XXI International Congress of Theoretical and Applied Mechanics
Warsaw, Poland, August 15-21, 2004

A Homogenization Based Laminated Beam Theory

Jorn S. Hansen (1), Sergio F. M. de Almeida (2)
1. University of Toronto, Institute for Aerospace Studies, Toronto, Canada
2. Instituto Tecnológico de Aeronáutica, Mechanical Engineering, São José dos Campos, Brasil

A sequence of theories is developed for laminated (including sandwich) beams. An homogenization approach is used in conjunction with far-field stress and strain solutions resulting from constant, linear, ... , n$^{th}$ degree bending states; these solutions are called Fundamental Solutions. Based on the Fundamental Solutions, through-thickness stress and strain moments are used to obtain definitions of homogenized flexural and shear stiffness, homogenized transverse Poisson's ratio as well as a unique shear strain moment correction. All developed models adopt a form similar to that of Classical Timoshenko Beam Theory; however, the system parameters of the present and the Timoshenko model have different meanings. Numerical comparisons are made with `exact' two-dimensional finite element results for a sequence of cantilever sandwich-beams. It is shown that all stress and strain components (in-plane, transverse and shear) are obtained with consistent and excellent accuracy which goes beyond the capability of conventional beam theories.

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