REFINED THEORY OF COMPOSITE BEAMS - THE ROLE OF SHORT-WAVELENGTH EXTRAPOLATION

The present paper presents an asymptotically-correct beam theory with nonclassical sectional degrees of freedom. The basis for the theory is the variational-asymptotical method, a mathematical technique by whic h the three-dimensional analysis of composite beam deformation can be split into a linear, two-dimensional, cross-sectional analysis and a n onlinear, one-dimensional, beam analysis. The elastic constants used i n the beam analysis are obtained from the cross-sectional analysis, wh ich also yields approximate, closed-form expressions for three-dimensi onal distributions of displacement, strain, and stress. Such theories are known to be valid when a characteristic dimension of the cross sec tion is small relative to the wavelength of the deformation. However, asymptotically-correct refined theories may differ according to how th ey are extrapolated into the short-wavelength regime. Thus, the re is no unique asymptotically-correct refined theory of higher order than c lassical (Euler-Bernoulli-like) theory. Different short-wavelength ext rapolations can be obtained by changing the meaning of the theory's on e-dimensional variables. Numerical results for the stiffness constants of a refined beam theory and for deformations from the corresponding one-dimensional theory are presented. It is shown that a theory can be asymptotically correct and still have non-positive-definite strain en ergy density, which is completely inappropriate mathematically and phy sically. A refined beam theory, which appropriately possesses a positi ve-definite strain energy density and agrees quite well with experimen tal results, is constructed by using a certain short-wavelength extrap olation.