Abstract
This paper first extends a classical solution concerning the shape optimization of a hanging bar. The well-known solution determines the optimal cross section of a homogeneous bar that minimizes elongation under its own weight and a given applied force, subject to a total volume constraint. Herein, the analytical solution is generalized to materials with a variable density and elastic modulus along the bar, subject to a total mass constraint. A gradient-based numerical optimization algorithm is developed and then used to solve the inverse problem to validate the analytical results. The approach is then extended to two-dimensional structures through the parameterization of the external boundary using nonuniform rational B-splines (NURBS) functions and the solution of repeated forward problems with updated meshes. Three different cases are studied: (1) homogeneous elastic, (2) homogeneous hyperelastic, and (3) inhomogeneous elastic materials. The results show the differences between the optimal shape of one- and two-dimensional models and the effect of material models on the optimal solutions.
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Acknowledgments
The first author would like to acknowledge the National Natural Science Foundation of China under Grant No. 51578211 and the Fundamental Research Funds for the Central Universities under Grant No. 2018B13814 for supporting this research. The third author acknowledges support from the Diane and Arthur B. Belfer Chair in Mechanics and Biomechanics.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 1 • January 2020
Copyright
©2019 American Society of Civil Engineers.
History
Received: Oct 18, 2018
Accepted: May 9, 2019
Published online: Oct 24, 2019
Published in print: Jan 1, 2020
Discussion open until: Mar 24, 2020
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