Using discrete optimization algorithms to find minimum energy configurations of slender cantilever beams with non-convex energy functions
This paper deals with a new solution technique for approximately solving certain variational problems in elasticity by using discrete optimization techniques that were originally used in information theory. This allows us to easily and approximately solve large deformation buckling problems for slen...
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| Vydáno v: | Mechanics research communications Ročník 36; číslo 7; s. 811 - 817 |
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Elsevier Ltd
01.10.2009
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| ISSN: | 0093-6413, 1873-3972 |
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| Abstract | This paper deals with a new solution technique for approximately solving certain variational problems in elasticity by using discrete optimization techniques that were originally used in information theory. This allows us to easily and approximately solve large deformation buckling problems for slender cantilever beams (including post-buckling behavior) as well as problems where the strain energy function is non-convex.
The core idea is to quantize or discretize the variables describing the possible configurations of the body. This, when combined with the fact that the variational problem has an inherent Markov structure allows us to use computationally efficient search techniques based on dynamic programming (equivalent to finding the shortest path in a weighted directed graph) to find optimal solutions within the quantized state space. The results can be used in two ways: (1) directly as a fast approximate solution to the variational problem (2) As a means for finding very good (nearly minimum energy) initial configurations for application of conventional minimization techniques, which might otherwise fail because of a poor starting configurations which are far from the global minimum. We demonstrate both these uses in the paper. |
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| AbstractList | This paper deals with a new solution technique for approximately solving certain variational problems in elasticity by using discrete optimization techniques that were originally used in information theory. This allows us to easily and approximately solve large deformation buckling problems for slender cantilever beams (including post-buckling behavior) as well as problems where the strain energy function is non-convex.
The core idea is to quantize or discretize the variables describing the possible configurations of the body. This, when combined with the fact that the variational problem has an inherent Markov structure allows us to use computationally efficient search techniques based on dynamic programming (equivalent to finding the shortest path in a weighted directed graph) to find optimal solutions within the quantized state space. The results can be used in two ways: (1) directly as a fast approximate solution to the variational problem (2) As a means for finding very good (nearly minimum energy) initial configurations for application of conventional minimization techniques, which might otherwise fail because of a poor starting configurations which are far from the global minimum. We demonstrate both these uses in the paper. |
| Author | Narayanan, Krishna R. Srinivasa, Arun R. |
| Author_xml | – sequence: 1 givenname: Krishna R. surname: Narayanan fullname: Narayanan, Krishna R. organization: Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX, USA – sequence: 2 givenname: Arun R. surname: Srinivasa fullname: Srinivasa, Arun R. email: asrinivasa@tamu.edu organization: Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA |
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| Cites_doi | 10.1098/rspa.2007.0256 10.1016/j.mechrescom.2007.03.001 10.1016/0045-7825(94)00056-S 10.1017/S0962492900002658 10.1016/S0020-7462(00)00047-0 10.1177/1081286504033010 10.1007/s10832-007-9130-6 10.1088/0964-1726/17/2/025021 10.1115/1.2839009 10.1007/s00211-003-0483-8 10.1109/PROC.1973.9030 10.1063/1.1148809 10.1016/S0045-7825(96)01213-3 |
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| Keywords | Non-convex energy function Viterbi algorithm Discrete optimization Direct minimization Variational problems Cantilever beams Buckling |
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| SubjectTerms | Buckling Cantilever beams Direct minimization Discrete optimization Non-convex energy function Variational problems Viterbi algorithm |
| Title | Using discrete optimization algorithms to find minimum energy configurations of slender cantilever beams with non-convex energy functions |
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