W. Scott Burton

Assessment of Shear Deformation Theories for Multilayered Composite Plates

A review is made of the different approaches used for modeling multilayered composite plates. Discussion focuses on different approaches for developing two-dimensional shear deformation theories; classification of two-dimensional theories based on introducing plausible displacement, strain and/or stress assumptions in the thickness direction; and first-order shear deformation theories based on linear displacement assumptions in the thickness coordinate. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of simply supported composite plates on the accuracy of the static and vibrational responses predicted by six different modeling approaches (based on two-dimensional shear deformation theories). The standard of comparison is taken to be the exact three-dimensional elasticity solutions. Some of the future directions for research on the modeling of multilayered composite plates are outlined.

Computational Models for Sandwich Panels and Shells

The focus of this review is on the hierarchy of computational models for sandwich plates and shells, predictor-corrector procedures, and the sensitivity of the sandwich response to variations in the different geometric and material parameters. The literature reviewed is devoted to the following application areas: heat transfer problems; thermal and mechanical stresses (including boundary layer and edge stresses); free vibrations and damping; transient dynamic response; bifurcation buckling, local buckling, face-sheet wrinkling and core crimping; large deflection and postbuckling problems; effects of discontinuities (eg, cutouts and stiffeners), and geometric changes (eg, tapered thickness); damage and failure of sandwich structures; experimental studies; optimization and design studies. Over 800 relevant references are cited in this review, and another 559 references are included in a supplemental bibliography for completeness. Extensive numerical results are presented for thermally stressed sandwich panels with composite face sheets showing the effects of variation in their geometric and material parameters on the accuracy of the free vibration response, and the sensitivity coefficients predicted by eight different modeling approaches (based on two-dimensional theories). The standard of comparison is taken to be the analytic three-dimensional thermoelasticity solutions. Some future directions for research on the modeling of sandwich plates and shells are outlined.

Assessment of computational models for multilayered anisotropic plates

A study is made of the effects of variation in the lamination and geometric parameters of multilayered anisotropic (nonorthotropic) plates on the accuracy of the static and vibrational responses predicted by eight modeling approaches, based on two-dimensional shear-deformation theories. Two key elements distinguish the present study from previous studies reported in the literature: (1) the standard of comparison is taken to be the exact three-dimensional elasticity solutions, and (2) quantities compared are not limited to gross response characteristics (e.g. vibration frequencies, strain energy components, average through-the-thickness displacements and rotations), but include detailed through-the-thickness distributions of displacements, stresses and strain energy densities. The modeling approaches considered include first-order shear-deformation theory (with five displacement parameters to characterize the deformation in the thickness direction); first-order theory with the transverse normal stresses and strains included (six displacement parameters); two higher-order theories (with 11 and 18 displacement parameters); a simplified higher-order theory (with five displacement parameters); discrete-layer theory (with piecewise linear variation of the in-plane displacements in the thickness direction); simplified discrete-layer theory with the continuity of transverse stresses imposed at layer interfaces to reduce the number of displacement parameters to five; and a predictor-corrector approach, used in conjunction with the first-order shear-deformation theory (with five displacement parameters in the predictor phase). Based on the numerical studies conducted, the predictor-corrector approach appears to be the most effective among the eight modeling approaches considered. For antisymmetrically laminated rectangular plates the response quantities obtained by the predictor-corrector approach are shown to be in close agreement with exact three-dimensional elasticity solutions for a wide range of lamination and geometric parameters. The potential of this approach for predicting the response of multilayered anisotropic plates with complicated geometry is also discussed.

Stress and free vibration analyses of multilayered composite plates

Abstract A two-phase computational procedure is presented for the accurate prediction of the vibration frequencies, stresses and deformations in multilayered composite plates. In the first phase a two-dimensional first-order shear deformation theory is used to predict the global response characteristics (vibration frequencies, ‘average’ through-the-thickness displacements and rotations) as well as the in-plane stress and strain components in the different layers. In the second phase, equilibrium equations and constitutive relations of the three-dimensional theory of elasticity are used to: (1) calculate the transverse stresses and strains as well as the transverse strain energy densities in the different layers; (2) provide better estimates for the composite shear correction factors; and (3) calculate corrected values for the vibration frequencies, displacements, and in-plane strains and stresses. For simply supported plates the predictions of the proposed procedure are shown to be in close agreement with exact three-dimensional elasticity solutions for a wide range of lamination and geometric parameters. Also, the potential of the proposed procedure for use in conjunction with large-scale finite element models of composite structures is discussed.

Three-dimensional solutions for antisymmetrically laminated anisotropic plates

Analytic three-dimensional elasticity solutions are presented for the stress and free vibration problems of multilayered anisotropic plates. The plates are assumed to have rectangular geometry and antisymmetric lamination with respect to the middle plane. A mixed formulation is used with the fundamental unknowns consisting of the six stress components and the three displacement components of the plate. Each of the plate variables is decomposed into-symmetric and antisymmetric components in the thickness direction, and is expressed in terms of a double Fourier series in the Cartesian surface coordinates

Assessment of computational models for multilayered composite cylinders

Abstract A study is made of the effects of variation in the lamination and geometric parameters of multilayered composite cylinders on the accuracy of the static and vibrational responses predicted by eight modeling approaches, based on two-dimensional shear-deformation shell theories. The standard of comparison is taken to be the exact three-dimensional elasticity solutions, and the quantities compared include both the gross response characteristics (e.g. vibration frequencies, strain energy components, average through-the-thickness displacements and rotations): and detailed, through-the-thickness. distributions of displacements, stresses and strain energy densities. Based on the numerical studies conducted, a predictor -corrector approach, used in conjunction with the first-order shear-deformation theory (with five displacement parameters in the predictor phase), appears to be the most effective among the eight modeling approaches considered. For multilayered orthotropic cylinders the response quantities obtained by the predictor corrector approach are shown to be in close agreement with the exact three-dimensional elasticity solutions for a wide range of lamination and geometric parameters. The potential of this approach for predicting the response of multilayered shells with complicated geometry is also discussed.

Assessment of computational models for sandwich panels and shells

Abstract A study is made of the effects of variation in the material and geometric parameters of curved sandwich panels on the accuracy of the static response predicted by nine different modeling appraoches based on two-dimensional shell theories. The standard of comparison is taken to be the exact three-dimensional thermoelasticity solutions, and the quantities compared include gross response characteristics (e.g. strain energy components, average through-the-thickness displacements and rotations); detailed, through-the-thickness distributions of displacements and stresses; and sensitivity coefficients of the response quantities (derivatives of response quantities with respect to material and geometric parameters of the sandwich structure). Extensive numerical studies are conducted to assess the accuracy of both the global and detailed response characteristics and their sensitivity coefficients obtained by nine two-dimensional modeling approaches. For accurate determination of detailed through-the-thickness distributions such as transverse stresses, either high-order discrete three-layer models or predictor-corrector approaches are required. The potential of predictor-corrector approaches for predicting the thermomechanical response of sandwich panels and shells with complicated geometry is also discussed.

Three-dimensional solutions for the free vibrations and buckling of thermally stressed multilayered angle-ply composite plates

Analytic three-dimensional elasticity solutions are developed for the free vibration and buckling of thermally stressed rectangular multilayered angle-ply anisotropic plates which are assumed to have an antisymmetric lamination with respect to the middle plane. Sensitivity derivatives are evaluated and used to investigate the sensitivity of the vibration and buckling responses to variations in the different lamination and material parameters of the plate. A Duhamel-Neumann-type constitutive model is used, and the material properties are assumed to be independent of temperature. Numerical results are presented, showing the effects of variations in the material characteristics and fiber orientation of different layers, as well as the effect of initial thermal deformation on the vibrational and buckling responses of the plate. 20 refs.

Structural analysis of the adhesive bond in a honeycomb core sandwich panel

Abstract Detailed finite element models are used to examine the effect of the adhesive joint between the honeycomb core and the face sheets on the load transfer and static response of sandwich panels. The square-cell honeycomb core panels considered have simply supported edges and are subjected to static uniform pressure loading. The sandwich core, face sheets and adhesive joint are modeled by using three-dimensional solid elements. The total strain energy in the finite element model of the adhesive joint material are used to investigate the effect of adhesive joint characteristics (thickness and adhesive joint fillet size) as well as the core cell size and wall thickness on the load transfer in the core/face sheet joint.

Hierarchical adaptive modeling of structural sandwiches and multilayered composite panels

Abstract Some recent advances in the hierarchical modeling strategies are reviewed with special emphasis on applications to multilayered composite panels. Discussion focuses on the key elements of hierarchical adaptive modeling; multimodel predictor and corrector modeling procedures; potential for solving large complex problems; and the needed development to realize this potential. Numerical studies are presented for free vibrations of thermally-stressed multilayered composite panels and structural sandwiches with composite face sheets demonstrating the effectiveness of the multimodel predictor–corrector modeling approaches.