MATLAB codes for "Fast In-Plane Dynamics of a Beam with Unilateral Constraints"

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http://dx.doi.org/10.13020/D6F30G
https://hdl.handle.net/11299/180885

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beam impact obstacles

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MATLAB codes for "Fast In-Plane Dynamics of a Beam with Unilateral Constraints"

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2016-06-02

Authors

Liakou, Anna

Detournay, Emmanuel

Denoël, Vincent

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Liakou, Anna
aliakou81@gmail.com

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Programming Software Code

Abstract

A computationally efficient technique to simulate the dynamic response of a beam colliding with rigid obstacles is described in this paper. The proposed method merges three key concepts. First, a low order discretization scheme that maximizes the number of nodes of the discrete model, where impacts are detected, at the expense of the degree of continuity of the constructed displacement field. Second, the constrained problem is transformed into an unconstrained one by formulating the impact by means of a complementarity Signorini's law involving the impulse generated by the collision and the pre- and post- impact velocity linked via a coefficient of restitution. Third, Moreau's midpoint time-stepping scheme developed within the context of colliding rigid bodies, is used to advance the solution.

Description

These MATLAB codes demonstrate the method proposed by the paper of the same name. HeMo evaluates the dynamic response of a cantilever beam against two symmetrical stops ((end)-point and/or horizontal wall). The impact motion is simulated by two methods: a) Moreau's midpoint method and b) Moreau-Jean's theta method. The second code, Rayleigh, measures the response of a Rayleigh beam for unit impulse load with beta=0.1 (Fourier series - 6 modes).

Referenced by

Liakou, A., Denoël, V., & Detournay, E. (2016). Fast In-Plane Dynamics of a Beam with Unilateral Constraints. Journal of Engineering Mechanics, 04016116.
http://dx.doi.org/10.1061/(ASCE)EM.1943-7889.0001175#sthash.np0C5C4K.dpuf

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Data Repository for U of M (DRUM)

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Liakou, Anna; Detournay, Emmanuel; Denoël, Vincent. (2016). MATLAB codes for "Fast In-Plane Dynamics of a Beam with Unilateral Constraints". Retrieved from the Data Repository for the University of Minnesota (DRUM), http://dx.doi.org/10.13020/D6F30G.

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