Erian A. Armanios

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.

The influence of coupling on the free vibration of anisotropic thin-walled closed-section beams

Abstract A solution procedure for thin-walled laminated composite beams is presented. Two configurations are considered, producing extension-twist and bending-twist coupling, respectively. The influence of coupling on the characteristic equations for free vibration is isolated. It is shown that the characteristic determinant for extension-twist coupling can be expressed as the product of the two decoupled ones. For the case of bending-twist coupling, a simple-quasi-decoupled procedure is developed. This model is shown to provide accurate predictions for natural frequencies of practical interest for slender, laminated composite box beams.

Anticlastic Stability Modeling for Cross-ply Composites

A viable aspect of fiber-reinforced composites is their elastic tailoring ability. Anticlastic curvature is one example of elastic tailoring that occurs with an unsymmetric cross-ply layup. Residual stresses resulting from differences in coefficients of thermal expansion and elastic properties in each lamina can cause large out-of-plane deformations. In the case of thin unsymmetric cross-ply laminates under thermal curing load, a cylindrical shape is observed because of this inherent geometrical nonlinearity as opposed to the saddle shape that classical lamination theory predicts. In this article, a finite element approach, using ABAQUS™, is implemented in order to predict the unsymmetric cross-ply laminate shapes under thermal curing stresses and understand the underlying limit point instability. Numerical results for curvatures of the predicted shapes are in agreement with published experimental and analytical data. The stability of the cylindrical laminates is also investigated. Depending on the aspect ratio of the rectangular laminate, a cylindrical shape may snap-through from its current stable configuration to another stable cylindrical shape with a different curvature. In particular, both the critical aspect ratio where snap-through will cease to occur and the buckling load are reported.

Families of Hygrothermally Stable Asymmetric Laminated Composites

Necessary and sufficient material-independent conditions are derived for hygrothermal stability of a laminated composite plate with plies made of the same specially orthotropic material based on classical lamination theory. The minimum number of plies required to obtain an asymmetric hygrothermally stable stacking sequence is proven to be five, and families of stable laminates are identified for six, seven, and eight plies. A sensitivity analysis demonstrates the robustness of hygrothermally stable solutions to small errors in ply orientation. A finite element analysis of geometric and ply orientation imperfections was performed to verify the robustness of the classical lamination theory results. Hygrothermally stable asymmetric laminate specimens were fabricated to confirm the analytical predictions.

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.

Delamination analysis of tapered laminated composites under tensile loading

A study was conducted to analyze tapered composite laminates under tensile loading. A tapered construction made of S2/SP250 glass/epoxy laminate was used to achieve a thickness reduction using three consecutive dropped plies over a distance of 60 ply thicknesses. The principle of minimum complementary potential energy was used to determine interlaminar stresses. The interlaminar peel stress distribution shows a higher tensile intensity at the taper/thin portion juncture. The total strain energy release rate is determined using a simplified membrane model. Results are compared with a finite element simulation.

Sublaminate analysis of interlaminar fracture in composites. Part I. Analytical model

A simple analysis method based upon a transverse shear deformation theory and a sublaminate approach is utilized to analyze a mixed-mode edge delamination specimen. The analysis provides closed form expressions for the interlaminar shear stresses ahead of the crack, the total strain energy release rate, and the strain energy release rate components. The parameters controlling the behavior are identified. The effect of specimen stacking sequence and delamination interface on the strain energy release rate components is investigated. Results are compared with a finite element simulation for reference. The simple nature of the method makes it suitable for preliminary design analyses which require a large number of configurations to be evaluated quickly and economically. In Part I of this work the analytical model is developed. A comparison of the characteristic roots controlling the behavior in the edge delamination specimen is provided. In Part II an extensive comparison with a finite element solution for 58 test cases is provided in order to validate the analytical model and assess its accuracy.

New families of hygrothermally stable composite laminates with optimal extension-twist coupling

The necessary and sufficient conditions for hygrothermal stability of laminated composites are presented. A thorough survey of hygrothermally stable families is performed to identify stacking sequences that produce maximum extension-twist coupling. This is achieved through a constrained optimization routine, where the objective function is derived from the constitutive law given in classical lamination theory and the constraints are the necessary conditions for hygrothermal stability. A representative sample of these optimized laminates are constructed and tested to demonstrate significant improvement in coupling over the previously known optima. Comparisons are made with a nonlinear model and finite element analysis. An investigation of the robustness of the optimal stacking sequences to errors in ply angle typical of hand-layup manufacturing is presented.

Calculation of the natural frequencies and steady state response of thin plates in bending by an improved rectangular element

Abstract This paper presents an application of a new improved rectangular finite element to the problems of free and forced harmonic oscillations of thin plates in bending. The proposed element, called the parametric element, has been presented in a previous paper by the same authors and applied to the problem of static bending of plates. The shape functions corresponding to the various nodal movements are expressed in simple parametric forms which scan the space between the Adini-Clough-Melosh model and the Papenfuss model. The performance of the parametric element is found to be at its best in both the statical and dynamical applications when the parameters included in the shape functions assume certain values. Like what happened in the statical application, the optimal parametric element has shown remarkable superiority over other simple elements when used in the prediction of the natural frequencies and harmonic response of several plates having different boundary conditions.