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

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 $\Gamma$-convergence theory, in two steps: firstly, we construct a suitable sequence of energy functionals; secondly, we show that this sequence $\Gamma$-converges to a functional representing the energy of a Timoshenko beam.