A Geometrically-exact rod model incorporating shear and torsion-warping deformation

A direct method for determining the effective elastic stiffnesses and deformation behavior of composite box-beam (BB) structures is developed analytically, validated, and demonstrated. The BB walls are modeled as orthotropic-ply laminated plates, so that the elastic properties vary both through the thickness and around the BB contour; deformation is described in terms of extension, bending, twisting, shearing, and torsion-related out-of-plane warping. Numerical results for several BB configurations are presented in tables and graphs and compared with experimental data and FEM computations (Stemple and Lee, 1989): good general agreement is obtained for cross-ply, antisymmetric, and symmetric layups, except for symmetric layups with ply orientation angles theta greater than 30 deg. Both out-of-plane warping and transverse shear coupling are found to have significant effects on BB elastic response.

Formulation and evaluation of an analytical model for composite box-beams

Theory of anisotropic thin-walled closed-cross-section beams

There is no lack of composite beam theories. Quite to the contrary, there might be too many of them. Different approaches, notation, etc., are used by the authors of those theories, so it is not always straightforward to compare the assumptions made and to assess the quantitative consequences of those assumptions. Moreover, there is a serious lack of experimental results and benchmark problems. As a result, one finds that most theories perform about equally well on the few extant benchmark problems. This can obscure differences among theories and simultaneously create the false expectation that a specific theory will perform as well in all cases. The goal of this paper is to attempt to objectively assess theories within a common framework. The validity and relative importance of various assumptions that are present in the literature are discussed. It is hoped that this will be a first step toward the clearly desirable situation in which an engineer can safely and easily choose a composite beam theory based on the type of application and specific needs for fidelity.

Assessment of Beam Modeling Methods for Rotor Blade Applications

Assessment of beam modeling methods for rotor blade applications

The paper considers the problem of determining stresses and deformations in elastic thin-walled, prismatical beams, subject to axial end forces and end bending and twisting moments, within the range of applicability of linear theory. The technically most significant aspect of the work has to do with the analysis of the effect of anisotropy of the material, which is associated with previously not determined modes of coupling between stretching, bending, and twisting. Use of the general formulas of the theory is illustrated for a class of shells consisting of an 'ordinary' material (unable to support stress moments with axes normal to the middle surface of the shell, and unable to undergo transverse shear deformation). Here explicit formulas are obtained for certain types of open as well as of closed-cross-section beams.

Pure Bending, Stretching, and Twisting of Anisotropic Cylindrical Shells

: The authors have recently proposed new definitions for the centers of twist and of shear, in terms of influence coefficients for tip-loaded cantilever beams. These definitions are here applied in conjunction with a minimum complementary energy method for the approximate determination of the influence coefficients of the problem of thin-walled open and closed cross section beams, with the possibility of a continuous transition from closed cross section to open cross section. The result is an explicit formula for the coordinate of the centers of twist and of shear of beams the cross sections of which have one axis of symmetry. This formula includes as special cases the known elementary formula for open cross sections, an extension of this formula so as to include the case of flat plates, and a known formula for closed cross section thin-shell beams. (Author)

W. T. Tsai

Papers

Pure Bending, Stretching, and Twisting of Anisotropic Cylindrical Shells

On the Determination of the Centers of Twist and of Shear for Cylindrical Shell Beams

On Pure Bending and Stretching of Orthotropic Laminated Cylindrical Shells

Note on the Center of Twist