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arXiv · 1502.01552

A Justification of the Timoshenko Beam Model through $\boldsymbolΓ$-Convergence

Lior Falach·Roberto Paroni·Paolo Podio-Guidugli
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Abstract

We validate the Timoshenko beam model as an approximation of the linear-elasticity model of a three-dimensional beam-like body. Our validation is achieved within the framework of $Γ$-convergence theory, in two steps: firstly, we construct a suitable sequence of energy functionals; secondly, we show that this sequence $Γ$-converges to a functional representing the energy of a Timoshenko beam.

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Lior Falach, Roberto Paroni, Paolo Podio-Guidugli. 2015-02-05. A Justification of the Timoshenko Beam Model through $\boldsymbolΓ$-Convergence. https://arxiv.org/abs/1502.01552

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