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This work presents a decision-tree-based Fuzzy Inference System (FIS) for making optimal choices in the development of reduced-order finite element (FE) models, in our case, shell-solid multifidelity models. FE analysis is widely used to simulate the real-world response of complex engineering structures and requires a high level of expertise for making a priori modeling decisions. Many times, these decisions are quite subjective in nature and lead to significant analyst-to-analyst variability, which in turn leads to considerable differences in engineering solutions. An expert system that recommends optimal modeling choices would notably reduce such variability. Expert systems use a knowledge base, developed by a subject matter expert, which is not always easy for complex structures. This work assesses the potential of interpretable machine learning (decision trees) to create data-driven rules that could be used by a FIS to make modeling choices for a multifidelity T-joint model. Specifically, the FIS takes the structural geometry and desired accuracy as inputs and infers the optimal two-dimensional/three-dimensional topology distribution. Once developed, the FIS is able to provide real-time optimal choices along with interpretability that fosters analysts’ confidence. Potential improvements to the presented framework that can enable its application to complex and nonlinear problems are discussed.

This research develops a highly effective deep-learning-based surrogate model that can provide the optimum topologies of 2D and 3D structures. In general, structural topology optimization requires plenty of computations because of a large number of finite element analyses to obtain optimal structural layouts by reducing the weight and satisfying the constraints. Therefore, many researchers have developed a deep-learning-based model using the initial static analysis results to predict the optimum designs. However, these studies still considered relatively simple example problems, such as a cantilever plate and MBB beam, even though they required a large number of data to achieve an accurate surrogate model for the simple application. To overcome these limitations, we propose a new framework, which 1) efficiently uses limited data by normalizing it and 2) employs a surrogate model capable of handling more practical cases, such as a 2D panel and 3D stiffened panel subjected to a distributed load, and can be used for local–global structural optimization. In all cases, the developed surrogate models can predict the optimum layouts with structural performance levels equal to those of the structures considered to be ground truths. Also, when the optimal structures were obtained using the proposed method, the total calculation time was reduced by 98% as compared to conventional topology optimization once the convolutional neural network had been trained.

This paper presents the use of Fredholm–Volterra integro-differential equation approach for determining the critical buckling load and natural frequencies of periodically supported nonprismatic Eul...

Flight and ground test applications for in-flow and near-wall flow temperature sensing demand robust and accurate sensing, making thermocouple sensors attractive. Even for these extremely well-deve...

The stress-intensity factors of box beams under torsion and crack propagation under torsion or/and bending moment are discussed here. This study is motivated by a previous work [1] that derived a c...

Optimization of complex structures using standard evolutionary algorithms, like genetic algorithm (GA), is known to be computationally expensive, because a very large number of finite element analy...

Honeycomb sandwich panels are used in aerospace structures for their high stiffness-to-mass ratio. Reducing structural mass is critical in aircraft and spacecraft development due to its direct impa...

Free vibrations of thick and skew quadrilateral laminates have been analyzed by using the Ritz method and a third-order shear and normal deformable plate theory (TSNDT) that does require a shear-co...

Because of their higher aerodynamic efficiency and lighter structural weight, thin composite wings with large aspect ratios are increasingly being used for civil transport aircraft wing design. How...

The coupled equations of motion of an unrestrained flexible body when derived using multibody dynamics or mean axes formulation consist of three mass coupling integrals, namely, the first-order and...

We delineate effects of 1) face-to-core stiffness ratio (FCSR) and mass density ratio (FCDR) in square laminates and sandwich plates and 2) the fiber and transverse direction elastic modulus ratio ...

Compared to straight fiber path laminates, variable-angle tow (VAT) laminates are known to redistribute the in-plane stress resultants for improving structural buckling response. The VAT laminates ...

This paper studies weight minimization of a composite flying-wing aircraft using bioinspired arbitrarily shaped spars and ribs, known as SpaRibs, for the internal structural layout design. A genera...

This study presents a new approach for the rapid transonic flutter analysis of large-aspect-ratio wings via a combination of time-linearized two-dimensional unsteady indicial functions and a databa...

This paper presents an efficient finite element approach to study the prestressed vibration mode results of a curvilinearly stiffened composite panel subjected to various in-plane loads. The present method models the plate and the stiffener separately, which allows the stiffener element nodes to not coincide with the plate shell-element nodes. The stiffness and mass matrices of a stiffener are transformed to those of the plate through the displacement compatibility conditions at the plate–stiffener interface via finite element interpolation. Convergence and validation studies have been conducted to verify the present method in the finite element vibration analysis by using the examples from the existing literature. Prestressed vibration mode results are examined for a stiffened composite panel with arbitrarily shaped composite stiffeners in the presence of the in-plane normal and shear loads. Numerical results show the possible benefits of using curvilinear stiffeners to improve the vibration response by ...

The structural optimization of a cantilever aircraft wing with stiffeners and curvilinear spars and ribs is described. The decomposition technique for the wing structure is widely used for the optimization of a complex wing. The optimization procedure is divided into two subsystems: the global wing optimization, which determines the geometry and location of spars and ribs, and local panel optimization to further reduce wing weight. Because the design variables that are changed in the global step have an impact on those changed in the local step and vice versa, an iterative process that iterates between the global and local optimizations is employed. Particle swarm optimization and gradient-based optimization are used to perform integrated global/local optimization. Parallel computing is used, implemented using Python, to reduce the central processing unit time. The license cycle-check method and memory self-adjustment method are developed and applied in the parallel processing framework to optimize the us...

Motivated by the need for high-fidelity modeling and accurate control of future hypersonic vehicles subjected to complex aerothermomechanical loads and many other such applications, a novel scheme is proposed to accurately compute higher modes of vibration for one-dimensional structures by coupling the classic Ritz method as a predictor and the linear two-point boundary value problem solver SUPORE as a corrector. The Ritz method is used to compute a preliminary estimate of the natural frequencies for the desired modes. These estimates are then used as initial guesses by SUPORE, which employs superposition and reorthonormalization to accurately solve the governing boundary value problem. Compared to a high-fidelity Ritz approximation or a highly refined finite element modeling procedure, this is a simple, computationally less expensive, and yet highly accurate method to compute mode shapes for applications that require higher modes. This scheme is used to compute mode shapes within an absolute and relative...

We investigated the natural frequencies and mode shapes of a freely vibrating, integrally stiffened and/or stepped plate. The stiffeners used here were plate-strip stiffeners as opposed to the normally employed rib stiffeners. Both the plate and stiffeners were analyzed using the first-order shear deformation theory. The deflections and rotations were assumed as a tensor product of Timoshenko beam functions, chosen appropriately according to the given boundary conditions. Unlike Navier and Levy solution techniques, the approach used in this paper can also be applied to fully clamped, free, and cantilever supported stiffened plates. The governing differential equations were solved using the Rayleigh–Ritz method. The development of the stiffness and the mass matrices in the Ritz analysis was found to consume a huge amount of CPU time due to recursive integration of Timoshenko beam functions. An approach is suggested to greatly decrease this amount of CPU time, by replacing the recursive integration in a loo...

A finite element method based approach is developed for studying the static, vibration, and buckling behaviors of curvilinearly stiffened plates in the presence of in-plane compressive and tensile stresses. The first-order shear deformation theory is employed for both the plate and the Timoshenko beam modeling. Interpolation functions are used to build the displacement mapping between the stiffener and the plate nodes to allow the stiffener to be placed anywhere within the plate. One of the advantages of the present method is that the plate need not be remeshed while the stiffener configuration is changed; another advantage is that the results obtained by the present method with a much fewer number of elements match well with the results obtained by using a commercial finite element method software. Several numerical examples are solved to study both the static and dynamic behaviors of stiffened plates. The effects of boundary conditions, stiffener eccentricity, stiffener curvature, stiffener-plate geomet...

The feasibility of harvesting energy using polyvinylidene fluoride patches mounted on a vibrating prestressed membrane, itself attached to a tensegrity structure, was investigated. Kinematics of the tensegrity structure and the attached membrane is described and conditions for stable equilibrium for the structure are derived. Nonlinear partial differential equations describing the dynamics of the membrane attached to the tensegrity structure and under the action of a time-dependent transverse pressure are derived using the principle of virtual work. These equations are linearized and the modes of the structure are obtained using the finite element method. These modes are used as basis functions in developing a reduced-order model to obtain the response of the complete structure under the applied transverse dynamic pressure. The polyvinylidene fluoride patch on the structure is connected to an electrical load resistance. The electrical current passing through the load resistance is calculated using Gauss’s...

The integrated local Petrov–Galerkin sinc method was used with an irreversible exponential traction-separation constitutive law for modeling mode I and mixed-mode delamination of an adhesively bonded aluminum and hybrid plane-strain and plane-stress structural specimen. The first-order shear deformable theory was used to model the specimen both above and below the delamination with the sublaminate interfaces coupled to each other through the cohesive zone model. Through-the-sublaminate-thickness distributions of interlaminar stresses were obtained using integration of the equilibrium equations of three-dimensional elasticity. An adaptive discretization technique is developed and implemented. Because the sinc points, distributed by the double exponential transformation, are biased toward the boundary in the integrated local Petrov–Galerkin sinc method, the adaptive sinc point distribution allows an accurate solution to be obtained with far fewer sinc points than when a single subdomain is used. The results...

A neurofuzzy system has been proposed to detect damage in a structure with multiple damage sites. A prestressed square membrane representing a gossamer structure has been taken as the example structure. Damage at various locations on the structure has been modeled as reduced stiffness. The structure undergoes transverse vibration under the action of a transverse dynamic pressure. Using the finite element package, “ABAQUS,” the strain histories at different sensor locations in the structure under the action of the transverse dynamic pressure were calculated. The vibration response of the structure has been decomposed into a set of subsignals using wavelet analysis to define a damage feature index vector, which has been used as an indicator of damage in the membrane. The neurofuzzy system accepts the wavelet-based damage feature index vector as the input and gives the damage status of the structure as the output.

loading,increasingfromzerotothebucklingload,onthenaturalfrequenciesisstudied.Severalnumericalexamples are compared with the other results available in the literature and mesh free results, illustrating the accuracy of the present approach. This paper also shows that the in-plane load can lead to a significant change in the natural frequency and also in some cases the corresponding mode shapes of plates with curvilinear stiffeners. Numerical results are presented for a range of plate aspect ratios, bending the stiffness ratios of the stiffener to that of the plate andthearearatiosofthestiffenertothatoftheplate.Theeffectoftheseparametersonthenaturalfrequenciesofthe plate with a different number of curvilinear stiffeners under in-plane loads is studied. For studying the influence of thein-planeloadonnaturalfrequency,bothaxial/biaxialandshearin-planeloadsareconsidered.Numericalresults show that the vibration behavior of the stiffened plate in the presence of in-plane loads is influenced by different parameters, such as the plate aspect ratio, the stiffener area ratio, the stiffener stiffness ratio, and the number of stiffeners in the panel.

With the advancement s being made in manufactu ring technology, it is now possible to manufacture panels with arbitrary curvilinear stiffeners. A plate with curvilinear stiffener s can in some cases yield a desired structural response but with a lower mass . In this paper , the Element Free Galerkin (EFG) method is employed for buckling and static analysis of stiffened plates. The formulation allows the placeme nt of any number of arbitrarily curvilinear stiffeners within a plate. The First Order Shear Deformation Theory (FSDT) is used to model the behav ior of the plate and the stiffener . Moving Least Squares (MLS) approximation is used to construct the shape function s. One of the major difficulties in the implementation of some mesh free methods is the imposition of essential boundary conditions as the appro ximations do not pass through the nodal parameter values. In this research , the penalty method is used for satisfying the boundary conditions. Using a meshfree method sets free the user from providing a nodal line on the plate along every stiffener. This i s very beneficial for performing optimization studies. Several numerical examples using both straight and curvilinear stiffener s are obtained and compared with those available in the literature and those obtained using ANSYS ® . This demonstrate s the validit y of th e presented approach .

Elastic and elastic―plastic analyses of tensioned panels with an elliptical center notch are performed using the integrated local Petrov―Galerkin sinc method. The method is extended for analysis of boundary-value problems for nonlinear materials. The integrated local Petrov―Galerkin sinc method is used to obtain stress concentrations and stress intensities, using the J integral for both elastic and elastic―plastic plane-stress panels. The material is assumed to behave in a bilinear manner with kinematic hardening. The results are compared with the analytic solution for an infinite elastic panel in tension and with a finite-element solution for the panel with material nonlinearity. Good correlation is seen with stress concentration; although, the method tends to overestimate the stress concentrations. The nonlinear results compare well with the finite-element results. The accuracy deteriorates as the plastic zone propagates into areas less densely populated by the sinc points. For the elastic―plastic material, the J integral was estimated within 5 % of the finite-element result, using the integrated local Petrov―Galerkin sinc method.

Application of a stationary Gaussian random process to describe a nondeterministic forcing function of a linear vibrating system is well studied and documented. Two algorithms, Karhunen-Loeve expansion method, and collocation technique for nonstationary and non-Gaussian forcing processes (narrow- or broadband, but not white noise) for linear dynamic systems are developed here. In the Karhunen-Loeve expansion method, the forcing random process autocovariance is decomposed using the well-known Karhunen-Loeve expansion. In the Karhunen-Loeve expansion, Galerkin projection (the weighted-residual method) and collocation technique (discretized covariance matrix) are used to get the eigenvalues and the eigenfunctions/eigenvectors of the autocovariance function, numerically. The steady-state and the transient response of a single-degree-of-freedom system for an exponential autocovariance (Gaussian random process) is obtained using three methods: 1) analytical, 2) semi-analytical and 3) numerical. In the semi-analytical method, the eigenvalues and the eigenfunctions of the exponential autocovariance function are obtained analytically by solving the Fredholm integral equation of the second kind and those definitions of the eigenfunctions and the eigenvalues are used to obtain the numerical response of the single-degree-of-freedom system. In the case of the steady-state response of the single-degree-of-freedom system, the convergence of the standard deviation of the response is shown to be a function of the number of Karhunen-Loeve expansion terms used in the expansion of the autocovariance of the forcing function. The transient analysis of the same single-degree-of-freedom system is carried out using an exponentially modulated nonstationary process. Comparison of the proposed methods with respect to the analytical solutions are presented for both the stationary and the nonstationary Gaussian excitations. The steady-state responses as well as the transient responses for non-Gaussian random processes (uniform, triangular, and beta) for the same single-degree-of-freedom system are also presented.

The element-free Galerkin method, which is based on the moving-least-squares approximation, is developed for vibration analysis of unitized structures (e.g., a plate with curvilinear stiffeners). The plate and stiffeners are modeled using the first-order shear deformation theory and Timoshenko beam theory, respectively. The moving-least-squares approximation does not satisfy the delta function property. Consequently, an approximation method (e.g., the well-known penalty method) must be used for imposing essential boundary conditions. A key benefit of using element-free Galerkin for the vibration analysis of a stiffened panel is that the locations and curvatures of the stiffeners can be changed without modifying the plate nodes. Numerical results for different stiffeners, configurations, and boundary conditions are presented. All results are verified using the commercial finite-element software ANSYS. Excellent agreement is seen in all cases. A comparison of the present formulations with other available results for stiffened plates is also made. The mesh-free approach yields highly accurate results for the plates with curvilinear stiffeners.

We propose a dynamic hysteresis model developed using a modified version of the Preisach hysteresis operator to simulate the change in electrical resistance with strain in conductive polymer nanocomposites. Result of the conductivity test on a conductive polymer nanocomposite sample has been presented to show its hysteretic variation of resistance with strain. A hysteresis model developed by modifications on the hysteresis operators and the governing equation of the Preisach model and addition of a dynamic operator has been described. Eectiveness of the model in simulating the behavior of conductive polymer nanocomposites has been explained. A mode shape based identification procedure to determine the parameters associated with the model has been described. Eciency of the model has been discussed by comparison of the result obtained from the model with the experimental result.

An integrated, local Petrov-Galerkin Sinc method is introduced and applied to static structural mechanics problems. The method approximates the highest derivative in the local weak form of the governing equation on a rectangular grid, and the lower derivatives and unknown function are found by numerical indenite integration. We suggest that the essential boundary conditions may be applied by the traditional penalty method or by a method in which the stiness matrix is reduced to eliminate dependent degrees of freedom. We propose and compare the performance of three basis functions in terms of their accuracy and convergence properties for two problems: a one-dimensional tapered bar and a two-dimensional plane-stress elasticity problem. Our results indicate that the present method can provide greater accuracy than the Sinc method based on Interpolation of Highest-Derivative, an integration based collocation method suggested by Li and Wu [Li, C. and Wu, X., Numerical solution of dierential equations using Sinc method based on

We present an analytical model, derived using the principle of virtual work, for closed and open thin-walled beams subjected to torsion. Non-classical effects like primary and secondary torsional warping are taken into account. A closed-form expression for Mode II stress intensity factor for thin-walled beams with a longitudinal crack is derived. We start by finding analytical solutions based on the Vlasov’s torsional beam theory for thin-walled beams with any cross-sections. We then use the calc ulated stress of a rectangular thin-walled beam to determine an analytical expression for Mode II stress intensity factor. Finally, we add a correction factor to account for complex beha vior of long cracks. Examples are presented to illustrate the effectiveness of the cu rrent model, and it is validated by comparison with detailed finite element results obt ained using the ABAQUS TM .

Flow-induced vibrations of sensors are traditionally predicted through use of the American Society of Mechanical Engineers Boiler and Pressure Vessel Code Section III Appendix N-1300. For an Euler―Bernoulli beam, this code provides engineers with a dynamic response prediction for a given sensor―fluid environment. Engineers can use this information to estimate fatigue life of a particular probe design. However, this tool provides no estimation of shear stresses experienced by the sensor under fluid-structure interaction and can give very conservative results in some cases. Because shear stresses are significant, especially for a low aspect ratio, minimally intrusive sensors or those which vibrate with very high frequencies, shear stresses must be included in the response prediction method. This can be achieved by moving away from Euler―Bernoulli to Timoshenko beam models. Upon making this step, American Society of Mechanical Engineers guidelines must be modified to allow inclusion of shear stresses. A modification to the code is presented which includes not only shear stresses experienced by the sensor, but also the mean response. The use of elliptical sections in preference to circular sections is also explored.

Computation of interlaminar stresses from one-dimensional equivalent-single-layer beam theories using the sinc method based on interpolation of the highest derivative is performed. The method is proposed to be an efficient tool for determining through-the-thickness variations of interlaminar stresses by the equilibrium equations of three-dimensional elasticity, because the required higher-order derivatives of displacements are accurately obtained without postprocessing, an improvement over presently used finite element methods. In functionally graded material, the sinc method offers additional benefits. Because the method employs numerical indefinite integration by double-exponential transformation, through-the-thickness integration can be performed numerically without computing additional integration weights. We obtain interlaminar stresses in symmetric cross-ply laminates and functionally graded sandwich composites using the sinc method based on interpolation of the highest derivative to approximately solve the static governing equations of the Timoshenko beam theory and the Bickford beam theory. Displacements and stresses from the present approach are compared with three-dimensional finite element method results obtained with ABAQUS/Standard. Our results indicate that the interlaminar stresses throughout the majority of the length of the beam are accurately approximated with the sinc method. The present results are significantly erroneous near the boundary because of three-dimensional edge effects not captured by the one-dimensional analysis.

In this paper, we present methodology for the placement optimization of both discretely and continuously distributed fiber-optic sensors in which many point or quasi-point sensors can be multiplexed along a single optical fiber. A unified sensor performance metric is defined for vibration monitoring and fault detection as the integration/ summation of a weighted functional of some strain measure over the optical fiber length for both discretely and continuously distributed fiber-optic sensors. The optical fiber is represented by a nonuniform rational B-splines curve. The design variables include the control point coordinates of the nonuniform rational B-splines curve and the arclength coordinates of the point sensing element positions along the fiber. The constraints common to all kinds of optical sensors include the maximum fiber length and maximum allowed initial curvature. The constraints are treated as the exact penalty functions in the fitness function for any genetic algorithm. For discretely distributed fiber-optic sensors, we briefly show by an example how to use a genetic algorithm-based traveling salesman problem solver to optimally connect those optimally distributed sensors using one single optical fiber by minimizing the total fiber length. For continuously distributed fiber-optic sensors, two sets of examples are given as applications to fluttering or vibrating panels in aerospace engineering and a clinical smart bed for patient vital signal monitoring in biomedical engineering. In both cases, the integrating bend-sensing fiber-optic sensors are used.

Static analysis of sandwich panels with a square honeycomb core is performed using the finite element approach applied to the plate theories. The constitutive behavior of an equivalent continuum to the core is obtained using the strain energy approach. The displacement field of the sandwich panel modeled using the equivalent continuum is then compared with results obtained from a highly detailed finite element method created in ABAQUS. The comparison shows the results of the higher-order shear deformation theory in error of 7.6% compared with the detailed model results. An equivalent single layer finite element method for the sandwich panel was then created in ABAQUS and the displacement results of this equivalent single layer model are compared with those obtained from the detailed finite element method. This comparison reveals an error of 6.1% in the results between the two models. A comparison between the equivalent single layer model and the highly detailed model is presented for different core relative densities at two locations of the sandwich panel. A detailed finite element method analysis of the unit cell of the square honeycomb was next performed using ABAQUS and the flexibility approach. Comparison between the equivalent strain energy approach and flexibility approach applied to detailed ABAQUS models of the unit cell proved the equivalent strain energy approach to be efficient.

An experimental and computational study of adhesively bonded test configuration of the double cantilevered beams (DCB) using Cohesive Zone Models under dynamic loading is presented. Explicit methods which have a marked advantage over implicit methods for dynamic analysis have been used. The response of the DCB test specimens were modeled in LS-DYNA R . Cohesive zone model (CZM) which define the interfacial tractions to the opening displacements are used to model crack initiation and crack growth in the adhesive. Parameters for the CZM law are determined using experimental data from simple test configurations like the DCB for Mode I. The CZM law implemented through a user defined material model (UMAT) was used to model the adhesive in the adhesively bonded DCBs. Simulations for DCB with aluminum adherends correlated very well to the experiments. Good correlation between the simulation and the experiment for the composite DCB is achieved if the displacement history of the adherend tip, obtained from digital images, is used as the prescribed boundary conditions, instead of the conventional assumption of a constant velocity being imparted to the adherends tips by the falling wedge in the drop tower.

A measurement-based load updating method for finite element models subjected to static loads was studied using a four-noded curved beam element for large displacements/rotations and a gradient-based variable metric optimizer. Finite element analysis was used to numerically calculate the geometrically linear and nonlinear responses and their sensitivities under a given load. The optimizer was used to recursively update the load so that it minimized the square of the difference between the calculated and prefiltered/noise-free measured (displacement or strain) data. For the basic studies, the extracted load was represented within an element by a linear combination of integrated Legendre polynomials, the coefficients of which were taken as design variables of the least-squares problem. Through a model order analysis, the benefits for solving load updating problems using the relative deformation measurement, the polynomials of lower orders, the elements of larger sizes (because of using the high precision four-noded beam element), and the denser measured points were studied for linear responses under different types of applied loads. It was confirmed that using the reduced number of unknown variables to obtain an overdetermined inverse problem helps get unique and stable extracted loads. Though this conclusion was verified mainly through illustrative examples for a cantilever beam, it was generally applicable to other load updating or inverse problems. Further examples were given for a three-dimensional portal frame load updating, extracting highly oscillating loads, and a strain-based cantilever beam load updating. The final examples were load updating for geometrically nonlinear finite element models under self-weight, snow, and/or pressure loads.

For shape control of smart structures, we have developed a series of micro-genetic-algorithms for optimal placement of a large number of piezoelectric actuators. Here, we investigate the effect on the solution quality of 1) different random seed generators; 2) restart criteria in micro-genetic-algorithms, specifically the two parameters, the number of generations used for the inner loop and the level of diversity in the population; and 3) different numbers of actuators. We also report a comparison of our genetic algorithms with two heuristic integer programming algorithms: worst-out-best-in and exhaustive single point substitution proposed by Haftka and Adelman ("Selection of Actuator Locations for Static Shape Control of Large Space Structures by Heuristic Integer Programming," Computers and Structures, Vol. 20, 1985, pp. 572-582). Using current genetic algorithms, we not only get better layouts of actuators than reported in our previous publications, but we also find that the most distinct nature of genetic algorithms is randomness and robustness. The best parameter setting of genetic algorithms is dependent on both the number of evaluations used for termination and the seed generator used. Moreover, the best parameter setting of genetic algorithms varies as the number of actuators changes. To get the highest quality of solutions, multiple runs using different random seed generators are necessary. The time of investigation can be significantly reduced using a coarse grain parallel computing. Comparison of our genetic algorithms with the worst-out-best-in and exhaustive single point substitution shows that for a group of runs our genetic algorithms usually converge faster in the first few thousand evaluations and are more likely to find better solutions than the worst-out-best-in and exhaustive single point substitution algorithms.

The dynamic response of flexible membrane structures to blast loads is described, with application toward shelter systems. Shelters such as the Tent Extendable Modular Personnel tents fall into the category of highly flexible membrane structures due to their large deformation behavior. Material testing was conducted to determine the material properties of the liner and the canvas material. A finite element model for the shelter structure was developed, and the dynamic response to blast loading conditions was obtained. Transient analysis was performed based on an implicit approach in which the time integration was done using the Newmark method, and the Newton-Raphson method was used for the nonlinear analysis. Dynamic responses consisting of displacement time histories and dynamic stresses were computed for the membrane model. A parametric study was performed, and design recommendations are presented.

A method for reducing the differences between experimental testing or real-world events and their finite element counterparts is presented. In this method system identification or finite element model updating are not performed; instead, the loads on the finite element model that would create equivaient displacements or strains are identified by various means, thus saving a large amount of computational effort. This method of finding an applied load is also extremely useful in the analysis of testing data for vehicles and other structures. Using methods based on classical least-squares methods, we present the basis for finite element load updating and sample application through the use of a computer program for a beam under static loads. We examine the conditioning number of the resulting system of equations and provide a least-squares solution that is more robust through the use of singular value decomposition. This allows an easier analysis of structural models, for example, of a prototype vehicle, by determining the loads that the prototype is subjected to in testing. These loads can then be used on other models of that vehicle during the design process to decrease the time spent in testing while increasing design's reliability by reducing uncertainties in the applied load.

Three models were developed to predict randomness in the free vibration response of unsymmetrically laminated beams: exact Monte Carlo simulation, sensitivity-based Monte Carlo simulation, and probabilistic finite element analysis (FEA). 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-degree-of-freedom beam element, based on the first-order shear deformation beam theory, is adapted for use in studying the probabilistic nature of the natural frequencies. With the use of variational principles, the element stiffness matrix and mass matrix are obtained through analytical integration. With the use of a random sequence, a large data set following normal distribution is generated, containing possible random ply orientations. The sensitivity derivatives are numerically calculated through an exact analytical formulation. The eigenvalues are expressed in terms of deterministic and probabilistic quantities, which allows the determination of how sensitive they are to variations in ply angles. The predicted mean value and coefficient of variation of the natural frequencies for sensitivity-based Monte Carlo simulation and probabilistic FEA are in good agreement with the exact Monte Carlo simulation. Results show that variations of ±5 deg in ply angles have little effect on the lower mode natural frequencies of unsymmetrically and symmetrically laminated beams.

condensation.7 That is because Guyan’s static condensation does not contain the effects of mass from added members in the modiŽ ed structure, whereas these effects are considered in the proposed method.FromEqs. (10) and (16–18), it canbe seen that littlecomputational effort is added in the proposedmethod. From the results, it can be also seen that the proposedmethod can also give high-quality accuracy for the large topologicalmodiŽ cations.

By use of equivalent plate modeling, an efficient 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 includes transverse shear effects by treating the wing as a plate, following the first-order shear deformation theory. The equations of motion are derived using the Ritz method with Legendre polynomials as trial functions. To model arbitrary wing planforms, the wing is composed of two plates, connected by distributed translatory and rotary springs of very high stiffness. The structural model has been validated for a set of examples by comparing the results with the ones obtained from MSC/NASTRAN. A distributed actuation scheme allows the modification of wing twist and camber for maneuver control of the vehicle. The model has been applied to study the roll performance of a flapless smart wing with morphing airfoils

This study concerns the direct measuring technique for skin-friction determination. Such a device measures the force on a small, movable surface element as a shear e ow passes over the surface. The typical direct-measuring skin-friction gauge uses a viscous liquid in the gap between the movable surface piece and the casing to dampen vibrations,tocreateanevensurface,tominimizetheeffectsofpressuregradients,andfortemperaturestabilization. In testing, the liquid slowly leaks out. Therefore, we have considered gauges with rubber to e ll all or some of the gap. This led to the development of a gauge with a thin rubber sheet to cover the face of the gauge instead of a previousdesign withrubbere lling theentireinternalvolume.First, ae niteelementmethodmodelwasemployed to fully understand the strain e eld involved and to e nalize the design. The resulting design consisted of a plastic skin frictiongaugewitha12.7-mm-diam e oatingelementonacantileverbeame exure,anapproximately0.51-mm-thick rubber sheet, a 1.6-mm-wide gap around the e oating element on a cantilever beam e exure, and semiconductor strain gauges at the beam base. Vibration tests were performed to determine if this design produced the required damping. These tests were successful. Supersonic wind-tunnel tests at Mach 2.4 with a total pressure of 3 atm and ambient total temperature demonstrated that the rubber sheet survived repeated tests and provided adequate damping. The skin-friction data obtained compared well with theory and other measurements.