Ahmed K. Noor

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 composite shells

A review is made of the different approaches used for modeling multilayered composite shells. 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; first-order shear deformation theories based on linear displacement assumptions in the thickness coordinate; and efficient computational strategies for anisotropic composite shells. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of simply supported composite cylinders on accuracy of the static and vibrational responses predicted by eight different modeling approaches (based on two-dimensional shear deformation theories). The standard of comparison is taken to be the exact three-dimensional elasticity solution. The quantities compared include both the gross response characteristics (eg, vibrational frequencies and strain energy components); and detailed, through-the-thickness distributions, stresses, and strain energy densities. Some of the future directions for research on the modeling of multilayered composite shells are outlined.

Computational strategies for flexible multibody systems

The status and some recent developments in computational modeling of flexible multibody systems are summarized. Discussion focuses on a number of aspects of flexible multibody dynamics including: modeling of the flexible components, constraint modeling, solution techniques, control strategies, coupled problems, design, and experimental studies. The characteristics of the three types of reference frames used in modeling flexible multibody systems, namely, floating frame, corotational frame, and inertial frame, are compared. Future directions of research are identified. These include new applications such as micro- and nano-mechanical systems; techniques and strategies for increasing the fidelity and computational efficiency of the models; and tools that can improve the design process of flexible multibody systems. This review article cites 877 references. @DOI: 10.1115/1.1590354#

Stability of multilayered composite plates

Abstract Quantitative assessment is made of the accuracy and range of validity of the classical and shear-deformation plate theories when applied to the stability analysis of multi-layered composite plates with large numbers of layers. The standard of comparison is taken to be the linear three-dimensional theory of orthotropic elasticity. In the shear-deformation theory, the composite correction are included and are shown to result in close agreement with three-dimensional elasticity solutions for a wide range of lamination and geometric parameters.

Computational Models for High-Temperature Multilayered Composite Plates and Shells

The focus of this review is on the hierarchy of composite models, predictor-corrector procedures, the effect of temperature-dependence of material properties on the response, and the sensitivity of the thermomechanical response to variations in material parameters. The literature reviewed is devoted to the following eight application areas: heat transfer; thermal stresses; curing, processing and residual stresses; bifurcation buckling; vibrations of heated plates and shells; large deflection and postbuckling problems; and sandwich plates and shells. Extensive numerical results are presented showing the effects of variation in the lamination and geometric parameters of temperature-sensitive angle-ply composite plates on the accuracy of thermal buckling response, and the sensitivity derivatives predicted by nine different modeling approaches (based on two-dimensional theories). The standard of comparison is taken to be the exact three-dimensional thermoelasticity solutions. Some future directions for research on the modeling of high-temperature multilayered composites are outlined. 448 ref., 16 figs., 11 tabs.

Recent advances in reduction methods for nonlinear problems

Abstract Status and some recent developments in the application of reduction methods to nonlinear structural mechanics problems are summarized. The aspects of reduction methods discussed herein include: (a) selection of basis vectors in nonlinear static and dynamic problems (b) application of reduction methods in nonlinear static analysis of structures subjected to prescribed edge displacements, and (c) use of reduction methods in conjunction with mixed finite element models. Numerical examples are presented to demonstrate the effectiveness of reduction methods in nonlinear problems. Also, a number of research areas which have high potential for application of reduction methods are identified.

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.

Three-dimensional solutions for coupled thermoelectroelastic response of multilayered plates

Abstract Analytic three-dimensional solutions are presented for the coupled thermoelectroelastic response of multilayered hybrid composite plates. The plates consist of a combination of fiber-reinforced cross-ply and piezothermoelastic layers. Both the thermoelectroelastic static response and its sensitivity coefficients are computed. The sensitivity coefficients measure the sensitivity of the response to variations in different mechanical, thermal and piezoelectric material properties of the plate. A linear constitutive model is used, and the material properties are assumed to be independent of the temperature and the electric field. The plates are assumed to have rectangular geometry and special material symmetries. A mixed formulation is used with the fundamental unknowns consisting of the three transverse stress components, three displacement components, transverse component of the electric displacement field, electric potential, transverse heat flux component and temperature change. Each of the fundamental unknowns is expressed in terms of a double Fourier series in the Cartesian surface coordinates. A state space approach is used to generate the static response and to evaluate the sensitivity coefficients. Extensive numerical results are presented showing the effects of variation in the geometric parameters of the plate on the different response quantities and their sensitivity coefficients.

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.