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Computation of transverse shear and transverse normal stresses or interlaminar stresses from one-dimensional equivalent single-layer beam theories using Sinc Method based on Interpolation of Highest Derivative (SIHD) [Li, C. and Wu, X., "Numerical Solution of Differential Equations Using Sinc Method Based on the Interpolation of the Highest Derivatives," Applied Mathematical Modeling, Vol. 31, 2007 pp. 1{9.] is preformed. SIHD, a form of the Sinc collocation method in which Sinc basis functions are used to approximate the highest derivative in the governing equation of the underlying boundary value problem, is proposed as an ecient method for determining through-the-thickness variations of interlaminar stresses by integration of the equilibrium equations of three-dimensional elasticity. Because the required higher-order derivatives of the displacements are obtained without post-processing, an improvement over presently used nite element based methods, SIHD is benecial for this application. In functionally graded material, SIHD oers additional benets. Because material properties may exhibit complicated variations through the thickness, determining transverse shear and normal stress components by integration of the threedimensional elasticity equations may become impossible to perform analytically. However, because SIHD employs numerical indenite integration by double exponential integration, the integration can be performed numerically without computing additional integration weights. In this paper, we obtain interlaminar stresses in symmetric cross-ply laminates and sandwich composites with functionally graded material using SIHD to approximately solve the static governing equations of the Timoshenko beam theory (FSDT), and Bickford’s consistent higher order beam theory. We compare stresses, including interlaminar stresses, and displacements for various thickness-to-length ratios obtained from SIHD with an approximate solution of three-dimensional elasticity obtained using the nite element method by ABAQUS/Standard. Our results indicate SIHD accurately approximates the interlaminar stresses throughout the majority of the length of the beam; however, near the boundary, our results are signicantly dierent

Monitoring accurate temperature and pressure profiles in harsh environments is currently in high demand for gas turbine engines and nuclear reactor simulators. The ability to measure both quantities continuously over a region, without thermal coupling, while maintaining a small design envelope is also highly desirable. High temperature electronic devices, such as MEMS (microelectromechanical systems), have provided industry with effective sensors. However, because they rely heavily on the silicon technology, their performance is limited to just above 500◦C. Beyond this temperature, silicon’s mechanical properties begin to break down. Researchers have shown MEMS sensors to be accurate at temperatures reaching 600◦C, but higher temperature sustainability will require a more durable material selection. Beyond the material shortcoming, the high temperatures do not effectively allow MEMS sensors to be multiplexed into large arrays. In general, fiber-optic based methods have been shown to offer many advantages over electronic based sensors and are the ideal choice for high temperature regimes and distributed sensing. In this ∗Graduate Student, Aerospace and Ocean Engineering, 215 Randolph Hall Blacksburg VA 24060 †Professor, Aerospace and Ocean Engineering, 215 Randolph Hall Blacksburg VA 2406, Associate Fellow. ‡Professor (Holder of the Fred D. Durham Chair), Aerospace and Ocean Engineering, 215 Randolph Hall Blacksburg VA 24060, Fellow. §Optical Physics Team/Optical Systems Group, 3157 State Street Blacksburg, VA 24060.

Developments in rapid manufacturing techniques have made it easier to manufacture objects with complex shapes. One such technique, Electron Beam Free Form Fabrication (EBF3), has promising features of fabricating panels with curvilinear stiffeners. Preliminary research has shown that panels with curvilinear stiffeners might have a reduced weight than panels with straight stiffeners. Thus, it is essential to have a computational design environment (CDE) to obtain optimum design for curvilinearly stiffened panels. In our earlier study, we have developed one such computer design environment that uses detailed finite element model to obtain optimum design. This design optimization scheme is very computational intensive. Therefore, to make it feasible from an industry point of view, surrogate modeling is required. This paper presents an efficient surrogate model to perform design optimization for panels with curvilinear stiffeners in terms of endpoint coordinates and shape design parameter of curvilinear stiffeners. Developed surrogate model predicts the mass of the panel within an accuracy of ± 1 % as compared to the mass obtained using the high fidelity FEM solver.

This paper investigates an analytical modeling, for 2-D tri-axial braided textile composites, that is based on the concept of Repeating Unit Cell (RUC) and micro-mechanical equations (Rule of mixtures and Self-Consistent method) for yarns. The material modeling for the tri-axial braids is implemented by a simple homogenization scheme using the concept of strain energy density. To find the three-dimensional effective moduli, the iso-strain assumption is applied to the Repeating Unit Cell components of 2-D tri-axial braids. A degraded braid is implemented by a simple damage scheme of micro-mechanical constitutive equations, i.e. crack density, and the damaged elastic properties of degraded yarns are fulfilled with an assumption of transverse micro-cracking in a matrix component of strands. To solve a damage constitutive equation, a function of stiffness and compliance matrices in the material model is considered. For the geometrical shape modeling, the geometrical surface equations of braids in the Repeating Unit Cell are introduced. The validation of present modeling is proved by comparisons with other previous models and shows considerably accurate numerical solutions. L = the project length of braider yarns b w = the width of braider yarns ' b w = the project width of braider yarns 0 L = the total length of axial yarns d p = the packing density f d = the fiber diameter 0 n = the filaments' number of axial yarns b n = the filaments' number of braider yarns 0 A = the cross-sectional area of axial yarns b A = the cross-sectional area of braider yarns 0 t = the thickness of axial yarns b t = the thickness of braider yarns

Structural health monitoring of tires is increasingly becoming very important and a number of studies have been or are being conducted to develop appropriate means to accomplish this very difficult task. A key to achieving this goal would be the development of appropriate sensors for predicting, and thus ultimately preventing, onset of failure in tires. The failure modes in tires are many and it may require a large number of sensors to detect onset of these failure modes. This article summarizes some of the sensors that are currently available for sensing strain in tires. Specifically, we review noncontacting sensors such as the sidewall torsion sensor, the developments of the Apollo project, a laser-sensing system, micropower impulse radar, ultrawideband (UWB) radar–based health monitoring, chromasonic sensors based on acoustic emission, acceleration sensing, force/friction sensing, and strain sensing. Keywords: capacitance-based sensing; fiber-optics-based sensing; smart tires; structural health monitoring; sensors

A one-dimensiona l finite element has been developed to study the aeroelastic behavior of wings of arbitrary geometry and material properties distribution ranging from beam plates to builtup box structures reinforced by stringers. The formulation takes into account the effect of transverse shear and the bending-stretching coupling inherent to unsymmetric composite structures and allows for unsymmetric cross sections. A modified aerodynamic strip theory along with the V-g method is used to solve the flutter equations. The formulation has been evaluated by solving a large number of problems available in the literature. An introductory study of the bending-stretching coupling introduced by unsymmetry and damage has been conducted. It was found that the unsymmetry can have a positive or a negative influence on the aeroelastic behavior of the structure and that this influence vanishes rapidly with a decrease in coupling. It is concluded that the unsymmetry of aeroelastic structures should be considered both during the tailoring process as an added degree of design freedom and during damage tolerance assessment.

Numerical simulation of fluid flows is increasing in popularity and utility in the study of wind effects on structures. Many different schemes, such as finite difference and finite elements, have been used. For this study, sponsored by the Federal Highway Administration, many of these methods were studied and compared. A Chebyshev-collocation Spectral method was eventually chosen for its extreme computational efficiency. Spectral Methods have been used in a variety of flow calculation problems. Others have applied it to channel flows and compressible flow problems. The current work is an attempt toward applying the spectral method to flow around bluff bodies, in particular rectangular prisms and flat plates. The first test of the technique was a model of bar deflecting along it's axis due only to it's own weight. Then, a two dimensional Poisson solver was implemented with the method. Next, a uni-domain Navier-Stokes solver was attempted. Currently, a multidomain two dimensional incompressible Navier Stokes solver is under development. In addition, a microcomputer flow visualization program has been developed using a steady state finite difference flow modeler to provide sample data. Finally, some conclusions and areas of future work will be discussed.

Stability analysis of perfect and imperfect cylindrical shells under combined wind pressures and snow loads is performed using the finite element method. A 48 degree-of-freedom (d.o.f.) thin shell element, free from both shear and membrane locking and capable of modelling shells with arbitrary imperfections, is used. Nonlinear effects due to prebuckling rotations are included. The nonlinear response is obtained using Riks-Wempner algorithm. Effect of the imperfection amplitude on the limit load points under combined wind and snow loads is studied. The snow loads are modelled as axial loads. The interaction diagrams for perfect and imperfect shells are given.

A simple, pseudo-spectral (collocation type) method is used to study Bratu's 2-parameter equation. The equation represent an important class of problems in both science and engineering. Simple polynomials are used to represent the dependent variable. The trial functions satisfy all the completeness requirement and make use of the various inherent symmetries of the problem to significantly reduce the size of the problem. The resulting nonlinear set of algebraic equations is solved using a constant-arc type method. For the 1-parameter Bratu's equation, the present results are found to be in good agreement with the previous results. Although the results were obtained using a main-frame computer, the present method can easily be used on a micro-computer. Results are obtained for variation of the value of the dependent parameter at the origin for different values of the two parameters. The present algorithm is capable of successfully obtaining the various turning points in both λ-u(0, 0) curves as well as e-u(0, 0) curves. A discussion of the future research work is also given.

Karhunen-Loeve(KL) expansion of auto-covariance of input Gaussian random process is carried out using standard normal variables as the basis of KL expansion. Input random processes for many practicle problems have non-Gaussian random process description, so an algorithm is developed to find the basis random variables of KL expansion for non-Gaussian processes. The basis random variables of KL expansion are obtained via nonlinear transformation of marginal cumulative distribution function using standard deviation. Results are obtained for three known skewed distributions, Log-Normal, Beta, and Exponential. In all the cases, it is found that the proposed algorithm matches very well with the known solutions and can be applied to solve non-Gaussian process using Spectral Stochastic Finite Element Method.

Optimization of stiffened Electron Beam Freeform Fabrication (EBF3) panels is carried using different types of Response Surfaces (RS). Placement and sizing variables are optimized using integrated software of NURBS, DistMesh, MSC.NASTRAN and MATLAB. This approach has two optimization loops; the first one being sizing optimization, carried out inside inner loop through NASTRAN using feasible direction method for different placement variables (RS factors). The next one, optimal placement of stiffeners is carried out in the outer loop through RS approach. So this approach does not suffer with local minima problems and yields global minimas. This technique is applied to square panels with in-plane bi-axial and uniform surface pressure loadings. Panel’s weight is minimized with buckling, displacement, and stress constraints. This effort is the first one to do placement and sizing optimization of stiffened panels.

*† A simple geometrical model to predict effective moduli of the 2-D braided textile composites is developed. To calculate homogenized material properties for 2-D braids, the concept of a Repeating Unit Cell (RUC) along with the iso-strain assumption and equivalence of strain energy of the RUC are used. The geometrical surface equations of the braid yarns, in terms of sinusoidal functions are introduced to describe three-dimensional braided yarn shapes. The micro-mechanical constitutive equations are employed to obtain appropriate elastic properties for the 2-D braided yarns. For a parametric study, various yarn sizes, yarn aspect ratios and braid angles are considered to investigate various characteristics of effective elastic moduli of the 2-D braided textile composites. Results from our analytical model for determining effective modulus for a 2-D braided textile composite were compared with available results in the existing literature. The comparison between our geometrical model and other models indicates excellent agreement, and the dependency of effective constitutive properties of a 2-D braided textile composite are established from a number of numerical examples. Nomenclature br θ + = the braid angle for the br θ + yarns br θ − = the braid angle for the br θ − yarns br c + θ = the crimp angle for the br θ + yarns br c − θ = the crimp angle for the br θ − yarns H = the total thickness for the 2-D braids’ RUC 1 u = the undulation length for the br θ + yarns in the x-y-z coordinate 2 u = the undulation length for the br θ − yarns in the x-y-z coordinate * 1 u = the undulation length for the br θ + yarns in the 1-2-3 coordinate * 2 u = the undulation length for the br θ − yarns in the 1-2-3 coordinate * 1 u u = the undulation arc-length for the br θ

This paper describes the development of a fractional calculus approach to model the hysteretic behavior shown by the variation of resistance with strain in nano-composites (like MetalRubberOˆ). Experiments have been carried out on MetalRubberOˆ to study the strain-resistance variation of this material under strains varying in a triangular manner. Combined fractional derivative and integer order integral model and fractional integral model (with two sub-models) have been developed to model this behavior. Effieiency of these models has been discussed by comparison of their results with the experimental result.

Optimal placement of actuators has been studied for more than 20 years. The typical optimization methods for the problem, including heuristic integer programming, tabu search, simulated annealing, and genetic algorithms, have been developed over the years. However, the comparison of various methods has not been addressed. This paper compares two heuristic integer programming algorithms: Worst-Out-Best-In (WOBI) and Exhaustive Single Point Substitution (ESPS) proposed by Haftka and Adelman in early 1980s with Genetic Algorithms (GAs) developed most recently by present authors. The problems considered here are the large-scale optimization of N piezoelectric strip actuator location from a set of M possible locations on the back surface of a hexagonal spherical mirror for thermal deformation control. The number of candidate placements for these problems are too large to use an exhaustive method. The comparison of GAs with WOBI and ESPS are made on two types of optimization problems: (i) to find the optimal locations and optimal voltages suitable for only a single type of thermal loads at a given time, and (ii) to determine just one set of actuator locations which will be good for all the four types of thermal loads considered in this study. Although both these problems are large, difficult and computationally intensive, combinatorial and continuous optimization problems, the latter is a more challenging, multi-criterion optimization problem. Several interesting results are observed. For example, the results show that both WOBI and ESPS usually converge to local optima and that the rate of the convergence of ESPS is much lower than that of WOBI and GAs and that the number of evaluations required for ESPS convergence might be too large to accept for large-scale optimization. As for the quality of final solutions they find in a group of runs, GAs are usually better than ESPS, and WOBI is the worst. Also, the paper explores reasonable use of these algorithms. For example, considering the fast rate of convergence in the early stage of the GA optimization and the fact that it is hard, if not impossible, to say whether GAs have reached the global optima using limited runs, the paper recommends that WOBI and ESPS might be used to check whether GAs have reached the optima in the sense of WOBI and ESPS. This check is not necessary if GAs are allowed to run enough time. Because the number of evaluations for ESPS convergence is quite large, the effect of the fast reanalysis by neglecting the stiffness effect of actuators is also investigated in the paper.

Lamb wave based structural health monitoring is a promising method for in-situ detection and identification of incipient damage in plate structures. Most of the previous research on Lamb wave based SHM methods has been experimental proof-of-concept studies aimed at showing the viability of particular sensors and actuators. This paper will investigate the use of a genetic algorithms (GA) for optimal placement of piezoelectric sensors and actuators in a damaged aluminum plate. Simulations of Lamb wave propagation in the plate are performed using the local interaction simulation approach, which is significantly more efficient than the finite element method. Using the simulated sensor data, a sensor performance metric (SPM) is then evaluated. A fitness function based on the SPM of each sensor is defined and the GA based optimization procedure that aims to maximize the SPM for the entire sensor/actuator array was performed. The optimization procedure was performed for two randomly distributed damage sets, and the results show that the optimized sensor locations perform significantly better than a nominal evenly distributed sensor array for the two damage sets that were investigated.

*† ‡ § ** tatic analysis of sandwich panels with square honeycomb core is presented. The displacement field of the sandwich panel is obtained. The analysis of the panel is done using the finite element approach applied to the Classical Laminated Plate theory (CLPT), the First Order Shear Deformation theory (FSDT) and the Higher Order Shear Deformation Theory (HSDT). The constitutive behavior of a continuum equivalent to the core is obtained using Hohe’s approach which is a homogenization approach based on the strain energy equivalence between a body containing cellular structure and a continuum body. The results of the displacement field of the sandwich panel are then compared to results obtained from a highly detailed FEM created in ABAQUS ® in which the cell walls of the honeycomb core are modeled as shell elements, this comparison shows that the displacement results of the HSDT are in error of 7.6% when compared to the detailed ABAQUS ® model. An alternative procedure for calculating the constitutive behavior of the continuum equivalent to the square honeycomb was pursued here by creating detailed FEM of the unit cell of the square honeycomb using ABAQUS ® to detailed representative models and applying static loads to these models then obtaining the properties by means of the flexibility approach. Comparison between the equivalent strain energy approach and flexibility approach applied to detailed ABAQUS models of the unit cell of the square honeycomb proved the equivalent strain energy approach to be efficient. Simple formulas for calculating the different Elastic properties of equivalent continuum to the square honeycomb are introduced. S

A simple model to calculate three-dimensional degraded strengths of plain woven textile composites is developed. These three-dimensional strengths are calculated by using the concept of a Repeating Unit Cell (RUC) in the plain weave textile composite based on geometric surface equations and homogenized material models obtained using micromechanics. The geometrical micro-mechanical modeling of the plain weave is formed using the sine function model (SFM). The ABAQUS program is used to solve the micromechanical model. To predict ultimate strengths of the plain woven textile composite, a simple repeating unit cell model and user material subroutines (UMAT) in ABAQUS program are used. In both the RUC and UMAT models, Rule of Mixture and the SelfConsistent Method are considered respectively. Degraded elastic properties for the fill and warp yarns and the matrix resin in the presence of transverse cracks are analyzed using a crack-density scheme. In the ABAQUS, to ensure that the RUC maintains straight shapes, a displacement control is used instead of the force control analyses. The predicted ultimate tensile and shear strengths are shown to be a close agreement with the results of previous papers. Nomenclature H = the total thickness for the RUC 1 u = the undulation length for the warp yarns 2 u = the undulation length for the fill yarns 1 t = the thickness of warp yarn 2 t = the thickness of the fill yarn m t = the thickness of the resin region 1 a = the width of the warp yarn 2 a = the width of the fill yarn 1 g = the gap length for the warp yarn 2 g = the gap length for the fill yarn up z 1 = the upper coordinate in the -axis for the warp yarn z up z 2 = the upper coordinate in the -axis for the fill yarn z lower z 1 = the lower coordinate in the -axis for the warp yarn z lower z 2 = the lower coordinate in the -axis for the fill yarn z u = the displacements of the warp direction v = the displacements of the fill direction

In this study, three-dimensional shape equations for the 2-D plain woven and braided textile composites were derived to find degraded elastic properties using a simple model. The degraded elastic properties of the plain woven and braided textile composites with transverse micro-cracks were investigated, and reduced elastic properties of textile yarn structures were calculated by a crack density scheme based on micro-mechanical constitutive equations. In addition the iso-strain assumption is considered to describe the effective modulus in sub-domains consisting of cracked fill, warp yarns and resin components. To determine the geometry of textile fabric structures, the concept of repeating unit cell, surface equations of sinusoidal functions and geometrical parameters were used. Finally, our analytical predictions for cracked plain woven and braided textiles were compared to results extracted from the literature. The comparisons between our simple model and other models indicate an excellent agreement.

A non statistical eigenvalues extraction algorithm that uses generalized polynomial chaos is presented for solving real and distinct stochastic eigenvalue problems. An iterative procedure, similar yet ecient from to the vector iteration method used for solving deterministic problems is developed. The proposed method uses eigenvalues obtained using the mean values of system properties and the eigenvalue shift theorem. This algorithm yields not only the fundamental but any higher eigenvalue. The uncertainties in the system inputs as well as the system response (eigenvalues and eigenvectors)are represented by the WienerAskey orthogonal polynomial functions. Galerkin projection is applied in the probabilty space to minimize the weighted residual of the error. Free vibration response of a discrete three degrees-of-freedom system and that of a simply supported beam in the presence of uncertainties in material properties is analyzed. First three eigenvalues of both types of systems are obtained. The convergence of eigenvalue polynomial coecients is studied. The accuracy of the proposed method is compared with the results obtained from Monte Carlo simulation using Latin Hypercube Sampling (LHS). Excellent agreement is observed.

Traditional Large Space Structure construction incorporates the use of light‐weight tubular metal alloys that have good strength to weight and stiness to weight ratio. Recently, however, space structure construction has shifted focus on materials that are light‐ weight, have high strength, have low package volume and possess excellent damping characteristics. Substantial damping enhancement is required for space structures since there is no surrounding medium to provide damping. One approach is to use composites in a fabric form that display highly damped behavior. The damped behavior is attributed to energy dissipation because of the shear stresses between the various fibrous strands that are kept in place by constraining viscoelastic layers. This type of vibration control falls under the rubric of passive damping of structures and has been found to have certain advantages over active damping such as less mechanical complexity. Dynamics and buckling behavior of a structure in the form of a tube made from this type of composite material with metallic end caps is modeled and analyzed using commercially available Finite Element Analysis code ABAQUS r . The current analysis deals with the non‐pressurized tube since the structure can maintain the tubular configuration as well as support end caps on account of its inherent stiness as a composite material. Since no analytical approaches are available to predict damping of these materials, experimental data was used to estimate the damping characteristics of the material. The mass of the end cap was also estimated from the experimental impulse response as exact mass of the end cap (that was rigidly fixed to the tube) was unknown.

To investigate the shape control of smart structures, we have developed a series of genetic algorithms ( GAs ) for an optimal placement of a large number of the piezoelectric actuators. Here we report results from extensive numerical experiments on the GAs, conducted using a coarse-grain parallel computing. We look at how GAs work, what their most distinct properties are, what their robustness means, and how to choose appropriate parameters in applying the micro-GAs. We address the following topics through a thorough comparison of solution quality as obtained by our latest micro-GAs version 3, running on a high performance Sun machine with 17 processors: (i) What is the effect of different random number seeds on the solution quality, specifically a comparison between the results obtained using a small seed and a large seed? (ii) What is the effect of restart criteria in micro-GAs, specifically the two parameters --- number of generations used for the inner loop and the level of diversity in the population on the solution quality? (iii) What is the effect on the solution quality as the number of actuators changes from 30 and 121 to 15, 60, and 90? Through these extended studies, we not only get better layouts of piezoelectric actuators in each of the cases than those reported in our previous publications, but also find that the most distinct natures of genetic algorithms are random and robust. By the random nature of GAs, we mean that we can not precisely predict the performance of genetic algorithms on future evaluations based on their performance on previous evaluations. By the robustness of GAs, we mean that although genetic algorithms have their random nature the range of their results are usually small from their different runs after a certain number of evaluations and they are capable of finding a very good solution by simply adjusting the parameter setting or using another random seed generator. To get high quality solutions in the design of complex adaptive structures using finite element analysis and genetic algorithm optimization, the multiple runs including different random seed generators are necessary. The time of the investigation can be significantly reduced using a very coarse grain parallel computing. We also find that although the RMS error reduces with the number of actuators, the reduction of RMS error may not be worth the effort of increasing the number of actuators. Overall, the methodology of using finite element analysis and genetic algorithm optimization is a very good approach and the GA version 3 is efficient, reliable and robust optimization tool for the challenging problem.

The present work describes methods for defining and estimating blast loading over a tent and the resulting pressure loading inside the tent due to transmitted blast waves and proposes a new methodology for estimating such loadings on flexible structures. For this purpose, loading conditions and structural responses of a flexible tent with an interior Collective Protection System (CPS) that was subjected to an explosion were analyzed. This CPS tent protects personnel from biological and chemical agents with a pressurized liner inside the tent as an environmental barrier. Field tests for this structure showed unexpected damage to the liner, and most of the damage occurred on the tent's leeward side. To solve this problem, various tests and analyses using a commercial finite element method, ANSYS, to model the structural dynamics and a Computational Fluid Dynamics code, Fluent, to model the flow field were performed involving: material characteristics of the liner, canvas, and zip seals; modeling of the blast loading over the tent and inside the tent; and structural response of the tent to the blast loading. The results were compared with the field test data obtained by the Air Force Research Laboratory. The experimental pressure data were gathered from pressure gauges attached to the tent surfaces at different locations. The comparison showed that the proposed methods can provide a good design tool to analyze the loading conditions for rigid or flexible structures under explosive loads. Also, it was found that the blast loading and the structural response cannot be analyzed separately, due to the interaction between the flexible structure and the dynamic pressure loading. Therefore, the effect of fluid-structure interaction should be considered in the pressure load calculation on the structure when the structural deflection rate can influence the solution of the flow field surrounding the structure.

An efficient approach for reliability-based design optimization (RBDO) of series systems is presented. A modified formulation of the RBDO problem is employed in which the reliabilities of the failure modes of a system are included in the set of the design variables. This allows for an optimal apportionment of the reliability of a system among its failure modes. A sequential optimization and reliability assessment method is used to efficiently determine the optimum design. Here, the constraints on the reliabilities of the failure modes of the RBDO problem are replaced with approximate deterministic constraints. The proposed approach is demonstrated on two example problems that have been solved in previous studies without optimizing the required reliability levels of the failure modes. The first example performs RBDO to a cantilever beam with a rectangular cross section under lateral and vertical loads. The constraints are on the strength and the maximum allowable displacement. The second example performs RBDO to a cable-stayed box girder with five failure modes. Compared to the designs found by previous studies, the new approach finds designs with lower mass but without reducing the system reliability.

This paper presents the development and numerical implementation of a rate dependent fracture model of an epoxy adhesive. Previous mode I fracture tests conducted under quasistatic, displacement controlled loading of an aluminum double cantilever beam (DCB) bonded with the epoxy exhibited unstable crack growth in the adhesive. Results from mode I fracture tests of compact tension specimens made from bulk adhesive at increasing cross head opening speeds are reported in this paper. The compact tension tests results showed a decreasing critical strain energy release rate with increasing cross head speed, with the critical energy release rate at 1 m/s cross head speed equal to about 20% of its quasi-static value. Two rate dependent cohesive zone models are formulated based on the compact tension test data. A cohesive de-cohesive relationship was postulated between the tractions acting across the crack faces and the opening displacement and opening velocity. These rate dependent cohesive zone models are implemented in a interface finite element to model discrete crack growth in the adhesive. The reaction force history from simulation of the DCB test is in good agreement with the test data using only the rate dependent interface element to model the adhesive.Copyright © 2005 by ASME

An investigation was performed to study the effect of uncertainty in applied loads, helix angles, and failure stresses on the probability of failure of composite cylinders. Also, the effect of the factor of safety on the probability of failure of the cylinder was studied. The probability of failure for a composite cylinder subject to axisymmetric loading was obtained using the First Order Reliability method (FORM). The failure of the cylinder was studied based on first ply failure. Ply failure was predicted using the non-smooth Hashin criterion. Hashin criterion is based on writing a different interaction equation for separate failure modes. Four failure modes are considered associated with matrix or fiber failure, in either tension or compression. The accuracy of FORM as applied to this problem was verified by comparing the FORM results to those obtained by Monte-Carlo Simulation method with importance sampling. i x µ = mean values of the design parameters i x

Measurement based load updating for linear finite element models is to find the parameters or coefficients of the applied load on the structure to minimize the sum of squares of the errors between the calculated and measured response entities. In this paper, we revisit this topic by using reduced number of unknown load coefficients to suppress unexpected oscillations of the extracted loads due to insufficient measured data and ill-conditioned Least Squares problems. Examples include simply-supported stiffened and un-stiffened plates and a foam cored mattress.

An experimental and computational study of an adhesively bonded, double cantilevered beam (DCB) under quasi-static loading is presented. The polymeric adhesives are either an acrylic or an epoxy, and the adherends are 6061 aluminum alloy. DCB tests bonded with the acrylic exhibited stable crack growth, while the DCB tests bonded with the epoxy exhibited unstable crack growth. The responses of the DCB test speciments were modeled in the ABAQUS/Standard® software package. Interface finite elements were located between bulk elements to model crack initiation and crack growth in the adhesive. These interface elements are implemented as user-defined elements in ABAQUS®, and the material law relating the interfacial tractions to the separation displacements is based on a cohesive zone model (CZM). Using interface elements only to model the acrylic adhesive, the simulation correlates very well to the test. Good correlation between the simulation and the test for the epoxy adhesive is achieved if both bulk modeling of the adhesive and inertia of the specimen are included.Copyright © 2004 by ASME

Because of the inherent complexity of fiber-reinforced laminated composites, it can be challenging to manufacture composite structures according to their exact design specifications, resulting in unwanted material and geometric uncertainties. Thus the understanding of the eect of uncertainties in laminated structures on their static and dynamic responses is highly important for a reliable design of such structures. In this research, we focus on the deterministic and probabilistic stability analysis of laminated structures subject to subtangential loading, a combination of conservative and nonconservative tangential loads, using the dynamic criterion. In order to study the dynamic behavior by including uncertainties into the problem, three models were developed: Exact Monte Carlo Simulation, Sensitivity-Based Monte Carlo Simulation, and Probabilistic FEA. These methods were integrated into the developed finite element analysis. Also, perturbation and sensitivity analysis have been used to study nonconservative problems, as well as to study the stability analysis using the dynamic criterion.

An obstacle in applying artificial neural networks (NNs) to system identification problems is that the dimension and the size of the training set for NNs can be too large to use them effectively in solving a problem with available computational resources. To overcome this obstacle, principal component analysis (PCA) can be used to reduce the dimension of the inputs for the NNs without impairing the integrity of data and orthogonal arrays (OAs) can be used to select a smaller number of training sets that can efficiently represent the given behavior system. NNs with PCA and OAs are used here in solving two parameter identification problems in two different fields. The first problem is identifying the location of damage in cantilever plates using the free vibration response of the structure. The free vibration response is simulated using the finite element method. The second problem is identifying an anomaly in an illuminated opaque homogeneous tissue using near-infrared light based on the simulation of the photon intensity and the photon mean time of flight in perfect and imperfect tissues using the finite element method.

A methodology for designing active control laws in a computational aeroelasticity environment is given. The methodology involves employing a systems identification technique to develop an explicit state-space model for control law design from the output of a computational aeroelasticity code. The particular computational aeroelasticity code employed in this paper solves the transonic small disturbance aerodynamic equation using a time-accurate, finite-difference scheme. Linear structural dynamics equations are integrated simultaneously with the computational fluid dynamics equations to determine the time responses of the structure. These structural responses are employed as the input to a modern systems identification technique that determines the Markov parameters of an "equivalent linear system". The Eigensystem Realization Algorithm is then employed to develop an explicit state-space model of the equivalent linear system. The Linear Quadratic Guassian control law design technique is employed to design a control law. The computational aeroelasticity code is modified to accept control laws and perform closed-loop simulations. Flutter control of a rectangular wing model is chosen to demonstrate the methodology. Various cases are used to illustrate the usefulness of the methodology as the nonlinearity of the aeroelastic system is increased through increased angle-of-attack changes.

This paper focuses on training neural networks to represent the unsteady incompressible aerodynamic forces acting over an airfoil and also to evaluate the aeroelastic response of adaptive airfoils. The adaptive behavior studied here is a spring having a variable torsional stiffness as a part of a two dimensional aeroelastic system. This property of a varying stiffness is used for flutter suppression. A distributed set of doublet panels on the airfoil surface are used to calculate the unsteady pressure at every point of the adaptable airfoil. The strength of the doublet panels is determined using Neumann type non-penetration boundary conditions. The unsteady aerodynamic loading over the airfoil is calculated using a time marching scheme. To capture the effect of the unsteady circulation on the airfoil, it is necessary to represent the wake also by doublets. This time-marching aerodynamics model, used in obtaining the impulse response, is compared to the time history of lift as given by the Wagner function. Numerical results for the response to a sudden change in the angle of attack, as described in the existing literature do not match with the Wagner solution. We describe the numerical problems concerned with the calculation of the unsteady lift generated by an airfoil under a sudden pitching velocity change. The adaptive nature of the structure is studied as a time-variant system, the stiffness of the airfoil is allowed to be time varying. The unsteady aerodynamic loads obtained from the panel method is coupled to a linear time variant structural dynamics code based on an approach of matrix exponential time marching. Using this numerical solver for time variant dynamic aeroelasticity, neural networks are trained for providing an efficient numerical representation of the aeroelastic behavior of adaptive airfoils. Feed-forward neural networks are used, since

A twenty-two degree-of-freedom beam element, based on the first order shear deformation beam theory, is derived to study the response of fiber-reinforced laminated composite structures. The element can be used for solving both static and dynamic problems. The element consists of four equally spaced nodes and a node at the middle. The nodal displacements measured at each node are: (i) at exterior nodes 1 & 2 ‐ axial displacement u, lateral deflection v, transverse deflection w, rotation of the transverse normals , in-plane rotation , and twist angle ; (ii) at two interior nodes 3 & 4 ‐ the torsion , and the derivatives of u, v, w with respect to x; (iii) at the interior middle node 5 ‐ rotations and . The beam element was derived for orthotropic materials subjected to a state of plane stress and is based under the assumption that lateral bending moment and resultant force are zero (Nyy = Myy = 0). The element linear stiness and mass matrices are obtained through analytical integration. The results for the case of free vibrations are in very good agreement with those available in the literature.

Artie cial neural networks (ANNs) are employed in solving inverse problems in damage detection in structures, as well as detection, using optical imaging, of an anomaly in a light-diffusive media, such as a human tissue. Both of these problems, namely, identifying the damage parameters in a damaged structure and identifying the representative properties in a tissue, require solving highly complex inverse problems. The neural networks (NNs) for both problems are similar, and a method found suitable for solving one type of problem can be applied for solving the other type of problem. In the damage identie cation problem, the natural frequencies of a damaged beam model obtained from analytical and numerical methods were used to identify damage parameters by employing feedforward backpropagation, and also radial basis NNs. In the optical imaging problem, the tissue under investigation was illuminated by a number of near-infrared light sources placed around the circumference of the tissue. Both the location and the size of the anomaly were identie ed by studying the ine uence of the anomaly on the light intensity received at the boundary of the tissue. The near-infrared light measurements are assumed to be available at a number of light detector positions, also along the circumference of the tissue. NNs were used to determine the location and the size of the anomaly in a tissue. The direct problem for the case of optical imaging was solved using the e nite element method to generate the training and testing sets for NNs.

The application of reliability-based optimization to an elastic-plastic beam is studied. The objective is to demonstrate the benefits of reliability-based optimization over the deterministic optimization in such applications where the design requirements of the member tolerate some plastic behavior. Also, some of the difficulties that one might encounter while performing reliability-based optimization of elastic-plastic beams are addressed. A graphical method was used here to avoid the problems of high nonlinearity and derivative discontinuity of the reliability function. The method starts by obtaining a deterministic optimum design that has the lowest possible weight for a prescribed safety factor, and, based on that design, the method obtains an improved optimum design that has either a higher reliability or a lower weight or cost. In this application three failure modes are considered for an elastic-plastic beam of T cross section under combined axial, bending, and shear loads. The failure modes are based on the beam total plastic failure in a section, buckling, and maximum allowable deflection. The results show that it is possible to get improved optimum designs (more reliable or lighter) using reliability-based optimization as compared to the design given by deterministic optimization. Also, the results show that the reliability function can be highly nonlinear with respect to the design variables with discontinuous derivatives.

New generations of highly maneuverable aircraft, uninhabited combat air vehicles or micro air vehicles, are likely to feature very flexible lifting surfaces. To enhance the performance and control characteristics of these vehicles, the replacement of hinged control surfaces by smart wings with morphing airfoils is investigated. This requires a fundamental understanding of the interaction between aerodynamics, structures, and control systems. The modeling of a smart wing with morphing airfoils is described. Trailing-edge flaps for maneuvering are replaced by airfoil morphing via distributed structural actuation. The goal is to build a model consistent with distributed control and to exercise this model to determine the progress possible in terms of flight control (lift, drag, and maneuver performance) with an adaptive wing. The model is used to study the roll performance and actuation power requirements of a smart wing with morphing airfoils. For selected flight conditions, actuation power requirements of a smart wing with morphing airfoils are compared to those of a conventional wing with trailing-edge flaps.

Genetic algorithms (GAs) are becoming increasingly popular due to their ability to solve large complex optimization problems which other methods have difficulty solving. In this paper, an introduction to the theory of GAs and its operators are presented. A brief overview of the current research using GAs in aerospace engineering applications is given. Based on the author's previous work, optimal piezoelectric actuator placement for space telescope mirrors using GAs is discussed. The problem discussed here involves finding optimal locations and optimal voltages for 15 piezoelectric actuators, selected from a maximum of 193 candidate locations. The GA was found to be effective and robust in solving this problem with more than 8.4*1021 possible solutions. Two sets of actuator placements are given as solutions to the multi-criteria optimization problem. The use of GAs for structural damage detection inverse problems for concentrated damage of a continuous beam is also shown. A real number encoded GA was found to provide relatively accurate solutions for this damage detection problem.

New generations of highly maneuverable aircraft, such as Uninhabited Combat Air Vehicles (UCAV) or Micro Air Vehicles (MAV) are likely to feature very flexible lifting surfaces. To enhance stealth properties and performance, the replacement of hinged control surfaces by smart wings and morphing airfoils is investigated. This requires a fundamental understanding of the interaction between aerodynamics, structures, and control systems. The goal is to build a model consistent with distributed control and to exercise this model to determine the progress possible in terms of flight control (lift, drag and maneuver performance) with an adaptive wing. Different modeling levels are examined and combined with a variety of distributed control approaches to determine what types of maneuvers and flight regimes may be possible. This paper describes the current progress of the project and highlights some recent findings.

By use of equivalent plate modeling, an efe cient method has been developed to study the structural behavior and static aeroelastic response of general builtup wing structures composed of skins, spars, and ribs. The model includestransversesheareffectsby treating the wing as a plate, following the e rst-order sheardeformation theory. The equations ofmotion arederived using theRitz method with Legendrepolynomials as trial functions. To model arbitrary wing planforms, the wing is composed of two plates, connected by distributed translatory and rotary springsofveryhighstiffness.Thestructuralmodelhasbeenvalidatedforasetofexamplesbycomparingtheresults withtheonesobtained fromMSC/NASTRAN.Adistributedactuationschemeallowsthemodie cationofwingtwist and camber for maneuver control of the vehicle. The model has been applied to study the roll performance of a e apless smart wing with morphing airfoils. It has been shown that a wing without conventional, hinged control surfaces can exhibit improved roll performance and an increased roll reversal speed due to both aerodynamic and structural advantages.

Monte Carlo Simulation and Stochastic FEA are used to predict randomness in the free vibration response of thin unsymmetrically laminated beams. For the present study, it is assumed that randomness in the response is only caused by uncertainties in the ply orientations. The ply orientations may become random or uncertain during the manufacturing process. A new 16-dof beam element, based on the first-order shear deformation beam theory, is used to study the stochastic nature of the natural frequencies. Using variational principles, the element stiffness matrix and mass matrix are obtained through analytical integration. Using a random sequence a large data set is generated, containing possible random ply-orientations. This data is assumed to be symmetric. The stochastic-based finite element model for free vibrations predicts the relation between the randomness in fundamental natural frequencies and the randomness in ply-orientation. The sensitivity derivatives are calculated numerically through an exact formulation. The squared fundamental natural frequencies are expressed in terms of deterministic and probabilistic quantities, allowing to determine how sensitive they are to variations in ply angles. The predicted mean-valued fundamental natural frequency squared and the variance of the present model are in good agreement with Monte Carlo Simulation. Results, also, show that variations between plus or minus 5 degrees in ply-angles can affect free vibration response of unsymmetrically and symmetrically laminated beams.

This paper describes the multidisciplinary design optimization (MDO) of a transonic strutbraced wing aircraft. The optimization considers aeroelastic deformations of the wing and passive load alleviation. The calculations reveal that the strut twist moment provides substantial load alleviation and significant reductions in structural wing weight. To benefit from the potential of appl ying passive load alleviation during preliminary aircraft design, a flexible wing sizing module has been linked to the MDO design tool to optimize the design of three different strut-braced wing aircraft configurations featuring fuselage mounted engines, underwing mounted engines, and wingtip mounted engines.