VABS: A new concept for composite rotor blade cross-sectional modeling

The computer program VABS (Variational Asymptotic Beam Section Analysis) uses the variational asymptotic method to split a three-dimensional nonlinear elasticity problem into a twodimensional linear cross-sectional analysis and a one-dimensional, nonlinear beam problem. This is accomplished by taking advantage of certain small parameters inherent to beam-like structures. VABS is able to calculate the one-dimensional cross-sectional stiffness constants, with transverse shear and Vlasov refinements, for initially twisted and curved beams with arbitrary geometry and material properties. Several validation cases are presented. First, an elliptic bar is modeled with transverse shear refinement using the variational asymptotic method, and the solution is shown to be identical to that obtained from the theory of elasticity. The shear center locations calculated by VABS for various cross sections agree well with those obtained from common engineering analyses. Comparisons with other composite beam theories prove that it is unnecessary to introduce ad hoc kinematic assumptions to build an accurate beam model. For numerical validation, values of the one-dimensional variables are extracted from an ABAQUS model and compared with results from a one-dimensional beam analysis using cross-sectional constants from VABS. Furthermore, point-wise three-dimensional stress and strain fields are recovered using VABS, and the correlation with the three-dimensional results from ABAQUS is excellent. Finally, classical theory is shown to be insufficient for general-purpose beam modeling. Appropriate refined theories are recommended for some classes of problems.

Validation of the Variational Asymptotic Beam Sectional Analysis

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

There are many technical applications in the field of lightweight construction as, for example, in aerospace engineering, where stress concentration phenomena play an important role in the design of layered structural elements (so-called laminates) consisting of plies of fiber reinforced plastics or other materials. A well known stress concentration problem rich in research tradition is the so-called free-edge effect. Mainly explained by the mismatch of the elastic material properties between two adjacent dissimilar laminate layers, the free-edge effect is characterized by the concentrated occurrence of three-dimensional and singular stress fields at the free edges in the interfaces between two layers of composite laminates. In the present contribution, a survey on relevant literature from more than three decades of scientific research on free-edge effects is given. The cited references date back to 1967 and deal with approximate closed-form analyses, as well as numerical investigations by the finite element method, the finite difference method, and several other numerical techniques. The progress in research on the stress singularities which arise is also reviewed, and references on experimental investigations are cited. Related problems are also briefly addressed. The paper closes with concluding remarks and an outlook on future investigations. In all, 292 references are included.

Free-Edge Effects in Composite Laminates

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

The equations of motion for the free vibration analysis of anisotropic thin-walled closed-section beams are derived using a variational asymptotic approach and Hamilton's principle. The analysis is applied to two laminated composite constructions. The circumferentially uniform stiffness produces extension-twist coupling and the circumferentially asymmetric stiffness produces bending-twist coupling. The effect of the elastic coupling mechanisms on the vibration behavior of thin-walled composite beams is evaluated analytically. The influence of stacking orientation on the frequencies associated with coupled vibration modes is investigated. The predictions are validated by comparison with a finite element simulation and test data.

Free Vibration Analysis of Anisotropic Thin-Walled Closed-Section Beams

Theory of composite thin-walled opened-cross-section beams

Buckling behavior of a graphite/epoxy composite plate under parabolic variation of axial loads

A shear deformation model including hygrothermal effects is developed for the analysis of local delaminations originating from transverse cracks in 90-deg plies located in and around the laminate midplane. A sublaminate approach is used and the model is applied to (+/- 25/90n)s T300/934 graphite/epoxy laminates for n values between 0.5 and 8, along with previously developed edge-delamination shear-deformation models. Critical loads and delamination modes are identified and compared with experimental results. Hygrothermal effects are included in all the models to make the comparisons realistic.

Ashraf M. Badir

Papers

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

Free Vibration Analysis of Anisotropic Thin-Walled Closed-Section Beams

Theory of composite thin-walled opened-cross-section beams

Buckling behavior of a graphite/epoxy composite plate under parabolic variation of axial loads

Fracture analysis of transverse crack-tip and free-edge delamination in laminated composites