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

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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