Finding minimum energy configurations for constrained beam buckling problems using the Viterbi algorithm

Doraiswamy, Srikrishna; Narayanan, Krishna R.; Srinivasa, Arun R.

doi:10.1016/j.ijsolstr.2011.10.003

Cited by 12 publications

(19 citation statements)

References 19 publications

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“…The technique presented here extend the work by Srikrishna et al [6] by introducing an "adaptive states quantization technique". To elaborate, in previous work the admissible positions of each node of beam can be determined without consideration of other nodes, since the possible vertical positions of each end of the beam are the same.…”

Section: Introductionmentioning

confidence: 70%

“…Note that the progressive appearance of buckled patterns are compatible with simulations in Figure 5 noted in previous work. [6] [10]. For the cantilever beam problem, the differential equation together with the initial conditions has a special Markov structure that can be gainfully exploited.…”

Section: Simulationmentioning

confidence: 99%

“…Although we are finding the lowest energy state among many possible configurations, we should observe that the Viterbi algorithm can be extended to find all local minima by employing a technique called list Viterbi [12]. Rather than keeping the lowest energy states, the list Viterbi algorithm can find a given number of lowest energy states [6].…”

Section: Simulationmentioning

confidence: 99%

“…Given these limitations, the Viterbi algorithm can be used as a means for identifying good initial configuration for subsequent gradient search algorithm [6]. Figure 3 illustrates the geometry of the problem.…”

Section: Simulationmentioning

confidence: 99%

“…we can get X through constraints if Y is known. However, the method based on the Viterbi algorithm also requires to discretize the range [6]. To that end, we will carefully restrict the elements of the vector Y to belong a finite subset Z = Y 1 , .…”

Section: Discretizationmentioning

confidence: 99%

See 4 more Smart Citations

A direct minimization technique for finding minimum energy configurations for beam buckling and post-buckling problems with constraints

Wang

Ruimi

Srinivasa

2015

International Journal of Solids and Structures

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Please cite this article as: Wang, Z., Ruimi, A., Srinivasa, A.R., A direct minimization technique for finding minimum energy configurations for beam buckling and post-buckling problems with constraints, International Journal of Solids and Structures (2015), doi: http://dx. AbstractWe present a novel technique to simulate the deformation of a cantilever elastic beam constrained in a curved solid channel subject to end forces.We pose this as the minimization of an energy functional and solve it by a variant of a Dynamic Programming Approach called the Viterbi algorithm.The core idea of this approach is to discretize the variables describing the potential energy and to construct a set of admissible configurations of the beam. The Viterbi algorithm is then employed to search through the set of possible beam configurations and locate the one with the minimum potential energy in a very computationally efficient way. The new approach does not require any gradient computations and could be considered as a direct search method, and thus can be guaranteed to find the global minimum potential energy. Also the constraints can be automatically satisfied by constructing the proper set of all the possible configurations. The approach can also be used to find feasible starting configurations associated with conventional minimizing algorithms.

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Section: Introductionmentioning

confidence: 70%

Section: Simulationmentioning

confidence: 99%

Section: Simulationmentioning

confidence: 99%

Section: Simulationmentioning

confidence: 99%

Section: Discretizationmentioning

confidence: 99%

See 3 more Smart Citations

A direct minimization technique for finding minimum energy configurations for beam buckling and post-buckling problems with constraints

Wang

Ruimi

Srinivasa

2015

International Journal of Solids and Structures

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Deformation and stability of an elastica constrained by curved surfaces

Chen

Hung

2014

International Journal of Mechanical Sciences

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Static and dynamic post-buckling analyses of irregularly constrained beams under the small and large deformation assumptions

Jiao

Borchani

Hasni

et al. 2017

International Journal of Mechanical Sciences

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Post-buckling phenomenon has been performing advantages in many applications. In particular, buckling snap-through of slender beams under lateral constraints is of great research interest since low-rate and low-frequency excitations can be transformed into high-rate motions. Electrical energy can be generated from ambient energies through the process. Efficient conversion of the energy phases requires sufficient control over post-buckling response. However, inadequate studies have been conducted to investigate the influence of different lateral constraints on buckling mode transitions. This study aims at developing static and dynamic theoretical models to capture buckling snap-though of slender beams subjected to irregularly bilateral constraints. The models are created based on small and large deformations assumptions, respectively. An algorithm is introduced to discretize the irregular constraints into a gap vector. The equilibrium equations in the presented models are solved using an energy method that minimizes the total energy in the gap vector with respect to the weight coefficient (C m ) of different buckling modes. Experiments were carried out to validate the theoretical results. Good agreements were observed. The proposed models are then used to investigate the effects of the linearly and sinusoidally varied constraints on the beams' post-buckling response. It is found that the deformed shapes of the beams meet the patterns of the constraints. Both the static and dynamic large deformation models are able to measure the end-shortenings that result in severe rotation of the beams' neutral axes. Significant shifting is observed between the deflected beam shapes solved by the static and dynamic models. The presented models are effective in understanding and predicting the static and dynamic post-buckling responses of irregularly constrained beams under small and large deformation assumptions.

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Finding minimum energy configurations for constrained beam buckling problems using the Viterbi algorithm

Cited by 12 publications

References 19 publications

A direct minimization technique for finding minimum energy configurations for beam buckling and post-buckling problems with constraints

A direct minimization technique for finding minimum energy configurations for beam buckling and post-buckling problems with constraints

Deformation and stability of an elastica constrained by curved surfaces

Static and dynamic post-buckling analyses of irregularly constrained beams under the small and large deformation assumptions

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