Vol. 3, No. 7, 2008

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Reliability of first-order shear deformation models for sandwich beams

Lorenzo Bardella

Vol. 3 (2008), No. 7, 1187–1206

We are interested in sandwich beams whose skin may be thick (as defined by H. G. Allen) and whose core stiffness along the sandwich longitudinal axis may be large enough to influence the deflection (that is, we also account for nonantiplane sandwiches), whereas the core is such that it is allowed to disregard its deformability along its height (the direction of the applied load). For such sandwiches we are particularly interested in investigating the reliability of simple models, such as the first-order shear deformation models, for accurate computation of the deflection in the linear elastic range. We therefore compare different theories on the basis of finite element simulations and focus on the case of a propped cantilever beam supporting a uniform load. In fact, this boundary value problem leads to slightly different conclusions than those previously drawn based on statically determinate cases, such as in three-point bending. The analysis suggests that known models may be largely inaccurate in predicting sandwich behaviour under bending and shear, depending on a peculiarity of the actual sandwich kinematics indirectly describing the interaction between skins and core, in turn due both to material and geometrical properties and to boundary conditions.

sandwich beam, total potential energy, Ritz method, Allen's superposition theory, Timoshenko beam theory, Jourawsky shear theory, Saint-Venant principle, finite element method
Received: 23 October 2007
Revised: 5 June 2008
Accepted: 10 June 2008
Published: 1 September 2008
Lorenzo Bardella
University of Brescia
Via Branze, 43
25123 Brescia