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The development of novel composite mechanics for the analysis of damping in composite laminates and structures and the more significant results of this effort are summarized. Laminate mechanics based on piecewise continuous in-plane displacement fields are described that can represent both intralaminar stresses and interlaminar shear stresses and the associated effects on the stiffness and damping characteristics of a composite laminate. Among other features, the mechanics can accurately model the static and damped dynamic response of either thin or thick composite laminates, as well as, specialty laminates with embedded compliant damping layers. The discrete laminate damping theory is further incorporated into structural analysis methods. In this context, an exact semi-analytical method for the simulation of the damped dynamic response of composite plates was developed. A finite element based method and a specialty four-node plate element were also developed for the analysis of composite structures of variable shape and boundary conditions. Numerous evaluations and applications demonstrate the quality and superiority of the mechanics in predicting the damped dynamic characteristics of composite structures. Finally, additional development was focused on the development of optimal tailoring methods for the design of thick composite structures based on the developed analytical capability. Applications on composite plates illustrated the influence of composite mechanics in the optimal design of composites and the potential for significant deviations in the resultant designs when more simplified (classical) laminate theories are used.

This report discusses the development and application of two alternative strategies in the form of global and sequential local response surface (RS) techniques for the solution of reliability-based optimization (RBO) problems. The problem of a thin-walled composite circular cylinder under axial buckling instability is used as a demonstrative example. In this case, the global technique uses a single second-order RS model to estimate the axial buckling load over the entire feasible design space (FDS) whereas the local technique uses multiple first-order RS models with each applied to a small subregion of FDS. Alternative methods for the calculation of unknown coefficients in each RS model are explored prior to the solution of the optimization problem. The example RBO problem is formulated as a function of 23 uncorrelated random variables that include material properties, thickness and orientation angle of each ply, cylinder diameter and length, as well as the applied load. The mean values of the 8 ply thicknesses are treated as independent design variables. While the coefficients of variation of all random variables are held fixed, the standard deviations of ply thicknesses can vary during the optimization process as a result of changes in the design variables. The structural reliability analysis is based on the first-order reliability method with reliability index treated as the design constraint. In addition to the probabilistic sensitivity analysis of reliability index, the results of the RBO problem are presented for different combinations of cylinder length and diameter and laminate ply patterns. The two strategies are found to produce similar results in terms of accuracy with the sequential local RS technique having a considerably better computational efficiency.

A framework for the multiscale design and analysis of composite materials and structures is presented. The ImMAC software suite, developed at NASA Glenn Research Center, embeds efficient, nonlinear micromechanics capabilities within higher scale structural analysis methods such as finite element analysis. The result is an integrated, multiscale tool that relates global loading to the constituent scale, captures nonlinearities at this scale, and homogenizes local nonlinearities to predict their effects at the structural scale. Example applications of the multiscale framework are presented for the stochastic progressive failure of a SiC/Ti composite tensile specimen and the effects of microstructural variations on the nonlinear response of woven polymer matrix composites.

Probabilistic composite micromechanics methods are developed that simulate expected uncertainties in unidirectional fiber composite properties. These methods are in the form of computational procedures using Monte Carlo simulation. The variables in which uncertainties are accounted for include constituent and void volume ratios, constituent elastic properties and strengths, and fiber misalignment. A graphite/epoxy unidirectional composite (ply) is studied to demonstrate fiber composite material property variations induced by random changes expected at the material micro level. Regression results are presented to show the relative correlation between predictor and response variables in the study. These computational procedures make possible a formal description of anticipated random processes at the intraply level, and the related effects of these on composite properties.

Aeroelasticity is the relationship between the elasticity of an aircraft structure and its aerodynamics. This relationship can cause instabilities such as flutter in a wing. Engineers have long studied aeroelasticity to ensure such instabilities do not become a problem within normal operating conditions. In recent decades structural tailoring has been used to take advantage of aeroelasticity. It is possible to tailor an aircraft structure to respond favorably to multiple different flight regimes such as takeoff, landing, cruise, 2-g pull up, etc. Structures can be designed so that these responses provide an aerodynamic advantage. This research investigates the ability to design and analyze tailored structures made from filamentary composites. Specifically the accuracy of tailored composite analysis must be verified if this design technique is to become feasible. To pursue this idea, a validation experiment has been performed on a small-scale filamentary composite wing box. The box is tailored such that its cover panels induce a global bend-twist coupling under an applied load. Two types of analysis were chosen for the experiment. The first is a closed form analysis based on a theoretical model of a single cell tailored box beam and the second is a finite element analysis. The predicted results are compared with the measured data to validate the analyses. The comparison of results show that the finite element analysis is capable of predicting displacements and strains to within 10 on the small-scale structure. The closed form code is consistently able to predict the wing box bending to 25 of the measured value. This error is expected due to simplifying assumptions in the closed form analysis. Differences between the closed form code representation and the wing box specimen caused large errors in the twist prediction. The closed form analysis prediction of twist has not been validated from this test.

An overview of an analytic procedure which can be used to provide comprehensive stress and strength analysis of composite structures with stress concentrations is given. The methodology provides designer/analysts with a user-oriented procedure which, within acceptable engineering accuracy, accounts for the effects of a wide range of application design variables. The procedure permits the strength of arbitrary laminate constructions under general bearing/bypass load conditions to be predicted with only unnotched unidirectional strength and stiffness input data required. Included is a brief discussion of the relevancy of this analysis to the design of primary aircraft structure; an overview of the analytic procedure with theory/test correlations; and an example of the use and interaction of this strength analysis relative to the design of high-load transfer bolted composite joints.

The design of polymer matrix composite joints is strongly influenced by the presence of out-of-plane or through-the-thickness stresses. These stresses can be critical, since out-of-plane interlaminar tension and shear strengths, as well as moduli, are strongly influenced by the low strength and stiffness of the polymer matrix constituents, as well as the fiber matrix interface. To aid in the design of these structures, this research develops a methodology for predicting structural adequacy of composites in the presence of through-the-thickness loadings. Specifically, this work details guidelines for the design of resin fillet tee-joints for use in marine applications. A combination of finite element analyses and approximate analytical formulations are used to create these practically oriented design guidelines. A parametric study, using finite element models, was conducted examining the effects of changing various material and geometric variables on the stresses and failure modes of the tee-joint structure. The tee-joint structure was sectioned in order to facilitate the creation of analytical approximations to predict the failure stresses in the various sections. This approach offers the added benefit of developing insight that guides the designer towards the most appropriate joint configuration for a specific application.

A general framework has been developed for the analysis of laminated smart structures with embedded and/or surface bonded piezoelectric actuators and sensors. The theory addresses the following issues: (1) accurate description of transverse shear effect in the laminated structural model, (2) presence of multiple delaminations and (3) characterization of delamination placement and size on dynamic characteristics. The mathematical model has been implemented using finite element method and extensive numerical investigations have been performed to validate the model with three-dimensional results and available experimental data. Results indicate that the presence of delaminations affect the modal strain distributions in smart composite laminates. The developed theory has been used to characterize delaminations in smart composite plates of arbitrary thickness and results indicate that dynamic strain is a better indicator of damage than frequencies or mode shapes. Significant differences are noted in the RMS values of the response, calculated using modal strain, indicating the presence of damage. A control system has also been designed to minimize the effect of damage. New damage indices based on modal strain are proposed and show promising results.

Aeroelasticity is the relationship between the elasticity of an aircraft structure and its aerodynamics. This relationship can cause instabilities such as flutter in a wing. Engineers have long studied aeroelasticity to ensure such instabilities do not become a problem within normal operating conditions. In recent decades structural tailoring has been used to take advantage of aeroelasticity. It is possible to tailor an aircraft structure to respond favorably to multiple different flight regimes such as takeoff, landing, cruise, 2-g pull up, etc. Structures can be designed so that these responses provide an aerodynamic advantage. This research investigates the ability to design and analyze tailored structures made from filamentary composites. Specifically the accuracy of tailored composite analysis must be verified if this design technique is to become feasible. To pursue this idea, a validation experiment has been performed on a small-scale filamentary composite wing box. The box is tailored such that its cover panels induce a global bend-twist coupling under an applied load. Two types of analysis were chosen for the experiment. The first is a closed form analysis based on a theoretical model of a single cell tailored box beam and the second is a finite element analysis. The predicted results are compared with the measured data to validate the analyses. The comparison of results show that the finite element analysis is capable of predicting displacements and strains to within 10% on the small-scale structure. The closed form code is consistently able to predict the wing box bending to 25% of the measured value. This error is expected due to simplifying assumptions in the closed form analysis. Differences between the closed form code representation and the wing box specimen caused large errors in the twist prediction. The closed form analysis prediction of twist has not been validated from this test.

Design of large composite structures requires striking a balance between permitted flaw size,strength margins, weight, and production rate. Stringent requirements manufacturing flaws can result in a lightweight structure because the strength properties are assumed to be closer to pristine. However, these stringent requirements can lead to production delays due to increased inspection and rework needed during the layup and rejection of parts after cure. Conversely, permitting larger flaws can reduce production delays, but will likely result in a heavier structure due to increased conservatism needed to maintain acceptable structural margins. The tradeoff between these criteria can vary between different structures and material systems, so the balance between manufacturing and design requirements is always a moving target. Assessment of this tradeoff requires having the ability to quickly evaluate the impact of flaw size on strength margin across an entire structure for a large number of load cases. The approach taken in this work is to implement an effects of defects analysis and sizing framework within HyperX. HyperX performs optimization of composite structures; this capability has been enhanced to include structural flaw data in the margin of safety calculations performed during optimization. Both the flaw import process and analysis of flaws have been generalized such that any flaw type from any source can be considered. The resulting tool enables rapid assessment of the impact of defects both at a vehicle and part level.