Asymptotic Behavior of Stable Structures Made of Beams

Abstract In this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made beams circular cross-section radius $r$ r when periodicity parameter and ratio ${r/\varepsilon }$ / simultaneously tend to 0. The analysis is performed within frame linear elasticity theory it based on known decomposition beam displacements into a centerline displacement, small rotation cross-sections warping (the deformation cross-sections). This allows obtain Korn type inequalities. We introduce two unfolding operators, one for homogenization set centerlines another dimension reduction beams. limit homogenized problem still elastic, second order PDE.