Geometrically Nonlinear Theory of Composite Beams with Deformable Cross Sections

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76337/1/AIAA-31620-757.pd

THE EFFECT OF POSTURE UPON THE COMPOSITION AND VOLUME OF THE BLOOD IN MAN

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Justification of the Bending-Gradient theory through asymptotic expansions

Abstract In a recent work, a new plate theory for thick plates was suggested where the static unknowns are those of the Kirchhoff-Love theory, to which six components are added representing the gradient of the bending moment [1]. This theory, called the Bending-Gradient theory, is the extension to multilayered plates of the Reissner-Mindlin theory which appears as a special case when the plate is homogeneous. This theory was derived following the ideas from Reissner [2] without assuming a homogeneous plate. However, it is also possible to give a justification through asymptotic expansions. In the present paper, the latter are applied one order higher than the leading order to a laminated plate following monoclinic symmetry. Using variational arguments, it is possible to derive the Bending-Gradient theory. This could explain the convergence when the thickness is small of the Bending-Gradient theory to the exact solution illustrated in [3]. However, the question of the edge-effects and boundary conditions remains open. 1.

XII-Apologies

A one-dimensional theory of slender structures with heterogeneous anisotropic materials is presented. It expands Cosserats description of beam kinematics by allowing deformation of the beam cross sections. For that purpose, a Ritz approximation is introduced on the cross-sectional warping field, which defines additional elastic degrees of freedom (finitesection modes) in the 1-D model. This results in an extended set of beam dynamic equations that includes direct measures of both the large global displacement and rotations of a certain reference line, and the small local deformations of the cross sections. Two situations of interest are then studied in which this approach provides a simpler alternative to nonlinear shell models: First, we look at the detailed structural response of thin-walled composite beams with distributed loads. In particular, the case of a composite construction with embedded piezoelectric actuators is considered. Second, this methodology is applied to study the low-frequency response characterization of a thin-walled composite beam. Numerical results are presented in both cases, in which a reduced set of finite-section modes allows a full characterization of the actual 3-D structure within a strictly 1-D framework solution.Published versio