A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity

Maria Giovanna Mora; Stefan Müller

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We consider the linearized elasticity system in a multidomain of $𝐑^{3}$ . This multidomain is the union of a horizontal plate with fixed cross section and small thickness , and of a vertical beam with fixed height and small cross section of radius $r^{ε}$ . The lateral boundary of the plate and the top of the beam are assumed to be clamped. When and $r^{ε}$ tend to zero simultaneously, with $r^{ε} ≫ ε^{2}$ , we identify the limit problem. This limit problem involves six junction conditions.

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Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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