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A systematic account is given in part I of the use of dimensional analysis in constructing similarity conditions for models and structures. The analysis covers large deflections, buckling, plastic behavior, and materials with nonlinear stress-strain characteristics, as well as the simpler structural problems. (author)
The postbuckling response and the collapse of composite specimens with a co-cured hat stringer are investigated experimentally and numerically. These specimens are designed to evaluate the postbuckling response and the effect of an embedded defect on the collapse load and the mode of failure. Tests performed using controlled conditions and detailed instrumentation demonstrate that the damage tolerance, fatigue life, and collapse loads are closely tied with the mode of the postbuckling deformation, which can be different between two nominally identical specimens. Modes that tend to open skin/stringer defects are the most damaging to the structure. However, skin/stringer bond defects can also propagate under shearing modes. In the proposed paper, the effects of initial shape imperfections on the postbuckling modes and the interaction between different postbuckling deformations and the propagation of skin/stringer bond defects under quasi-static or fatigue loads will be examined.
As a step towards developing a new design philosophy, one that moves away from the traditional empirical approach used today in design towards a science-based design technology approach, a recent test series of 5 composite shells carried out by Waters at NASA Langley Research Center is used. It is shown how the hierarchical approach to buckling load calculations proposed by Arbocz et al can be used to perform an approach often called "high fidelity analysis", where the uncertainties involved in a design are simulated by refined and accurate numerical methods. The Delft Interactive Shell DEsign COde (short, DISDECO) is employed for this hierarchical analysis to provide an accurate prediction of the critical buckling load of the given shell structure. This value is used later as a reference to establish the accuracy of the Level-3 buckling load predictions. As a final step in the hierarchical analysis approach, the critical buckling load and the estimated imperfection sensitivity of the shell are verified by conducting an analysis using a sufficiently refined finite element model with one of the current generation two-dimensional shell analysis codes with the advanced capabilities needed to represent both geometric and material nonlinearities.
As a step towards developing a new design philosophy, one that moves away from the traditional empirical approach used today in design towards a science-based design technology approach, a test series of 7 isotropic shells carried out by Aristocrat and Babcock at Caltech is used. It is shown how the hierarchical approach to buckling load calculations proposed by Arbocz et al can be used to perform an approach often called 'high fidelity analysis', where the uncertainties involved in a design are simulated by refined and accurate numerical methods. The Delft Interactive Shell DEsign COde (short, DISDECO) is employed for this hierarchical analysis to provide an accurate prediction of the critical buckling load of the given shell structure. This value is used later as a reference to establish the accuracy of the Level-3 buckling load predictions. As a final step in the hierarchical analysis approach, the critical buckling load and the estimated imperfection sensitivity of the shell are verified by conducting an analysis using a sufficiently refined finite element model with one of the current generation two-dimensional shell analysis codes with the advanced capabilities needed to represent both geometric and material nonlinearities.
Theoretical studies were conducted to determine analytically the tensile buckling of advanced propeller blades (turboprops) in centrifugal fields, as well as the effects of tensile buckling on other types of structural behavior, such as resonant frequencies and flutter. Theoretical studies were also conducted to establish the advantages of using high performance composite turboprops as compared to titanium. Results show that the vibration frequencies are not affected appreciably prior to 80 percent of the tensile speed. Some frequencies approach zero as the tensile buckling speed is approached. Composites provide a substantial advantage over titanium on a buckling speed to weight basis. Vibration modes change as the rotor speed is increased and substantial geometric coupling is present.
This report describes the preliminary results of an investigation on component reliability analysis and reliability-based design optimization of thin-walled circular composite cylinders with average diameter and average length of 15 inches. Structural reliability is based on axial buckling strength of the cylinder. Both Monte Carlo simulation and First Order Reliability Method are considered for reliability analysis with the latter incorporated into the reliability-based structural optimization problem. To improve the efficiency of reliability sensitivity analysis and design optimization solution, the buckling strength of the cylinder is estimated using a second-order response surface model. The sensitivity of the reliability index with respect to the mean and standard deviation of each random variable is calculated and compared. The reliability index is found to be extremely sensitive to the applied load and elastic modulus of the material in the fiber direction. The cylinder diameter was found to have the third highest impact on the reliability index. Also the uncertainty in the applied load, captured by examining different values for its coefficient of variation, is found to have a large influence on cylinder reliability. The optimization problem for minimum weight is solved subject to a design constraint on element reliability index. The methodology, solution procedure and optimization results are included in this report.
This special publication contains a collection of structural mechanics papers honoring Dr. James H. Starnes, Jr. presented at the 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference held in Austin, Texas, April 18-21, 2005. Contributors to this publication represent a small number of those influenced by Dr. Starnes' technical leadership, his technical prowess and diversity, and his technical breath and depth in engineering mechanics. These papers cover some of the research areas Dr. Starnes investigated, which included buckling, postbuckling, and collapse of structures; composite structural mechanics, residual strength and damage tolerance of metallic and composite structures; and aircraft structural design, certification and verification. He actively pursued technical understanding and clarity, championed technical excellence, and modeled humility and perseverance.
Buckling resistance is often a controlling criterion in the design of structures composed of plate elements. Design concepts that lead to increased buckling loads (or strains) of these plate elements can directly lower the structural cost and/or weight by a number of means. This study quantifies the improvements that can be achieved in compression buckling loads of rectangular composite plates by using a simple stiffness-tailoring concept. The approach is to position the unidirectional lamina through the thickness and over the planform of the plate so that the buckling load is increased with no loss in in-plane stiffness or increase in weight. Finite element analyses have been used to determine the effects of tailoring on the buckling loads of plates with various boundary conditions, aspect ratios, thicknesses, and membrane stiffnesses. Increases in buckling loads (or strains) of 200 percent or more compared to the uniform plate-buckling loads are shown possible with this tailoring concept.
Limitations in the validity of the continuum beam model for carbon nanotubes (NTs) and nanorods are examined. Applicability of all assumptions used in the model is restricted by the two criteria for geometric parameters that characterize the structure of NTs. The key non-dimensional parameters that control the NT buckling behavior are derived via dimensional analysis of the nanomechanical problem. A mechanical law of geometric similitude for NT buckling is extended from continuum mechanics for different molecular structures. A model applicability map, where two classes of beam-like NTs are identified, is constructed for distinct ranges of non-dimensional parameters. Expressions for the critical buckling loads and strains are tailored for two classes of NTs and compared with the data provided by the molecular dynamics simulations. copyright 2001 Elsevier Science Ltd. All rights reserved.
Combined inplane compressive and shear buckling analysis was conducted on flat rectangular sandwich panels using the Raleigh-Ritz minimum energy method with a consideration of transverse shear effect of the sandwich core. The sandwich panels were fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that slightly slender (along unidirectional compressive loading axis) rectangular sandwich panels have the most desirable stiffness-to-weight ratios for aerospace structural applications; the degradation of buckling strength of sandwich panels with rising temperature is faster in shear than in compression; and the fiber orientation of the face sheets for optimum combined-load buckling strength of sandwich panels is a strong function of both loading condition and panel aspect ratio. Under the same specific weight and panel aspect ratio, a sandwich panel with metal matrix composite face sheets has much higher buckling strength than one having monolithic face sheets.
Combined inplane compressive and shear buckling analysis was conducted on flat rectangular sandwich panels using the Raleigh-Ritz minimum energy method with a consideration of transverse shear effect of the sandwich core. The sandwich panels were fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that slightly slender (along unidirectional compressive loading axis) rectangular sandwich panels have the most desirable stiffness-to-weight ratios for aerospace structural applications; the degradation of buckling strength of sandwich panels with rising temperature is faster in shear than in compression; and the fiber orientation of the face sheets for optimum combined-load buckling strength of sandwich panels is a strong function of both loading condition and panel aspect ratio. Under the same specific weight and panel aspect ratio, a sandwich panel with metal matrix composite face sheets has much higher buckling strength than one having monolithic face sheets.
Minimum mass designs are obtained for a simple box beam structure subject to bending, torque and combined bending/torque load cases. These designs are obtained subject to point strain and linear buckling constraints. The present work differs from previous efforts in that special attention is payed to including the effects of subcomponent panel interaction in the optimal design process. Two different approaches are used to impose the buckling constraints. When the global approach is used, buckling constraints are imposed on the global structure via a linear eigenvalue analysis. This approach allows the subcomponent panels to interact in a realistic manner. The results obtained using this approach are compared to results obtained using a traditional, less expensive approach, called the local approach. When the local approach is used, in-plane loads are extracted from the global model and used to impose buckling constraints on each subcomponent panel individually. In the global cases, it is found that there can be significant interaction between skin, spar, and rib design variables. This coupling is weak or nonexistent in the local designs. It is determined that weight savings of up to 7% may be obtained by using the global approach instead of the local approach to design these structures. Several of the designs obtained using the linear buckling analysis are subjected to a geometrically nonlinear analysis. For the designs which were subjected to bending loads, the innermost rib panel begins to collapse at less than half the intended design load and in a mode different from that predicted by linear analysis. The discrepancy between the predicted linear and nonlinear responses is attributed to the effects of the nonlinear rib crushing load, and the parameter which controls this rib collapse failure mode is shown to be the rib thickness. The rib collapse failure mode may be avoided by increasing the rib thickness above the value obtained from the (linear analysis based) optimizer. It is concluded that it would be necessary to include geometric nonlinearities in the design optimization process if the true optimum in this case were to be found.
Theoretical and experimental results of the modeling and control of a flexible ribbed antenna are presented. The antenna consists of eight flexible ribs which constitutes a smart antenna in the sense that the actuator and sensors are an integral part of the structure. The antenna exhibits closely space and repeated modes, thus multi-input multi-output (MIMO) control is necessary for controllability and observability of the structure. The structure also exhibits mode localization phenomenon and contains post buckled members making an accurate finite element model of the structure difficult to obtain. An identified MIMO minimum order model of the antenna is synthesized from identified single-input single-output (SISO) transfer functions curve fit in the frequency domain. The identified model is used to design a positive position feedback (PPF) controller that increases damping in all of the modes in the targeted frequency range. Due to the accuracy of the open loop model of the antenna, the closed loop response predicted by the identified model correlates well wtih experimental results.
Buckling-critical launch-vehicle structures require structural concepts that have high bending stiffness and low mass. Fluted-core, also known as truss-core, sandwich construction is one such concept. In an effort to identify an analysis method appropriate for the preliminary design of fluted-core cylinders, the current paper presents and compares results from several analysis techniques applied to a specific composite fluted-core test article. The analysis techniques are evaluated in terms of their ease of use and for their appropriateness at certain stages throughout a design analysis cycle (DAC). Current analysis techniques that provide accurate determination of the global buckling load are not readily applicable early in the DAC, such as during preliminary design, because they are too costly to run. An analytical approach that neglects transverse-shear deformation is easily applied during preliminary design, but the lack of transverse-shear deformation results in global buckling load predictions that are significantly higher than those from more detailed analysis methods. The current state of the art is either too complex to be applied for preliminary design, or is incapable of the accuracy required to determine global buckling loads for fluted-core cylinders. Therefore, it is necessary to develop an analytical method for calculating global buckling loads of fluted-core cylinders that includes transverse-shear deformations, and that can be easily incorporated in preliminary design.
A new approach to the design of structures for improved global damage tolerance is presented. In its undamaged condition the structure is designed subject to strength, displacement and buckling constraints. In the damaged condition the only constraint is that the structure will not collapse. The collapse load calculation is formulated as a maximization problem and solved by an interior extended penalty function. The design for minimum weight subject to constraints on the undamaged structure and a specified level of the collapse load is a minimization problem which is also solved by a penalty function formulation. Thus the overall problem is of a nested or multilevel optimization. Examples are presented to demonstrate the difference between the present and more traditional approaches.
The new construction method indicated, which makes possible a considerably better material utilization and hence a saving in weight, has been tested in a number of Focke-Wulf types also in series production and has fully justified itself.
The external shell of the Project Viking capsule, which will provide atmospheric deceleration for the 1976 landing of an unmanned spacecraft on the surface of Mars, is a wide-angle, stiffened cone subject to buckling under entry aerodynamic pressure. Complex, highly optimized structural prototype and flight designs were evolved through the application of relatively advanced buckling analysis methodology. Both designs were evaluated through tests and analysis with improved shell-of-revolution computer programs. Deviations between the analyses and experiments were resolved only by modeling the thin-walled rings as shell branches. The results illustrate the great complexity of shell behavior and the designer's need for reliable analysis tools capable of representing detailed structural behavior with greater accuracy than is current practice.
Composite structures with hat-stiffened panels have gained traction in modern aircraft because they help reduce weight, increase durability, and provide stability to airframe skins. For weight reduction, skins should be designed to operate in the post-buckling regime. This causes possible interlaminar and intralaminar failure. However, composite panels stiffened with multiple hat-stringers are subject to cyclic loading even in the post-buckling regime. Under the NASA Advanced Composites Project (ACP), composite panels with multiple hatstringers were subject to a cyclic loading sequence from a pre-buckling state to a post-buckling state. This effort aimed to predict interlaminar failure for cyclic compression loading with pre-existent impact-induced damage. This work uses the Abaqus FEA Virtual Crack Closure Technique (VCCT), capabilities enhanced through an empirical method to integrate fatigue R-curve effects (different from R-ratio) into the Paris Law via user-defined subroutine to simulate the fatigue response o