We obtain the asymptotically exact weighted Korn inequality for a thin (of thickness δh) periodically corrugated (with step δ) beam clamped at its ends. The constant in the inequality is… Click to show full abstract
We obtain the asymptotically exact weighted Korn inequality for a thin (of thickness δh) periodically corrugated (with step δ) beam clamped at its ends. The constant in the inequality is independent of both small parameters δ and h, but the distribution of weighted factors under longitudinal and transverse displacements essentially differs from the optimal one in the case of a straight beam.
               
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