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A compliance based design problem of structures under multiple load cases

A compliance based design problem of structures under multiple load cases
A compliance based design problem of structures under multiple load cases
There are two popular methods concerning the optimal design of structures. The first is the minimization of the volume of the structure under stress constraints. The second is the minimization of the compliance for a given volume. For multiple load cases an arising issue is which energy quantity should be the objective function. Regarding the sizing optimization of trusses, Rozvany proved that the solution of the established compliance based problems leads to results which are awkward and not equivalent to the solutions of minimization of the volume under stress constraints, unlike under single loading 1. In this paper, we introduce the "envelope strain energy" problem where we minimize the volume integral of the worst case strain energy of each point of the structure. We also prove that in the case of sizing optimization of statically non-indeterminate2 trusses, this compliance method gives the same optimal design as the stress based design method.
Structural optimization · Truss optimization ·Compliance methods · Envelope strain energy method ·Stress based methods
1615-147X
739-743
Makrodimopoulos, A.
ba87ad2d-2351-4bd4-bd22-de921b3a8070
Bhaskar, A.
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Keane, A.J.
26d7fa33-5415-4910-89d8-fb3620413def
Makrodimopoulos, A.
ba87ad2d-2351-4bd4-bd22-de921b3a8070
Bhaskar, A.
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Keane, A.J.
26d7fa33-5415-4910-89d8-fb3620413def

Makrodimopoulos, A., Bhaskar, A. and Keane, A.J. (2010) A compliance based design problem of structures under multiple load cases. Structural and Multidisciplinary Optimization, 42, 739-743. (doi:10.1007/s00158-010-0524-8).

Record type: Article

Abstract

There are two popular methods concerning the optimal design of structures. The first is the minimization of the volume of the structure under stress constraints. The second is the minimization of the compliance for a given volume. For multiple load cases an arising issue is which energy quantity should be the objective function. Regarding the sizing optimization of trusses, Rozvany proved that the solution of the established compliance based problems leads to results which are awkward and not equivalent to the solutions of minimization of the volume under stress constraints, unlike under single loading 1. In this paper, we introduce the "envelope strain energy" problem where we minimize the volume integral of the worst case strain energy of each point of the structure. We also prove that in the case of sizing optimization of statically non-indeterminate2 trusses, this compliance method gives the same optimal design as the stress based design method.

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Published date: 3 July 2010
Keywords: Structural optimization · Truss optimization ·Compliance methods · Envelope strain energy method ·Stress based methods

Identifiers

Local EPrints ID: 155971
URI: http://eprints.soton.ac.uk/id/eprint/155971
ISSN: 1615-147X
PURE UUID: 1ba71f0a-9388-42c5-a1d8-c3c4d700c777
ORCID for A.J. Keane: ORCID iD orcid.org/0000-0001-7993-1569

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Date deposited: 01 Jun 2010 13:34
Last modified: 14 Mar 2024 02:39

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Contributors

Author: A. Makrodimopoulos
Author: A. Bhaskar
Author: A.J. Keane ORCID iD

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