Ashraf M. Badir

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

A variationally and asymptotically consistent theory is developed in order to derive the governing equations of anisotropic thin-walled beams with closed sections. The theory is based on an asymptotic analysis of two-dimensional shell theory. Closed-form expressions for the beam-stiffness coefficients, stress and displacement fields are provided. The influence of material anisotropy on the displacement field is identified. A comparison with the displacement fields obtained by other analytical developments is performed. The stiffness coefficients and static response are also compared with finite element predictions, closed-form solutions and test data.

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

The equations of motion for the free vibration analysis of anisotropic thin-walled closed-section beams are derived using a variational asymptotic approach and Hamiltons 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.

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

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.

Hygrothermal influence on mode I edge delamination in composites

Abstract A shear deformation theory is developed to calculate the interlaminar stresses and energy release rate associated with mid-plane edge delamination growth in graphite/epoxy laminates. The analysis includes the effect of residual thermal and moisture stresses. Results indicate that residual thermal stress increases the interlaminar stresses and strain energy release rate, while moisture content tends to alleviate thermal effects. Moreover, the value of moisture content at which the interlaminar stresses and strain energy release rate are totally alleviated is not affected by the stacking sequence.

Constrained optimization of thin-walled composite beams with coupling

A constrained optimization scheme is developed in order to analyze and design thin-walled, laminated composite, closed cross section beams with mechanical couplings. Both elliptical and rectangular cross section shapes are considered in order to isolate the influence of the geometry on the coupled modes. The design variables are expressed in terms of material properties, stacking sequence and number of layers. This work focuses on finding the optimal stacking sequence for a beam with extension-twist or bendingtwist coupling with no hygrothermal deformation, and with constraints on the natural frequencies. Introduction Elastically tailored thin-walled laminated composites provide flexibility to meet design requirements efficiently. Coupling between deformation modes such as extension-twist, bendingtwist, extension-flap bending, extension-sweep bending, and flap-sweep bending is created by an appropriate selection of fiber orientation, stacking sequence, materials, and geometric parameters. These mechanical couplings can be tailored to produce favorable static and dynamic response. For a given cross section, extension-twist coupling can be created by a layup which provides a Circumferencially Uniform Stiffness (CUS). Such a configuration is achieved by wrapping the composite layup using a winding technique. Bending-twist coupling is created by a Circumferencially Antisymmetric Stiffness (CAS) layup. A CAS beam has a (+9j) layup on one side of the cross section midplane, and (-dj on the other side. This approach provides a simple means to obtain the desired coupling, and the question remains as to the stacking sequences which maximize the extension-twist or bending-twist coupling. The existence of an optimum design may be ascertained by formulating the problem as a constrained optimization one. The objective of this work is to address the optimal design of a beam with maximized coupling and little or no hygrothermal warping while avoiding a specified natural frequency. The hygrothermal response of the beam is an important design factor since hygrothermal stresses could induce fracture and precipitate failure of a part during manufacturing. Moreover, a hygrothermally stable configuration is desired in service. There are many applications where it may be advantageous to avoid specific natural frequencies to prevent resonance from occurring. The robustness of the optimum design configurations are assessed by investigating their sensitivity to variations in material constants and manufacturing tolerances as expressed by variation in fiber angles. 1 Student Member, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA. 2 Associate Fellow, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA. 3 Member, Department of Engineering, Clark Atlanta University, Atlanta, GA. Copyright© 1996 by W. Karl Lentz. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. 2326 American Institute of Aeronautics and Astronautics The coupling response is predicted from the variational asymptotic anisotropic beam theory of Ref. 1. Closed form expressions for the displacement field are obtained and the influence of the materials anisotropy is explicitly identified. Closed form expressions for the compliance coefficients in terms of material and geometric parameters are provided through the constitutive relationships