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
Hlavní autoři: Narayanan, Krishna R., Srinivasa, Arun R.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.10.2009
Témata:
Buckling
Cantilever beams
Direct minimization
Discrete optimization
Non-convex energy function
Variational problems
Viterbi algorithm
Non-convex energy function
Viterbi algorithm
Discrete optimization
Direct minimization
Variational problems
Cantilever beams
Buckling
ISSN:0093-6413, 1873-3972
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Shrnutí: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.
ISSN:0093-6413
1873-3972
DOI:10.1016/j.mechrescom.2009.05.011