

DOI

EISSN

1615-1488

ISSN

1615-147X

Publication Date

May 1, 2011

Volume

43

Issue

5

Start / End Page

657 / 664

Related Subject Headings

  • Design Practice & Management
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences
 

Citation

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Plaut, R. H., & Virgin, L. N. (2011). Optimal design of cantilevered elastica for minimum tip deflection under self-weight. Structural and Multidisciplinary Optimization, 43(5), 657–664. https://doi.org/10.1007/s00158-010-0611-x
Plaut, R. H., and L. N. Virgin. “Optimal design of cantilevered elastica for minimum tip deflection under self-weight.” Structural and Multidisciplinary Optimization 43, no. 5 (May 1, 2011): 657–64. https://doi.org/10.1007/s00158-010-0611-x.
Plaut RH, Virgin LN. Optimal design of cantilevered elastica for minimum tip deflection under self-weight. Structural and Multidisciplinary Optimization. 2011 May 1;43(5):657–64.
Plaut, R. H., and L. N. Virgin. “Optimal design of cantilevered elastica for minimum tip deflection under self-weight.” Structural and Multidisciplinary Optimization, vol. 43, no. 5, May 2011, pp. 657–64. Scopus, doi:10.1007/s00158-010-0611-x.
Plaut RH, Virgin LN. Optimal design of cantilevered elastica for minimum tip deflection under self-weight. Structural and Multidisciplinary Optimization. 2011 May 1;43(5):657–664.
Journal cover image

Published In

Structural and Multidisciplinary Optimization

DOI

EISSN

1615-1488

ISSN

1615-147X

Publication Date

May 1, 2011

Volume

43

Issue

5

Start / End Page

657 / 664

Related Subject Headings

  • Design Practice & Management
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences