ALBERT

Description: The following constitutes a summary of this paper: on-orbit identification methodology starts with nonparametric techniques for a priori system identification; development of the nonparametric identification and model determination experiment software has been completed; the validation experiments to be performed on the JPL Control and Identification Technology Validation Laboratory have been designed.

Description: An integrated approach to dynamic testing and mathematical model analysis is described. The overall approach addresses four key tasks, namely, pretest planning and analysis, test data acquisition, data reduction and analysis, and test/analysis correlation and mathematical model updates. Several key software programs are employed to accomplish this task. They are a leading finite element code, a sophisticated data analysis processor and a graphical pre- and post-processor along with an advanced interface utility. Several practical structures are used to illustrate tools and concepts employed in the integrated test analysis process.

Description: The paper covers two distinct parts: theory and application. The goal of this work was the reduction of model size with an increase in eigenvalue/vector accuracy. This method is ideal for the condensation of large truss- or beam-type structures. The theoretical approach involves the conversion of a continuum transfer matrix beam element into an 'Exact' dynamic stiffness element. This formulation is implemented in a finite element environment. This results in the need to solve a transcendental eigenvalue problem. Once the eigenvalue is determined the eigenvectors can be reconstructed with any desired spatial precision. No discretization limitations are imposed on the reconstruction. The results of such a combined finite element and transfer matrix formulation is a much smaller FEM eigenvalue problem. This formulation has the ability to extract higher eigenvalues as easily and as accurately as lower eigenvalues. Moreover, one can extract many more eigenvalues/vectors from the model than the number of degrees of freedom in the FEM formulation. Typically, the number of eigenvalues accurately extractable via the 'Exact' element method are at least 8 times the number of degrees of freedom. In contrast, the FEM usually extracts one accurate (within 5 percent) eigenvalue for each 3-4 degrees of freedom. The 'Exact' element results in a 20-30 improvement in the number of accurately extractable eigenvalues and eigenvectors.

Description: A solution to the correlation between structural dynamic test results and finite element analyses of the same components is presented in this paper. Basically, the method can be categorized as a Levenberg-Marquardt type Gauss-Newton method which requires only the differences between FE modal analyses and test results and their first derivatives with respect to preassigned design variables. With proper variable normalization and equation scaling, the method has been made numerically better-conditioned and the inclusion of the Levenberg-Marquardt technique overcomes any remaining difficulty encountered in inverting singular or near-singular matrices. An important feature is that each iteration requires only one function evaluation along with the associated design sensitivity analysis and so the procedure is computationally efficient.

Description: A model identification methodology for structural dynamics has been applied to simulated vibrational data as a first step in evaluating its accuracy. The evaluation has taken into account a wide variety of factors which affect the accuracy of the procedure. The effects of each of these factors were observed in both the response time histories and the estimates of the parameters of the model by comparing them with the exact values of the system. Each factor was varied independently but combinations of these have also been considered in an effort to simulate real situations. The results of the tests have shown that for the chain model, the procedure yields robust estimates of the stiffness parameters under the conditions studied whenever uniqueness is ensured. When inaccuracies occur in the results, they are intimately related to non-uniqueness conditions inherent in the inverse problem and not to shortcomings in the methodology.

Description: An elastic-plastic finite-element analysis with a critical crack-tip-opening displacement criterion was used to simulate fracture of various size compact and bend specimens made of HY-130 steel. From the calculated load-crack-extension and load-displacement curves, J-resistance (J-R) curves were determined by several methods. The simulated 3-R curves were insensitive to specimen size up to maximum load but were sensitive to specimen configuration for crack extensions greater than 10 percent of the initial uncracked ligament length.

Description: Identification of large space structures' distributed mass, stiffness, and energy dissipation characteristics poses formidable analytical, numerical, and implementation difficulties. Development of reliable on-orbit structural identification methods is important for implementing active vibration suppression concepts which are under widespread study in the large space structures community. Near the heart of the identification problem lies the necessity of making a large number of spatially distributed measurements of the structure's vibratory response and the associated force/moment inputs with sufficient spatial and frequency resolution. In the present paper, we discuss a method whereby tens of active or passive (retro-reflecting) targets on the structure are tracked simultaneously by the focal planes of two or more video cameras mounted on an adjacent platform. Triangulation (optical ray intersection) of the conjugate image centroids yield inertial trajectories of each target on the structure. Given the triangulated motion of the targets, we apply and extend methodology developed by Creamer, Junkins, and Juang to identify the frequencies, mode shapes, and updated estimates for the mass/stiffness/damping parameterization of the structure. The methodology is semi-automated, for example, the post experiment analysis of the video imagery to determine the inertial trajectories of the targets typically requires less than thirty minutes of real time. Using methodology discussed herein, the frequency response of a large number of points on the structure (where reflective targets are mounted) on the structure can be determined from optical measurements alone. For comparison purposes, we also utilize measurements from accelerometers and a calibrated impulse hammer. While our experimental work remains in a research stage of development, we have successfully tracked and stereo triangulated 20 targets (on a vibrating cantilevered grid structure) at a sample frequency of 200 HZ, and have established conclusively the feasibility and desirability of this approach. We discuss, in summary, recent advances in analog and digital video processing methodology, actuation methods, and bring them to bear on the structural identification problem. We include a brief discussion of our experimental hardware and some recent experimental results which support the practical feasibility of this structural vibration sensing approach.

Description: Limitations of the frequency domain methods in analyzing structura1 vibrations has created an awareness of the comparative merits of the time domain methods. Although time domain methods would be ideal for modeling large precisions space systems, the popular methods based on fitting theoretical response to actual data by least squares are too sensitive to noise and require too much data to be suitable for orbiting space crafts. This paper briefly reviews the theory and illustrative applications of a time domain methodology called Data Dependent Systems (DDS) that eliminates these limitations. Simulation results are presented to demonstrate a better than 4-place accuracy in the identifications of all system parameters, both modal (frequencies, damping ratios, and mode shapes) and physical (mass, stiffness, and damping matrices).

Description: The objective of the 12-meter truss modal test is to experimentally determine the frequencies, damping, and mode shapes for the first 6 modes in both principle axes and to use this information to update the FEM. These objectives will lead us to our goal of actively controlling the flexible modes of the truss. A secondary objective is to evaluate our capabilities to ground test this class of structures.

Description: The objectives of this program are as follows: modelling of guided waves in fiber-reinforced plates in terms of different modes; and analysis of scattering by transverse cracks using modal representation. A hybrid numerical method combining the finite element representation of a region around the crack with the modal representation in the exterior region will be used in this program. Modes will be obtained using the through-the-thickness discretization of the displacement field.

Description: This paper considers complex transcendental eigenvalue problems where one is interested in pairs of eigenvalues that are restricted to take real values only. Such eigenvalue problems arise in dynamic stability analysis of nonconservative physical systems, i.e., flutter analysis of aeroelastic systems. Some available solution methods are discussed and a new method is presented. Two computational approaches are described for analytical evaluation of the sensitivities of these eigenvalues when they are dependent on other parameters. The algorithms presented are illustrated through examples.

Description: The paper presents the descriptions of recently developed numerical algorithms that prove to be useful for the solution of the free vibration problem of spinning structures. First, a generalized procedure for the computation of nodal centrifugal forces in a finite element owing to any specified spin rate is derived in detail. This is followed by a description of an improved eigenproblem solution procedure that proves to be economical for the free vibration analysis of spinning structures. Numerical results are also presented which indicate the efficacy of the currently developed procedures.

Description: The analysis of empirical modal models of structural components using techniques based on the modal assurance criterion (MAC) defined by Ewins (1984) is discussed and demonstrated for the case of the Space Shuttle Orbiter aft bulkhead. Modal models of the bulkhead are constructed before and after environmental acoustic tests equivalent to 30 or 100 missions and compared (by computing their MACs) to detect significant structural changes; subdivision of the modal vector followed by computation of the MAC for each part is used to localize the changes. Numerical data demonstrating the usefulness of the MAC approach are presented in tables and diagrams.

Description: An assessment is made of the potential of different global-local analysis strategies for predicting the nonlinear and postbuckling responses of structures. Two postbuckling problems of composite panels are used as benchmarks and the application of different global-local methodologies to these benchmarks is outlined. The key elements of each of the global-local strategies are discussed and future research areas needed to realize the full potential of global-local methodologies are identified.

Description: Formal approaches are summarized to evaluate design concepts and perform sensitivity analyses on design parameters of composite structural components for vehicles. The formal approaches include structural analyses coupled with composite micromechanics to assess the structural response of beams made from various intraply hybrids, finite element analysis in conjunction with composite mechanics to assess the structural response of panels made from strip hybrids, and sensitivity analysis through optimization to assess the effects of various design parameters on the optimum design of a panel made from angleplied composite laminates. Results obtained from these approaches are presented in graphical and tabular form to illustrate parametric studies and acceptable ranges of various design parameters.

Description: Vibration absorbers are introduced into an asymmetric configuration of thin cylinders and tori enclosing an acoustic medium. The absorbers consist of thin axial strips bonded to the cylinder with a thin viscoelastic layer. The constrained layer dissipates the energy of relative motions between strip and cylinder. The absorber is most effective on response modes with two or more circumferential waves. The use of transfer matrices is extended to the coupled cylinder-absorber system.

Description: An arbitrarily laminated, anisotropic cylindrical shell of finite length, under uniform internal pressure, is analyzed using Love-Timoshenko's kinematic relations and under the framework of classical lamination theory. The previously obtained solutions for asymmetrically laminated orthotropic (cross-ply) as well as unbalanced-symmetric and balanced-unsymmetric (angle-ply) cylindrical shells under the same loading conditions have been shown to be special cases of the present closed-form solution. Numerical results have been presented for a two-layer cylindrical shell and compared with those obtained using finite element solutions based on the layerwise constant shear-angle theory. These are expected to serve as benchmark solutions for future comparisons and to facilitate the use of unsymmetric lamination in design.

Description: The stress-intensity factors are determined for a cracked orthotropic sheet adhesively bonded to an orthotropic stringer where the adhesive layer is modeled with a nonlinear stress-strain curve. By the use of Green's functions and the complex variable theory of orthotropic elasticity, a set of integral equations is obtained. The integral equations are replaced by an equivalent set of algebraic equations, which are solved to obtain the shear stress distribution in the adhesive layer, with which the crack-tip stress-intensity factors are found. When the adhesive was modeled with a nonlinear stress-strain curve, the peak shear stresses in the adhesive were considerably reduced in comparison to the solution for the linear elastic adhesive. This resulted in increases in the stress-intensity factors for the nonlinear adhesive solution compared to the linear adhesive solution. The nonlinear adhesive has no significant effect on the stress-intensity factor unless the near crack tip is beneath the stringer. It is assumed that the adhesive bond remains intact and it is predicted that onset of adhesive failure occurs at decreasing levels of applied stress as the crack propagates beneath the stringer.

Description: Unified constitutive material models were developed for structural analyses of aircraft gas turbine engine hot section components with particular application to an isotropic material used for combustor liners. Differential forms of models independently developed were considered in this study. These models combine the interactions of time-dependent (creep) and time-independent (plasticity) inelastic behavior of a material. Predicted stress-strain responses from these models were evaluated against cyclic isothermal and nonisothermal test results for uniaxial specimens of a nickel-base superalloy. The unified models were implemented in a nonlinear structural analysis code. Two unique NASA Lewis test facilities were used in the evaluation of the models for complex geometry specimens and evaluation of advanced temperature and high-temperature strain measurement instrumentation. Predicted nonlinear structural responses from one of the models for a flat plate and a segment of a conventional combustor liner are presented.

Description: This paper outlines a technique for preliminary sizing of the adherends for cracked-lap-shear specimen to assure delamination instead of adherend failure. The cracked-lap-shear specimen is a popular specimen used for determination of mixed mode interlaminar fracture toughness of composites. Thin adherends, on the order of three plies thick, have been used successfully in the past for determination of fracture toughness of rather brittle matrix systems. However, the tougher matrices now being considered for composite applications require thicker adherends in order to get composite delamination rather than adherend failure. The optimum thickness is obtained on the basis that the critical value of the strain energy release rate is reached at the delamination front before the ultimate strength is reached in the adherend. By proper design the specimen would delaminate and not use excessive material or load. A simple analysis for the optimum adherend thickness and experimental verification are included.

Description: Future space structures will have a low mass density and high flexibility, with ground test dynamic behavior differing significantly from that in zero-G orbit. Attention is presently given to the vibration behavior of a beam deformed by its own weight; the results obtained by the differential equations for both the static and dynamic responses of a large, simply supported beam, which are derived and solved analytically, allow ground test experiment measurements to be used for orbital dynamic characteristics verification efforts.

Description: In this paper the authors summarize the activities at the Jet Propulsion Laboratory (JPL) in modifying the structural mathematical model to correlate with its modal test results. In addition to the results from the Viking and Galileo spacecrafts, developments in the parameter estimation of structural mathematical models of large flexible structures using Multiple Boundary Condition Tests (MBCT) are presented.

Description: Adaptive p-version based hierarchical finite element formulations in conjunction with a posteriori error estimation concepts are described with emphasis on applicability for thermal modeling/analysis of structural configurations. The basic concepts and formulations of hierarchical p-versiion finite element for thermal analysis are first described. A posteriori error estimation features are utililzed to steer the process of adaptive refinement. Several configurations comprised of one-dimensional structures are evaluated to validate the applicability of the proposed formulations and to demonstrate the potential of the p-version adaptive formulations for thermal modeling/analysis. The methodology offers potential and promises to be an attractive alternative to conventional finite element thermal modeling/analysis approaches.

Description: Different elementary clamping models are discussed for a three layer crossply laminate to study the sensitivity of clamping to the definition of cross-sectional rotation. All of these models leave a considerable residual warping at the edges. Using a complimentary energy principle and principle of superposition, an analysis is conducted to reduce this residual warping. This led to the identification of exact interior solution corresponding to the ideal clamping. This study also suggests a presence of stress singularities at the corners and between different layers near the fixed edge.

Description: The isothermal and thermomechanical fatigue (TMF) crack initiation response of a hypothetical material was analyzed. Expected thermomechanical behavior was evaluated numerically based on simple, isothermal, cyclic stress-strain-time characteristics and on strainrange versus cyclic life relations that have been assigned to the material. The attempt was made to establish basic minimum requirements for the development of a physically accurate TMF life-prediction model. A worthy method must be able to deal with the simplest of conditions: that is, those for which thermal cycling, per se, introduces no damage mechanisms other than those found in isothermal behavior. Under these assumed conditions, the TMF life should be obtained uniquely from known isothermal behavior. The ramifications of making more complex assumptions will be dealt with in future studies. Although analyses are only in their early stages, considerable insight has been gained in understanding the characteristics of several existing high-temperature life-prediction methods. The present work indicates that the most viable damage parameter is based on the inelastic strainrange.

Description: Crack extension in elastic-plastic material involves energy dissipation through the creation of new crack surfaces and additional yielding around the crack front. An analytical procedure, using a two-dimensional elastic-plastic finite element method, was developed to calculate the energy dissipation components during a quasi-static crack extension. The fracture of an isotropic compact specimen was numerically simulated using the critical crack-tip-opening-displacement (CTOD) growth criterion. Two specimen sizes were analyzed for three values of critical CTOD. Results from the analysis showed that the total energy dissipation rate consisted of three components: the crack separation energy rate, the plastic energy dissipation rate, and the residual strain energy rate. All three energy dissipation components and the total energy dissipation rate initially increased with crack extension and finally reached constant values.

Description: The use of the compromise decision support problem in hierarchical design of structural systems is described. The mathematical template that supports the underlying precepts of hierarchical design in the context of the decision support problem technique is presented. A structural example that demonstrates the efficacy of the approach is included.

Description: A study was conducted to investigate the stress ratio effect on cyclic debond growth behavior in adhesively bonded composite joints. The system studied consisted of graphite/epoxy adherends bonded with a toughened epoxy adhesive. This study showed that the strain energy release rate range was the driving factor for cyclic debonding of the tested bonded system when subjected to cyclic loads with different stress ratios for both mode I and mixed mode I-II loadings.

Description: A simple matrix expression is obtained for the strain components of a beam in which the magnitudes of neither beam displacements nor rotations are explicitly restricted. The only kinematical restrictions are that: (1) strains are small compared to unity and (2) components of local rotation, a newly identified kinematical quantity, are of the order of the strains to a fractional power equal to at least one half. Local rotations are defined as the change of orientation of material elements off the beam reference axis relative to those on the beam reference axis. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of both open- and closed-section beams in applications of the theory. The resulting strain components are expressed in a local Cartesian coordinate system and can be calculated directly in that way. Thus, one can use a curvilinear coordinate system that is natural to the beam problem without the complications that usually surround such an approach. Examples show the simplicity and the generality of the present approach as well as why previously published results differ among themselves concerning tension-torsion coupling.

Description: Two computational techniques are developed analytically to generate global approximation vectors for use in the nonlinear large-deflection analysis of symmetric structures with asymmetric boundary conditions. One method is based on linear combinations of FEM-generated symmetric and antisymmetric vector components, while the other employs a preconditioned-conjugate-gradient technique. The derivation of the procedures is explained in detail, and their effectiveness is evaluated in sample computations for an elliptic toroid and a cylindrical panel; the results are presented in tables and graphs and characterized.

Description: The wave propagation in a circular plate after impact by a cylindrical projectile is studied. In the vicinity of impact, the pressure is computed numerically. An intense pressure pulse is generated that peaks 0.2 microns after impact, then drops sharply to a plateau. The response of the plate is determined adopting a modal solution of Mindlin's equations. Velocity and acceleration histories display both propagating and dispersive features.

Description: A unified set of composite micromechanics equations is summarized and described. This unified set is for predicting the ply microstresses when the ply stresses are known. The set consists of equations of simple form for predicting three-dimensional stresses (six each) in the matrix, fiber, and interface. Several numerical examples are included to illustrate use and computational effectiveness of the equations in this unified set. Numerical results from these examples are discussed with respect to their significance on microcrack formation and, therefore, damage initiation in fiber composites.

Description: The acoustic damping for single modes of a finite rectangular panel, simply supported in an infinite baffle, is theoretically determined from the ratio of the acoustic energy radiated per cycle to the vibratory energy of the panel. Asymptotic solutions for the low-frequency region are presented for a panel mode driven at an arbitrary frequency and for a panel mode vibrating at its natural frequency. Curves of acoustic damping for a panel mode vibrating at resonance, as a function of the panel thickness-to-length ratio, are presented for various panel aspect ratios. For panels vibrating below the critical frequency, the damping depends on the aspect ratio with square panels developing the smallest value. For panels vibrating above the critical frequency, the damping is nearly independent of the aspect ratio.

Description: The delamination resistance of graphite-reinforced PEEK composites was quantified by conducting static and cyclic edge delamination tests on (35n/-35n/0n/90n)s AS4/PEEK laminates, where n = 1, 2. The experimentally determined mechanical delamination onset strains were used to calculate the critical strain-energy release rate for delamination onset as a function of fatigue cycle. The delamination onset strains decreased dramatically with fatigue cycles and then began to level off to an endurance limit at 1 million cycles. Although the static interlaminar fracture toughness of the AS4/PEEK composite is much greater than the toughness of graphite epoxy composites, the delamination fatigue threshold, calculated from the cyclic strain endurance limit at 1 million cycles, was only slightly greater than the threshold for graphite epoxy composites. The contribution of residual thermal stresses to delamination in the AS4/PEEK is substantial due to the large temperature range between the manufacture and the room temperatures.

Description: A model is described for estimating the impact damage of fiber reinforced composite plates. The displacements and stresses are calculated by a three dimensional transient, finite element method of solution of the governing equations applicable to a linearly elastic body. The region in which damage occurs is estimated using the Tsai-Wu failure criterion. A computer code was developed which can be used to calculate the impact force, displacements and velocities of the plate and the impact body, stresses and strains in the plate, and the damage area. Sample numerical results are presented illustrating the type of information provided by the code. Comparisons between measured and calculated damage areas are also given.

Description: The development status and applicational range of techniques in computational structural mechanics (CSM) are evaluated with a view to advances in computational models for material behavior, discrete-element technology, quality assessment, the control of numerical simulations of structural response, hybrid analysis techniques, techniques for large-scale optimization, and the impact of new computing systems on CSM. Primary pacers of CSM development encompass prediction and analysis of novel materials for structural components, computational strategies for large-scale structural calculations, and the assessment of response prediction reliability together with its adaptive improvement.

Description: The dynamic behavior of a spinning linear-elastic paraboloid subject to nonaxisymmetric deformation is investigated analytically, applying the Rayleigh-Ritz procedure described by Utku et al. (1983). Energy-density, strain-displacement, and velocity-displacement expressions are generated; expressions for the generalized strain and position vector are derived; and the discretized dynamic equations are obtained. Numerical results obtained with a computer-program implementation of the method are presented in extensive tables and graphs. The effects of spin rate and bending rigidity and results for the special case of a spinning disk are included.

Description: This report examines tuning a finite element model using vector optimization techniques. Structural models using finite element theory often need to be adjusted so they can accurately simulate the real structure. The goal is to tune the model such that it will reproduce data derived from structural tests. First, the performance indices are extremized using multiple objective optimization theory, producing a set of possible solutions. Next, the solutions are rank ordered according to a decision maker's preferences to select the best answer. The tuning process was applied to a T-38 horizontal stabilizer. Numerous weighted solutions contained a best static deformation model, a best frequency model and three intermediate combinations of these two models. This automated procedure proved to be a versatile method capable of producing solutions for many types of tuning problems.

Description: A method which has evolved in the laboratories for the past 20 yr is re-examined with the intent of improving its accuracy and simplicity of application to engineering problems. Several modifications are introduced both to the analytical formulation of the Damage Curve Approach, and to the procedure for modifying this approach to achieve a Double Linear Damage Rule formulation which immensely simplifies the calculation. Improvements are also introduced in the treatment of mean stress for determining fatigue life of the individual events that enter into a complex loading history. While the procedure is completely consistent with the results of numerous two level tests that have been conducted on many materials, it is still necessary to verify applicability to complex loading histories. Caution is expressed that certain phenomenon can also influence the applicability - for example, unusual deformation and fracture modes inherent in complex loading especially if stresses are multiaxial. Residual stresses at crack tips, and metallurgical factors are also important in creating departures from the cumulative damage theories; examples of departures are provided.

Description: The static stiffnesses for torsional and flexural deformation of a tapered beam under axial loading are determined analytically, extending the Bernoulli-Euler/Bessel-function approach of Banerjee and Williams (1985). The derivation of the expressions is explained in detail, and numerical results for sample problems are presented in tables and shown to be in excellent agreement with those obtained using stepped beams of 400 or 500 elements.

Description: The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.

Description: An analysis is presented of the shear buckling load of an arbitrary simply-supported prismatic plate assembly or stiffened panel configuration. The method utilizes stiffness matrices developed by Wittrick (1968). For the restraint of simple support along edges perpendicular to the longitudinal direction, various wavelengths of response are combined using an energy method that involves only a boundary integral. Numerical results for plate and panel configurations show the accuracy and convergence of the method.

Description: A study was undertaken to characterize the debond growth mechanism of adhesively bonded composite joints under mode I, mixed mode I-II, and mode II static loadings. The bonded system consisted of graphite/epoxy (T300/5208) composite adherends bonded with a toughened epoxy (EC 3445) adhesive. The mode I, mode II and mixed-mode I-II fracture energies of the tested adhesive were found to be equal to each other. Furthermore, the criterion for mixed mode fracture in composite bonded joints was determined.

Description: Elastic displacements and stress intensity measurements for a mode II specimen have been obtained over a range of a/W values between 0.500 and 0.900 using the MARC general purpose finite element program. Stress intensity factors were experimentally determined using load point displacement values. Good general agreement between numerical and experimental results for crack mouth, crack surface, and load point displacements, and for stress intensity factors, demonstrates the accuracy of the present method.

Description: It has been observed that the residual stresses and dislocations during the silicon crystal growth for photovoltaic applications are caused by thermal stresses. The temperatures along the boundaries of the silicon crystal ribbon are prescribed to meet the requirements of the crystal growth. It is shown that by allowing the temperatures to satisfy a second-order partial differential equation in the ribbon, all thermal stresses, and others induced by them, may be eliminated for the stress-free growth of the silicon crystal.

Description: An improved plate theory that accounts for the transverse shear deformation is presented, and mixed and displacement finite element models of the theory are developed. The theory is based on an assumed displacement field in which the inplane displacements are expanded in terms of the thickness coordinate up to the cubic term and the transverse deflection is assumed to be independent of the thickness coordinate. The governing equations of motion for the theory are derived from the Hamilton's principle. The theory eliminates the need for shear correction factors because the transverse shear stresses are represented parabolically. A mixed finite element model that uses independent approximations of the displacements and moments, and a displacement model that uses only displacements as degrees of freedom are developed. A comparison of the numerical results for bending with the exact solutions of the new theory and the three-dimensional elasticity theory shows that the present theory (and hence the finite element models) is more accurate than other plate-theories of the same order.

Description: Computational finite-element and boundary-element methods are reviewed, and their application to the mechanics of solids is discussed. Stability conditions for general FEMs are considered in addition to the use of least-order, stable, invariant, or hybrid/mixed isoparametric elements as alternatives to the displacement-based isoparametric elements. The use of symbolic manipulation, adaptive mesh refinement, transient dynamic response, and boundary-element methods for linear elaslticity and finite-strain problems of inelastic materials are also discussed.

Description: In this expository paper a first-order shear deformation laminate theory that accounts for the von Karman strains is described and its finite element model is developed. The element also accounts for Hill's elastic-perfectly plastic material model. Sample applications of the present element to linear and nonlinear bending of laminated plates and shells are presented. Numerical results showing the effects of boundary conditions, lamination scheme, and loading on the deflections and stresses are also presented. It is found that the effect of shear deformation and boundary conditions on deflections are significant.

Description: A variational approach is used to model the moisture content and distribution profiles which cause swelling in polymers and composites which are used as aircraft structural components. The moisture intrusion stems from humidity, which makes the problem one of diffusion of mass from the environment into a semiinfinite plate with a given diffusion coefficient and thickness. Lagrangian, ordinary differential equations are defined for the mass diffusion, including driving force, mass potential and volume dissipation expressions. Account is taken of the effects of stress on diffusivity, including the dilatational stress caused by inhomogeneous swelling of the material. It is noted that material near the top and bottom of a part undergoes the most swelling, and the evolution of moisture diffusion in the materials is traced. Finally, experimental data are used to define differential equations for predicting the final moisture distribution within the material.

Description: Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

Description: A list of books, reports, periodicals, and conference proceedings, as well as individual papers, centered on specific aspects of fracture phenomenon has been compiled by the ASTM Committee E-24 on Fracture Testing. A list of basic references includes the articles on the development of fracture toughness, evaluation of stress intensity factors, fatigue crack growth, fracture testing, fracture of brittle materials, and fractography. Special attention is given to the references on application of fracture mechanics to new designs and on reevaluation of failed designs, many of them concerned with naval and aircraft structures.

Description: A model is presented which can be used to determine the appropriate values of the process variables for filament winding a cylinder. The model provides the cylinder temperature, viscosity, degree of cure, fiber position and fiber tension as functions of position and time during the filament winding and subsequent cure, and the residual stresses and strains within the cylinder during and after the cure. A computer code was developed to obtain quantitative results. Sample results are given which illustrate the information that can be generated with this code.

Description: The effects of pretwist, precone, setting angle and Coriolis forces on the vibration and buckling behavior of rotating, torsionally rigid, cantilevered beams were studied. The beam is considered to be clamped on the axis of rotation in one case, and off the axis of rotation in the other. Two methods are employed for the solution of the vibration problem: (1) one based upon a finite-difference approach using second order central differences for solution of the equations of motion, and (2) based upon the minimum of the total potential energy functional with a Ritz type of solution procedure making use of complex forms of shape functions for the dependent variables. The individual and collective effects of pretwist, precone, setting angle, thickness ratio and Coriolis forces on the natural frequencies and the buckling boundaries are presented. It is shown that the inclusion of Coriolis effects is necessary for blades of moderate to large thickness ratios while these effects are not so important for small thickness ratio blades. The possibility of buckling due to centrifugal softening terms for large values of precone and rotation is shown.

Description: A standard stiffness matrix procedure which permits any combination of rigid, elastic, pinned or sliding connections of the degrees of freedom at the ends of a member to the nodes of its parent structure is described, in order to show how easily it can be extended to allow an existing algorithm to be used to ensure that no eigenvalues of the parent structure can be missed even when 'exact' member theory is used. The eigenvalues are the natural frequencies of undamped free vibration analyses or the critical load factors of buckling problems. The method preserves the exactness of the member theory and an efficient method for computer application is indicated. The theory also permits any combination of rigid, elastic, pinned or sliding connections between the freedoms of a substructure and those of its parent structure.

Description: A simple rectangular finite element was developed for two-dimensional analysis of laminated composite materials. The rectangular laminated composite element eliminates the need to add elements to a model simply to account for the material properties of various laminae. This is particularly advantageous for thick laminates with many lamina. Explicit integration in terms of generalized displacements minimizes the algebraic effort required to derive the element stiffness and the thermal load vector. A substitute shape function technique is used to improve the performance of the element in modeling bending type deformation. Results for several example problems are discussed.

Description: This paper is concerned with the development of an efficient eigenproblem solution algorithm and an associated computer program for the economical solution of the free vibration problem of complex practical spinning structural systems. Thus, a detailed description of a newly developed block Lanczos procedure is presented in this paper that employs only real numbers in all relevant computations and also fully exploits sparsity of associated matrices. The procedure is capable of computing multiple roots and proves to be most efficient compared to other existing similar techniques.

Description: A new unified computational approach for applicability to nonlinear/linear thermal-structural problems is presented. Basic concepts of the approach including applicability to nonlinear and linear thermal structural mechanics are first described via general formulations. Therein, the approach is demonstrated for thermal stress and thermal-structural dynamic applications. The proposed transfinite element approach focuses on providing a viable hybrid computational methodology by combining the modeling versatility of contemporary finite element schemes in conjunction with transform techniques and the classical Bubnov-Galerkin schemes. Comparative samples of numerical test cases highlight the capabilities of the proposed concepts.

Description: A three-dimensional virtual crack-closure technique is presented which calculates the strain energy release rates and the stress intensity factors using only nodal forces and displacements from a standard finite element analysis. The technique is an extension of the Rybicki-Kanninen (1977) method, and it assumes that any continuous function can be approximated by a finite number of straight line segments. Results obtained by the method for surface cracked plates with and without notches agree favorably with previous results.

Description: The Rayleigh-Ritz method was used to find the postbuckling static displacement pattern of a composite plane (CFRP) under uniaxial in-plane compression of uniform edge-shortening. The resonance frequencies and mode shapes at various postbuckled states are then evaluated by eigenvalue analysis of the dynamical matrix equation consisting of up-dated tangential stiffness matrix at corresponding static configuration. The theoretical results are compared with experimental results obtained in 16-layered CFRP laminate of aspect ratio 1.5. The resonance frequencies and mode shapes obtained are used to interpret the multimodal and nonlinear strain responses to high level of acoustic excitation. The dominance of second-mode contribution and softening-spring behavior are found in the strain response of postbuckled plates.

Description: A method is developed for sensitivity analysis and optimization of nodal point locations in connection with vibration reduction. A straightforward derivation of the expression for the derivative of nodal locations is given, and the role of the derivative in assessing design trends is demonstrated. An optimization process is developed which uses added lumped masses on the structure as design variables to move the node to a preselected location - for example, where low response amplitude is required or to a point which makes the mode shape nearly orthogonal to the force distribution, thereby minimizing the generalized force. The optimization formulation leads to values for added masses that adjust a nodal location while minimizing the total amount of added mass required to do so. As an example, the node of the second mode of a cantilever box beam is relocated to coincide with the centroid of a prescribed force distribution, thereby reducing the generalized force substantially without adding excessive mass. A comparison with an optimization formulation that directly minimizes the generalized force indicates that nodal placement gives essentially a minimum generalized force when the node is appropriately placed.

Description: This paper represents an attempt to apply extensions of a hybrid transfinite element computational approach for accurately predicting thermoelastic stress waves. The applicability of the present formulations for capturing the thermal stress waves induced by boundary heating for the well known Danilovskaya problems is demonstrated. A unique feature of the proposed formulations for applicability to the Danilovskaya problem of thermal stress waves in elastic solids lies in the hybrid nature of the unified formulations and the development of special purpose transfinite elements in conjunction with the classical Galerkin techniques and transformation concepts. Numerical test cases validate the applicability and superior capability to capture the thermal stress waves induced due to boundary heating.

Description: This ASTM Round Robin was conducted to evaluate the state of the art in stress analysis of adhesively bonded joint specimens. Specifically, the participants were asked to calculate the strain-energy-release rate for two different geometry cracked lap shear (CLS) specimens at four different debond lengths. The various analytical techniques consisted of 2- and 3-dimensional finite element analysis, beam theory, plate theory, and a combination of beam theory and finite element analysis. The results were examined in terms of the total strain-energy-release rate and the mode I to mode II ratio as a function of debond length for each specimen geometry. These results basically clustered into two groups: geometric linear or geometric nonlinear analysis. The geometric nonlinear analysis is required to properly analyze the CLS specimens. The 3-D finite element analysis gave indications of edge closure plus some mode III loading. Each participant described his analytical technique and results. Nine laboratories participated.

Description: The present study evaluates a higher-order modal method proposed by Leung for transient structural analysis entitled the force-derivative method. This method repeatedly integrates by parts with respect to time the convolution-integral form of the structural response to produce successively better approximations to the contribution of the higher modes which are neglected in the modal summation. Comparisons are made of the force-derivative, the mode-displacement, and the mode-acceleration methods for several numerical example problems for various times, levels of damping, and forcing functions. The example problems include a tip-loaded cantilevered beam and a simply-supported multispan beam. The force-derivative method is shown to converge to an accurate solution in fewer modes than either the mode-displacement or the mode-acceleration methods. In addition, for problems in which there are a large number of closely-spaced frequencies whose mode shapes have a negligible contribution to the response, the force derivative method is very effective in representing the effect of the important, but otherwise neglected, higher modes.

Description: Delamination growth caused by local buckling of a delaminated group of plies was investigated. Delamination growth was assumed to be governed by the strain energy release rates, G(1), G(2) and G(3). The strain energy release rates were calculated using a geometrically nonlinear three-dimensional finite element analysis. The program is described and several checks of the analysis are discussed. Based on a limited parametric study, the following conclusions were reached: (1) the problem is definitely mixed mode (in some cases G(1) is larger than G(2), for other cases the opposite is true); (2) in general, there is a large gradient in the strain energy release rates along the delamination front; (3) the locations of maximum G(1) and G(2) depend on the delamination shape and the applied strain; (4) the mode 3 component was negligible for all cases considered; and (5) the analysis predicted that parts of the delamination would overlap. The results presented did not impose contact constraints to prevent overlapping. Further work is needed to determine the effects of allowing the overlapping.

Description: The propagation of elastic waves of the type induced by impact are studied for a special class of cylinders. In this class are thin finite cylinders, for which Mindlin's equations are appropriate, on which point masses are attached. An approximation is derived valid for frequencies below cutoff of the lowest shear mode. An eigenfunction expansion is used to compute the transient response of the coupled system.

Description: The method of boundary elements is adapted to the dynamics of elastic axisymmetric solids. Three scalar potentials are used, each satisfying the Helmholtz equation and each represented by its own source distribution. The sources are distributed over a surface enclosing the solid boundary. Stress or displacement conditions on the boundary are realized by third-order derivatives of the potentials. Discrete ring elements on the source enclosure combine their influences at discrete ring elements on the solid boundary.

Description: While the standard mode acceleration formulation in structural dynamics has often been interpreted to suggest that the reason for improved convergence obtainable is that the dynamic correction factor is divided by the modal frequencies-squared, an alternative formulation is presented which clearly indicates that the only difference between mode acceleration and mode displacement data recovery is the addition of a static correction term. Attention is given to the advantages in numerical implementation associated with this alternative, as well as to an illustrative example.

Description: A key step in the application of formal automated design techniques to structures under transient loading is the calculation of sensitivities of response quantities to the design parameters. This paper considers response quantities to the design parameters. This paper considers structures with general forms of damping acted on by general transient loading and addresses issues of computational errors and computational efficiency. The equations of motion are reduced using the traditional basis of vibration modes and then integrated using a highly accurate, explicit integration technique. A critical point constraint formulation is used to place constraints on the magnitude of each response quantity as a function of time. Three different techniques for calculating sensitivities of the critical point constraints are presented. The first two are based on the straightforward application of the forward and central difference operators, respectively. The third is based on explicit differentiation of the equations of motion. Condition errors, finite difference truncation errors, and modal convergence errors for the three techniques are compared by applying them to a simple five-span-beam problem. Sensitivity results are presented for two different transient loading conditions and for both damped and undamped cases.

Description: A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.

Description: Assuming a single-mode transverse displacement, a simple formula is derived for the transverse load-displacement relationship of a plate under in-plane compression. The formula is used to derive a simple analytical expression for the nonlinear dynamic response of postbuckled plates under sinusoidal or random excitation. The highly nonlinear motion of snap-through can be easily interpreted using the single-mode formula. Experimental results are obtained with buckled and cylindrical aluminum panels using discrete frequency and broadband excitation of mechanical and acoustic forces. Some important effects of the snap-through motion on the dynamic response of the postbuckled plates are described. Static tests were used to identify the deformation shape during snap-through.

Description: An experimental investigation of composite to composite bonded joints was undertaken to study the effect of bond thickness on debond growth rate under cyclic loading and critical strain energy release rate under static loading. Double cantilever beam specimens of graphite/epoxy adherends bonded with EC 3445 were tested under mode I loading. A different behavior of fracture and fatigue strength was observed with variation of bondline thickness.

Description: The antiplane strain problem of an edge cracked elastic plate subjected to a surface displacement load is solved, and the surface line loads are obtained using conformal mapping techniques. Results are presented for the yield, stress, strain and displacement distributions, and stress intensity factors in the plate. A superposition technique and Green's functions are used to determine the strain field on the upper plate surface due to arbitrarily applied tensile stress on the lower plate surface.

Description: The sublaminate or ply-level analysis of composite structures is presently undertaken by a computational procedure yielding the stresses in regions affected by delaminations, transverse cracks, and discontinuities that are related to material properties, geometries, and loads. Attention is given to layers or groups of layers that are immediately affected by flaws; these are analyzed as if they were homogeneous bodies in equilibrium, in isolation from the rest of the laminate. Computed stresses agree with those from a three-dimensional FEM analysis.

Description: A computational method/procedure is described which can be used to simulate individual and mixed mode interlaminar fracture progression in fiber composite laminates. Different combinations of Modes 1, 2, and 3 fracture are simulated by varying the crack location through the specimen thickness and by selecting appropriate unsymmetric laminate configurations. The contribution of each fracture mode to strain energy release rate is determined by the local crack closure methods while the mixed mode is determined by global variables. The strain energy release rates are plotted versus extending crack length, where slow crack growth, stable crack growth, and rapid crack growth regions are easily identified. Graphical results are presented to illustrate the effectiveness and versatility of the computational simulation for: (1) evaluating mixed-mode interlaminar fracture, (2) for identifying respective dominant parameters, and (3) for selecting possible simple test methods.

Description: Standard means of representing finite rotation in rigid-body kinematics, including orientation angles, Euler parameters, and Rodrigues parameters, are reviewed and compared. General kinematical relations for a beam theory that treats arbitrarily large rotation are then presented. The standard methods of representing finite rotations are applied to these kinematical expressions, and comparison is made among the standard methods and additional methods found in the literature, such as quasi-coordinates and linear combinations of projection angles. The method of Rodrigues parameters is shown to stand out for both its simplicity and generality when applied to beam kinematics, a result that is really missing from the literature.

Description: A simple computational procedure is presented for reducing the size of the analysis model for a symmetric structure with asymmetric boundary conditions to that of the corresponding structure with symmetric boundary conditions. The procedure is based on approximating the asymmetric response of the structure by a linear combination of symmetric and antisymmetric global approximation vectors (or modes). The key elements of the procedure are (1) restructuring the governing finite-element equations to delineate the contributions to the symmetric and antisymmetric components of the asymmetric response, (2) successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite-element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique. The effectiveness of the computational procedure is demonstrated by means of numerical examples of linear static problems of shells, and its potential for solving nonlinear problems is discussed.

Description: Thermal, elastic, and feedback analyses are applied to the case of a beam with a distributed thermal actuator. The actuator is capable of producing a thermal gradient across the section of the beam. One candidate for such an actuator uses the Peltier effect, which appears in certain semiconductors. These devices act as heat pumps when a voltage is applied, causing a temperature gradient. It is shown that the thermal gradients can induce deflection in the beam. If the thermal gradients are applied in the proper sense to a vibrating beam, it is possible to increase the vibration damping exhibited by the structure. Experimental results are given for a cantilever beam, whose first vibrational mode damping ratio was increased from 0.81 to 7.4 percent with simple lead compensation.

Description: The feasibility of using a viscoplastic model developed by Robinson to perform a nonlinear structural analysis was investigated. The paper presents analytical solutions for three classical problems: (1) a pressurized thick-walled cylinder, (2) a thin rotating disk, and (3) a pressurized thick-walled sphere. The analytical expressions derived for the stress and the strain rates for these components are general in nature as they consider both the mechanical and thermal loadings to be time-dependent. A computer program VISTAN (VIscoplastic STructural ANalyzer) was developed to obtain the stress and strain distributions. The finite element solutions for these problems are also presented. The numerical results pertaining to isothermal loading conditions are provided. The results obtained demonstrate the feasibility of using the viscoplastic model developed by Robinson to perform nonlinear structural analyses.

Description: A new higher order theory has been proposed for the analysis of composite cylindrical shells. The formulation allows for arbitrary variation of inplane displacements. Governing equations are presented in the form of a hierarchy of sets of partial differential equations. Each set describes the shell behavior to a certain degree of approximation. The natural frequencies of simply-supported isotropic and laminated shells and stresses in a ring loaded composite shell have been determined to various orders of approximation and compared with three dimensional solutions. These numerical studies indicate the improvements achievable in estimating the natural frequencies and the interlaminar shear stresses in laminated composite cylinders.

Description: The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by conparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.

Description: Mode II and Mode I calibrations of the NASA Lewis Research Center Mode II fatigue specimen were performed experimentally over crack length to specimen width ratios (a/W) of 0.5 to 0.9. Mode II displacements were measured both at the specimen notch mouth and at the intersection of the notch with the centerline of the loading pin holes. Mode I displacements were measured across the span of the specimen at the loading pins' centerline. Analytical stress intensity factor coefficients for both Mode II and Mode I are also presented.

Description: Fatigue crack growth rate changes caused by single overloads and an overload followed by an underload have been studied in the high-strength aluminum alloy 7091. Crack-tip plasticity parameters were measured at each step in the loading sequence using the stereoimaging technique. Effective stress-intensity factor was measured with high resolution immediately at the crack tip both before an overload and during the subsequent growth rate retardation period. Crack-tip opening displacement and strain were altered in the same way as growth rate following the overload/underload events, and similitude with respect to crack-tip plasticity was preserved during the growth retardation period. Effective stress-intensity factor was found to correlate well with crack growth rate. Strains within the plastic zone were converted to stress at each step in load change. These stresses were then summed to determine the zone of residual stress caused by the overload. The region of compressive residual stress ahead of the crack tip was found to increase with overload severity but was limited to yield stress in magnitude. An underload shrank the spatial extent of the residual stresses caused by the overload.