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

2015/02/05 by Lior Falach, Falach, Lior, Roberto Paroni +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1502.01552

arxiv created 2015/02/05 · arxiv updated 2015/02/06

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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