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A finite-element analysis of the end-notch flexure specimen for Mode II interlaminar fracture toughness measurement was conducted. The effects of friction between the crack faces and large deflection on the evaluation of G(IIc) from this specimen were investigated. Results of this study are presented in this paper.
Finite element analysis of the Space Shuttle 2.5-inch frangible nut was conducted to improve understanding of the current design and proposed design changes to this explosively-actuated nut. The 2.5-inch frangible nut is used in two places to attach the aft end of the Space Shuttle Orbiter to the External Tank. Both 2.5-inch frangible nuts must function to complete safe separation. The 2.5-inch frangible nut contains two explosive boosters containing RDX explosive each capable of splitting the nut in half, on command from the Orbiter computers. To ensure separation, the boosters are designed to be redundant. The detonation of one booster is sufficient to split the nut in half. However, beginning in 1987 some production lots of 2.5-inch frangible nuts have demonstrated an inability to separate using only a single booster. The cause of the failure has been attributed to differences in the material properties and response of the Inconel 718 from which the 2.5-inch frangible nut is manufactured. Subsequent tests have resulted in design modifications of the boosters and frangible nut. Model development and initial analysis was conducted by Sandia National Laboratories (SNL) under funding from NASA Lyndon B. Johnson Space Center (NASA-JSC) starting in 1992. Modeling codes previously developed by SNL were transferred to NASA-JSC for further analysis on this and other devices. An explosive bolt with NASA Standard Detonator (NSD) charge, a 3/4-inch frangible nut, and the Super*Zip linear separation system are being modeled by NASA-JSC.
Finite element analysis was used to investigate the temperature and stress profiles that develop in 316L stainless steel membranes being irradiated using different proton beam conditions in contact with a molten salt environment. It was shown that in addition to a nonuniform irradiation profile, a focused 2 MeV proton beam leads to very strong temperature and stress gradients in the membrane, introducing highly localized driving forces that complicate and even compromise the integrity and reliability of the experimental results of corrosion studies. Here, the use of a focused beam in corrosion studies can create experimental artifacts that may misrepresent the true corrosion behavior. In contrast, the use of a rastered beam is shown to distribute the protons and resulting radiation damage uniformly across the membrane face, and more importantly, results in temperature and stress profiles that are not only very uniform but are of much lower magnitude. The use of a rastered beam during molten salt corrosion experiments is therefore recommended to achieve uniform damage rates, thereby reducing both gradients and magnitudes of the temperature and stress distributions.
A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.
A method of selecting grid size for the finite element analysis of gear tooth deflection is presented. The method is based on a finite element study of two cylinders in line contact, where the criterion for establishing element size was that there be agreement with the classical Hertzian solution for deflection. The results are applied to calculate deflection for the gear specimen used in the NASA spur gear test rig. Comparisons are made between the present results and the results of two other methods of calculation. The results have application in design of gear tooth profile modifications to reduce noise and dynamic loads.
The objective of adaptive meshing and automatic error control in finite element analysis is to eliminate the need for the application engineer from re-meshing and re-running design simulations to verify numerical accuracy. The user should only need to enter the component geometry and a coarse finite element mesh. The software will then autonomously and adaptively refine this mesh where needed, reducing the error in the fields to a user prescribed value. The ideal end result of the simulation is a measurable quantity (e.g. scattered field, input impedance), calculated to a prescribed error, in less time and less machine memory than if the user applied typical uniform mesh refinement by hand. It would also allow for the simulation of larger objects since an optimal mesh is created.
A conceptual/preliminary level structural design system has been developed for structural integrity analysis and weight estimation of advanced space transportation vehicles. The system includes a three-dimensional interactive geometry modeler, a finite element pre- and post-processor, a finite element analyzer, and a structural sizing program. Inputs to the system include the geometry, surface temperature, material constants, construction methods, and aerodynamic and inertial loads. The results are a sized vehicle structure capable of withstanding the static loads incurred during assembly, transportation, operations, and missions, and a corresponding structural weight. An analysis of the Space Shuttle external tank is included in this paper as a validation and benchmark case of the system.
Iterative techniques for the solution of the algebraic equations associated with the direct boundary element analysis (BEA) method are discussed. Continuum structural response analysis problems are considered, employing single- and multizone boundary element models with and without zone condensation. The impact on convergence rate and computer resource requirements associated with the sparse and blocked matrices, resulting in multizone BEA, is studied. Both conjugate gradient and generalized minimum residual preconditioned iterative solvers are applied for these problems and the performance of these algorithms is reported. Included is a quantification of the impact of the preconditioning utilized to render the boundary element matrices solvable by the respective iterative methods in a time competitive with direct methods.
Evaluation of finite element analysis for longitudinal vibrations of liquid propellant launch vehicle
A finite-element analysis was conducted to evaluate the stress distributions within mode I and mode II failure specimens, assuming both isotropic and orthotropic elastic material properties. The effects of anisotropy on both the magnitude and the location of the highest stress concentration at the vicinity of the crack tip are significant. The results from modeling realistic blunt crack tip geometry and resin-rich zones imply that local variations in the microstructure strongly influence the stress state near the crack tip and therefore the measured fracture properties. In addition, the features of a viscoelastic model for thermoplastic matrices are described. This model will be used in future investigations of matrix-dominated failure phenomena.
The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.
The accuracy and robustness of a two-dimensional smoothing methodology is examined for the problem of recovering accurate interlaminar shear stress distributions in laminated composite and sandwich plates. The smoothing methodology is based on a variational formulation which combines discrete least-squares and penalty-constraint functionals in a single variational form. The smoothing analysis utilizes optimal strains computed at discrete locations in a finite element analysis. These discrete strain data are smoothed with a smoothing element discretization, producing superior accuracy strains and their first gradients. The approach enables the resulting smooth strain field to be practically C1-continuous throughout the domain of smoothing, exhibiting superconvergent properties of the smoothed quantity. The continuous strain gradients are also obtained directly from the solution. The recovered strain gradients are subsequently employed in the integration o equilibrium equations to obtain accurate interlaminar shear stresses. The problem is a simply-supported rectangular plate under a doubly sinusoidal load. The problem has an exact analytic solution which serves as a measure of goodness of the recovered interlaminar shear stresses. The method has the versatility of being applicable to the analysis of rather general and complex structures built of distinct components and materials, such as found in aircraft design. For these types of structures, the smoothing is achieved with 'patches', each patch covering the domain in which the smoothed quantity is physically continuous.
Understanding of the basic principles which control errors of discretization in finite element analysis has increased very substantially since 1980. The main milestones were: (1) development of the theoretical basis of p-extensions (1981); (2) understanding of the proper interplay between mesh design and assignment of polynomial degree to elements. Practical realization of exponential convergence rates, independently of the smoothness of the exact solution (1984); and (3) industrial experience with the new finite element technology known as the p- or hp-version of the finite element method: General Dynamics reported thirty- to forty-fold savings in terms of human time and large savings in computer time (1986). Lockheed reported favorably on their evaluation of error estimation and quality control capabilities of the p-version in industrial settings (1987). The gains in our understanding of how to control the errors of discretization represent only half of the control necessary to ensure that a numerical model is in fact an accurate representation of the corresponding physical system. Control of the errors of idealization is equally important. A brief overview of the main ideas of how to ensure the quality and reliability of mathematical models of structural systems is presented.
A static and dynamic finite element analysis is conducted on a U.S. Army OH-58 composite tail boom and compared with test data. The tail boom is a filament-wound graphite/epoxy monocoque structure. The structural design of the composite tail boom skin is based on 50-percent graphite fiber volume. However, material tests on representative samples of the tail boom skin reveal that the graphite fiber-volume fraction varied from 44.6 to 49.3 percent. To determine the effect of using measured material properties, static and dynamic finite element analyses are conducted for three fiber-volume conditions of 45, 48, and 50 percent. The static and dynamic model with the 45-percent fiber-volume graphite skins gives the closest agreement with test data.
The development of a microcomputer system is described. A series of finite element analysis programs are evaluated in terms of their cost effective application within the microcomputer system. It is shown that the system is practically maintenance free and can be sustained by individual laboratories of standard scale in the educational or academic environment.
A three-dimensional finite element analysis was performed for a biaxially loaded composite laminate (with a centered hole) consisting of several fiber-reinforced composite layers each with a specified fiber orientation. The detailed stress distribution around the hole was determined. Also, the locations of initial damage zones due to different failure mechanisms were indicated.
The accuracy of a new class of concurrent procedures for transient finite element analysis is examined. A phase error analysis is carried out which shows that wave retardation leading to unacceptable loss of accuracy may occur if a Courant condition based on the dimensions of the subdomains is violated. Numerical tests suggest that this Courant condition is conservative for typical structural applications and may lead to a marked increase in accuracy as the number of subdomains is increased. Theoretical speed-up ratios are derived which suggest that the algorithms under consideration can be expected to exhibit a performance superior to that of globally implicit methods when implemented on parallel machines.
A three-dimensional hybrid-stress finite element analysis of composite laminates containing cutouts and cracks is presented. Fully three-dimensional, hexahedral isoparametric elements of the hybrid-stress model are formulated on the basis of the Hellinger-Reissner variational principle. Traction-free edges, cutouts, and crack surfaces are modeled by imposition of exact traction boundary conditions along element surfaces. Special boundary and surface elements are constructed by introducing proper constraints on assumed stress functions. The Lagrangian multiplier technique is used to enforce ply-interface continuity conditions in hybrid bimaterial composite elements for modeling the interface region in a composite laminate. Two examples are given to illustrate the capability of the present method of approach: (1) the well-known delamination problem in an angle-ply laminate, and (2) the important problem of a composite laminate containing a circular hole. Results are presented in detail for each case. Implications of interlaminar and intralaminar crack initiation, growth and fracture in composites containing cracks and cutouts are discussed.