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Equilibrium paths of Hencky pantographic beams in a three-point bending problem. (English) Zbl 1434.74076
Summary: We investigate the mechanical behavior of so-called pantographic beams undergoing large deformations. To this aim, an exact-kinematics Hencky pantographic beam model has been employed in a three-point bending test. Given the occurrence of local snap-through instabilities and limit points, said Hencky model has been solved by means of a step-by-step strategy based on Riks’s arc-length method. Such a method has been particularly adapted for the case of problems with prescribed displacements, as opposed to those with prescribed forces. Numerical simulations performed by varying the stiffness parameters are discussed, aimed at getting an insight into the different behaviors which can be exhibited by pantographic beams. Numerical simulations performed by varying the quantity of unit cells for fixed total length allow instead to understand whether the observed features are inherent to the pantographic beam structure or size-dependent. Therefore, beyond being interesting for possible future engineering exploitation, we believe this phenomenological evidence to be useful in guiding the formulation of conjectures regarding observed microscale local snap-through instability phenomena in the framework of a previously proposed macroscale continuum model for pantographic beams obtained by asymptotic homogenization.
MSC:
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74B20 Nonlinear elasticity
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