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Nonlinear structural analysis techniques for engine structures and components are addressed. The finite element method and boundary element method are discussed in terms of stress and structural analyses of shells, plates, and laminates.
Most dynamic components in helicopters are designed with a safe-life constant-amplitude testing approach that has not changed in many years. In contrast, the fatigue methodology in other industries has advanced significantly in the last two decades. Recent research at the NASA Langley Research Center and the U.S. Army Aerostructures Directorate at Langley are reviewed relative to fatigue and fracture design methodology for metallic components. Most of the Langley research was directed towards the damage tolerance design approach, but some work was done that is applicable to the safe-life approach. In the areas of testing, damage tolerance concepts are concentrating on the small-crack effect in crack growth and measurement of crack opening stresses. Tests were conducted to determine the effects of a machining scratch on the fatigue life of a high strength steel. In the area of analysis, work was concentrated on developing a crack closure model that will predict fatigue life under spectrum loading for several different metal alloys including a high strength steel that is often used in the dynamic components of helicopters. Work is also continuing in developing a three-dimensional, finite-element stress analysis for cracked and uncracked isotropic and anisotropic structures. A numerical technique for solving simultaneous equations called the multigrid method is being pursued to enhance the solution schemes in both the finite-element analysis and the boundary element analysis. Finally, a fracture mechanics project involving an elastic-plastic finite element analysis of J-resistance curve is also being pursued.
The merits of various numerical and experimental methods for computing sound fields radiated from vibrating structures are examined. The finite difference method, the finite element method, direct boundary element method, indirect boundary element near-field acoustic holography, two-microphone methods, and spatial transformation of sound fields are considered. The proper utilization of the methods is discussed.
Prediction of rotordynamic behavior for high energy concentration centrifugal pumps is a challenging task which still imposes considerable difficulties. While the mechanical modeling of the rotor is solved most satisfactorily by finite element techniques, accurate boundary conditions for arbitrary operating conditions are known for journal bearings only. Little information is available on the reactive forces of annular seals, such as neck ring and interstage seals and balance pistons, and on the impeller interaction forces. The present focus is to establish reliable boundary conditions at annular seals. For this purpose, a full scale test machine was set up and smooth and serrated seal configurations measured. Dimensionless coefficients are presented and compared with a state of the art theory.
This paper presents an overview of some of the recent (1984-1991) developments in computational/analytical methods in the mechanics of fracture: (i) analytical solutions for elliptical or circular cracks embedded in isotropic or transversely isotropic solids (the crack-plane being at an arbitrary angle to the axis of transverse isotropy), with crack-faces being subjected to arbitrary tractions; (ii) finite-element or boundary-element alternating methods for two- and three-dimensional crack problems; (iii) a "direct-stiffness" method for stiffened panels with flexible fasteners and with multiple cracks, using the alternating method; (iv) multiplesite-damage near a row of fastener holes; (v) analysis of cracks with bonded repair patches; (vi) methods for generation of weight-functions for 2- and 3-D crack problems, and (vii) domain-integral methods for elastic-plastic or inelastic crack mechanics.
A hybrid numerical method combining finite elements and the boundary integral representation is used to investigate the transient scattering of ultrasonic waves by a crack in a plate. The incident wave models the guided waves generated by a steel ball impact on the plate. Two surface-breaking cracks and one subsurface crack are studied here. The results show that the location and depth of cracks have measurable effects on the surface responses in time and frequency domains. Also, the scattered fields have distinct differences in the three cases.
Cyclic Damage Accumulation (CDA) computer program performs high-temperature, low-cycle-fatigue life prediction for materials analysis. Designed to account for effects on creep-fatigue life of complex loadings involving such factors as thermomechanical fatigue, hold periods, wave-shapes, mean stresses, multiaxiality, cumulative damage, coatings, and environmental attack. Several features practical for application to actual component analysis using modern finite-element or boundary-element methods. Although developed for use in predicting crack-initiation lifetimes of gas-turbine-engine materials, also applied to other materials as well. Written in FORTRAN 77.
Numerical and analytical micromechanical models are presented to predict the thermoelastic behavior of a textile composite. In the numerical model, the unit-cell is discretized with finite elements, and periodic boundary conditions are imposed between opposite faces of the unit-cell. For a thin textile composite, stress gradients effects through the thickness are demonstrated. The consequent difference in the stiffness and strength behavior of thick and thin composites are discussed. The numerical model is implemented to predict 3-D thermo-elastic constants for a thick textile composite, and the plate thermo-mechanical properties for a thin textile composite. The numerical model is extended to compute the thermal residual microstresses due to processing to predict the composite failure envelopes. An analytical model - Selective Averaging Method (SAM) - is proposed, which is based on a judicious combination of stiffness and compliance averaging to estimate the 3-D elastic constants. Both the models are tested and verified for several examples by comparing the stiffness properties with elasticity solutions and available results.
This project involves fundamental studies of the role of nonlinearity in determining the motion of liquid masses under the principal influences of surface tension, viscosity and inertia. Issues to be explored are relevant to aspects of terrestrial processes, as well as being immediately applicable to fluid management in a low-gravity environment. Specific issues include: (1) the mechanic's of liquid masses in large-amplitude motions, (2) the influence of bounding surfaces on the motion, and (3) the ability of such surfaces to control liquid motion by wetting forces, especially when they are augmented by various surface treatments. Mathematical techniques include asymptotic analysis of the governing equations, for problem simplification, and numerical simulation, using both boundary-element and finite-difference methods. The flow problem is divided into an 'outer' or inviscid potential-flow region and one or more inner, or viscous dominated, regions. Relevant to one inner region, the vicinity of the contact line, we discuss time-dependent simulation of slow droplet motion, on a surface of variable wettability, using the lubrication approximation. The simulation uses a disjoining pressure model and reproduces realistic wetting-dewetting behavior.
Compressive buckling analysis was performed on metal-matrix composite (MMC) plates with central square holes. The MMC plates have varying aspect ratios and hole sizes and are supported under different boundary conditions. The finite-element structural analysis method was used to study the effects of plate boundary conditions, plate aspect ratio, hole size, and the composite stacking sequence on the compressive buckling strengths of the perforated MMC plates. Studies show that by increasing the hole sizes, compressive buckling strengths of the perforated MMC plates could be considerably increased under certain boundary conditions and aspect ratios ("anomalous" buckling behavior); and that the plate buckling mode could be symmetrical or antisymmetrical, depending on the plate boundary conditions, aspect ratio, and the hole size. For same-sized plates with same-sized holes, the compressive buckling strengths of the perforated MMC plates with [90/0/0/90]2 lamination could be as much as 10 percent higher or lower than those of the [45/- 45/- 45/45]2 laminations, depending on the plate boundary conditions, plate aspect ratios, and the hole size. Clamping the plate edges induces far stronger "anomalous" buckling behavior (enhancing compressive buckling strengths at increasing hole sizes) of the perforated MMC plates than simply supporting the plate edges.
Robust gear designs consider not only crack initiation, but crack propagation trajectories for a fail-safe design. In actual gear operation, the magnitude as well as the position of the force changes as the gear rotates through the mesh. A study to determine the effect of moving gear tooth load on crack propagation predictions was performed. Two-dimensional analysis of an involute spur gear and three-dimensional analysis of a spiral-bevel pinion gear using the finite element method and boundary element method were studied and compared to experiments. A modified theory for predicting gear crack propagation paths based on the criteria of Erdogan and Sih was investigated. Crack simulation based on calculated stress intensity factors and mixed mode crack angle prediction techniques using a simple static analysis in which the tooth load was located at the highest point of single tooth contact was validated. For three-dimensional analysis, however, the analysis was valid only as long as the crack did not approach the contact region on the tooth.
The active acoustic and structural noise control characteristics of a double wall cylinder with and without ring stiffeners were numerically evaluated. An exterior monopole was assumed to acoustically excite the outside of the double wall cylinder at an acoustic cavity resonance frequency. Structural modal vibration properties of the inner and outer shells were analyzed by post-processing the results from a finite element analysis. A boundary element approach was used to calculate the acoustic cavity response and the coupled structural-acoustic interaction. In the frequency region of interest, below 500 Hz, all structural resonant modes were found to be acoustically slow and the nonresonant modal response to be dominant. Active sound transmission control was achieved by control forces applied to the inner or outer shell, or acoustic control monopoles placed just outside the inner or outer shell. A least mean square technique was used to minimize the interior sound pressures at the nodes of a data recovery mesh. Results showed that single acoustic control monopoles placed just outside the inner or outer shells resulted in better sound transmission control than six distributed point forces applied to either one of the shells. Adding stiffeners to the double wall structure constrained the modal vibrations of the shells, making the double wall stiffer with associated higher modal frequencies. Active noise control obtained for the stiffened double wall configurations was less than for the unstiffened cylinder. In all cases, the acoustic control monopoles controlled the sound transmission into the interior better than the structural control forces.
The integrated Finite Element Analysis–Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program was used to simulate the formation of mudflat-cracks from thermomechanical loading on a multi-layered Environmental Barrier Coating (EBC) system deposited on a ceramic substrate. FEAMAC/CARES combines MAC/GMC multiscale composite micromechanics code with CARES/Life probabilistic multiaxial failure criteria code and Abaqusfinite element analysis. In this work, step function elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio finite elements enabled the depiction of crack boundaries and formation of mudflat patterned damage. Demonstrated examples include finite element models of button–sized disk–shaped 3-D specimen, and a 2-D model of through-the-thickness cross-section. All models were subjected to a progressive cool down from 1300oC to room temperature. Mudflat crack damage in the coating system resulted from the buildup of residual tensile stresses between the individual material constituents from thermal expansion mismatch. A 2-parameter Weibull distribution characterized the coating layer stochastic strength response and the effect of the Weibull modulus on the formation of damage was studied here.
The integrated Finite Element Analysis Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program was used to simulate the formation of mudflat-cracks from thermomechanical loading on a multi-layered Environmental Barrier Coating (EBC) system deposited on a ceramic substrate. FEAMAC/CARES combines MAC/GMC (Micromechanics Analysis Code/Generalized Method of Cells) multiscale composite micromechanics code with CARES/Life probabilistic multiaxial failure criteria code and Abaqusfinite element analysis. In this work, step function elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio finite elements enabled the depiction of crack boundaries and formation of mudflat patterned damage. Demonstrated examples include finite element models of button-sized disk-shaped 3-D specimen, and a 2-D model of through-the-thickness cross-section. All models were subjected to a progressive cool down from 1300 degrees Centigrade to room temperature. Mudflat crack damage in the coating system resulted from the buildup of residual tensile stresses between the individual material constituents from thermal expansion mismatch. A 2-parameter Weibull distribution characterized the coating layer stochastic strength response and the effect of the Weibull modulus on the formation of damage was studied here.
A new treatment of the classical beam torsion boundary value problem is applied. Using the p-version finite element method with shape functions based on Legendre polynomials, torsion solutions for generic cross-sections comprised of isotropic materials are developed. Element shape functions for quadrilateral and triangular elements are discussed, and numerical examples are provided.
The primary project was the numerical simulation, by a finite element/finite difference method, of the viscous flow about an airfoil. The secondary project involved the numerical simulation of the three-dimensional separated and vortex-dominated flow about a hemispherically capped cylinder in the transonic regime. Preliminary calculations were started for the hemisphere-cylinder at 0 and 5 degree angle of attack. The solution of the flow field about airfoils and wings is required to determine the important parameters of lift, moment, and drag. Viscous effects must be accounted for if the drag is to be accurately calculated. At present there are basically two approaches to the numerical simulation of the flow field, the use of fully viscous models and the inviscid/viscous models. The fully viscous models require the solution of an approximation of the Navier-Stokes equations and therefore should simulate most of the physical mechanisms. A fast, accurate, and computationally efficient inviscid flow solver was recently developed by Hartwich. It is thought that Hartwich's program coupled to a fast, accurate, and computationally efficient boundary layer code, will make an excellent tool for airfoil design. The purpose of the primary project was to develop a compressible boundary layer code using the semidiscrete Galerkin finite element method. The numerical scheme employed used the combination of a Dorodnitsyn formulation of the boundary layer equations, with a finite difference/finite element procedure (semidiscrete Galerkin method), in the solution of the compressible two-dimensional boundary layer equations. A laminar compressible boundary layer code was developed and tested for a NACA 0012 airfoil at a Mach number of 0.5, a Reynolds number of 5000, and zero angle of attack. At present the boundary layer program solves up to, but not beyond, separation.
The accurate simulation of boundary- and interface-dominated problems on complex geometries remains challenging when boundary- or interface-fitted meshes are difficult to generate, particularly for curved boundaries, polycrystalline microstructures, and dense interface networks. The Shifted Boundary Method (SBM) alleviates this meshing burden by shifting the enforcement of boundary conditions from the true boundary to a nearby surrogate boundary and recovering the effect of the true boundary through geometric correction terms, thereby enabling standard finite element spaces on non-boundary-fitted meshes. In this report, we develop a general shiftedboundary and shifted-interface framework within the open-source MOOSE framework. We first present a general SBM implementation for complex geometries on non-boundary-fitted meshes. We then adopt the Shifted Interface Method (SIM) for internal interfaces and develop a unified shifted-interface treatment in which the interface law is enforced on a surrogate interface and the effect of the true interface is recovered through shifted jumps, fluxes, and tractions. This perspective brings scalar thermal-contact and vector-valued cohesive-zone mechanics into a single framework, the latter realized as the Shifted Cohesive Zone Method (SCZM) and coupled with history-dependent constitutive models from NEML2. We further extend the MOOSE mesh infrastructure to support cohesive-zone calculations on distributed meshes. The framework is verified and demonstrated through three progressive studies: Poisson’s equation on a smoothed starshaped domain, a manufactured thermal-contact problem on a non-interface-fitted mesh, and a two-dimensional polycrystalline representative volume element combining crystal plasticity with cohesive grain-boundary interfaces. Across these studies, the shifted formulations reproduce boundary- and interface-fitted reference solutions with high fidelity, indicating that the proposed framework provides an accurate and efficient route to boundary- and interface-dominated simulations on arbitrary geometries without requiring fitted meshes.
A comparison of the finite element method (FEM) and boundary element method (BEM) for the solution of two-dimensional plane strain problems in fracture mechanics is presented in this paper. Stress intensity factors (SIF's) were calculated using both methods for elastic plates with either a single-edge crack or an inclined-edge crack. In particular, two currently available programs, ANSYS for finite element analysis and BEASY for boundary element analysis, were used.