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Three dimensional stress analysis of spiral bevel gears in mesh using the finite element method is presented. A finite element model is generated by solving equations that identify tooth surface coordinates. Contact is simulated by the automatic generation of nonpenetration constraints. This method is compared to a finite element contact analysis conducted with gap elements.
The basic theory of solid mechanics was deemed complete circa 1860 when St. Venant provided the strain formulation or the field compatibility condition. The strain formulation was incomplete. The missing portion has been formulated and identified as the boundary compatibility condition (BCC). The BCC, derived through a variational formulation, has been verified through integral theorem and solution of problems. The BCC, unlike the field counterpart, do not trivialize when expressed in displacements. Navier s method and the stiffness formulation have to account for the extra conditions especially at the inter-element boundaries in a finite element model. Completion of the strain formulation has led to the revival of the direct force calculation methods: the Integrated Force Method (IFM) and its dual (IFMD) for finite element analysis, and the completed Beltrami-Michell formulation (CBMF) in elasticity. The benefits from the new methods in elasticity, in finite element analysis, and in design optimization are discussed. Existing solutions and computer codes may have to be adjusted for the compliance of the new conditions. Complacency because the discipline is over a century old and computer codes have been developed for half a century can lead to stagnation of the discipline.
Dynamic characterization of a thin film inflatable elliptical structure is described in detail. A two-step finite element modeling approach in MSC/NASTRAN is utilized, consisting of (1) a nonlinear static pressurization procedure used to obtain the updated stiffness matrix, and (2) a modal "restart" eigen solution that uses the modified stiffness matrix. Unique problems encountered in modeling of this large Hexameter lightweight inflatable arc identified, including considerable difficulty in obtaining convergence in the nonlinear finite element pressurization solution. It was found that the extremely thin polyimide film material (.001 in or 1 mil) presents tremendous problems in obtaining a converged solution when internal pressure loading is applied. Approaches utilized to overcome these difficulties are described. Comparison of finite element predictions for frequency and mode shapes of the inflated structure with closed-form solutions for a flat pre-tensioned membrane indicate reasonable agreement.
Developments in design sensitivity analysis (DSA) method have been made using two fundamentally different approaches as shown. In the first approach, a discretized structural finite element model is used to carry out DSA. There are three different methods in the discrete DSA approach: finite difference, semi-analytical, and analytical methods. The finite difference method is a popular one due to its simplicity, but a serious shortcoming of the method is the uncertainty in the choice of a perturbation step size of design variables. In the semi-analytical method, the derivatives of stiffness matrix is computed by finite differences, whereas in the analytical method, the derivatives are obtained analytically. For the shape design variable, computation of analytical derivative of stiffness matrix is quite costly. Because of this, the semi-analytical method is a popular choice in discrete shape DSA approach. However, recently, Barthelemy and Haftka presented that the semi-analytical method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. They found that accuracy problems occur even for a simple cantilever beam. In the second approach, a continuum model of the structure is used to carry out DSA.
A new generation of adaptive x-ray optics (AXO) is being installed on high-coherent-flux x-ray beamlines worldwide to correct and control the optical wavefront with sub-nm precision. These ultra-smooth mirrors achieve high reflectivities at glancing angles of incidence and can be hundreds of mm long. One type of adaptive x-ray mirror relies on piezoelectric ceramic strips which are segmented into channels and actuated to induce local, longitudinal bending, generating one-dimensional shape changes in the mirror substrate. A recently described mirror model uses a three-layer geometry with parallel actuators on the front and back surfaces of a thicker mirror substrate. By analogy to a solved problem in the thermal actuation of a tri-metal strip, we show that the achievable bending radius varies approximately as the square of the substrate thickness. We provide an analytic solution and simulate bending using a finite-element model.
The stress evolution occurring in UMo/Al dispersion fuel is important since it affects the fuel performance during irradiation. In this study, a new analytical model was developed to predict the local stresses in UMo/Al dispersion fuel. In the model, a hypothetical unit sphere composed of a UMo fuel particle, interaction layer (IL), and Al matrix was considered, and the governing equations for the stress-strain relationship, strain-displacement, and mechanical equilibrium were established using a spherical coordinate system. The mathematical derivations were obtained for local stresses in the radial and circumferential direction using a thick-walled sphere model. Furthermore, this analytical model employed the stress distribution as the boundary condition, which is calculated using a finite element model with homogenized fuel meat. The developed model’s solution scheme was verified against Abaqus solutions obtained for two irradiated plates with heterogeneous meat. The model calculated consistent results for interfacial stresses in the IL and Al matrix, indicating that the newly developed model was reliable when simultaneously calculating fission gas pressurization on the UMo/IL/Al composite, and the use of the stress distribution in the homogenized fuel meat as the boundary condition for the analytical model was acceptable
The development process of electrified vehicles can benefit significantly from computer-aided engineering tools that predict themultiphysics response of batteries during abusive events. A coupled structural, electrical, electrochemical, and thermal model framework has been developed within the commercially available LS-DYNA software. The finite element model leverages a three-dimensional mesh structure that fully resolves the unit cell components. The mechanical solver predicts the distributed stress and strain response with failure thresholds leading to the onset of an internal short circuit. In this implementation, an arbitrary compressive strain criterion is applied locally to each unit cell. A spatially distributed equivalent circuit model provides an empirical representation of the electrochemical responsewith minimal computational complexity.The thermalmodel provides state information to index the electrical model parameters, while simultaneously accepting irreversible and reversible sources of heat generation. The spatially distributed models of the electrical and thermal dynamics allow for the localization of current density and corresponding temperature response. The ability to predict the distributed thermal response of the cell as its stored energy is completely discharged through the short circuit enables an engineering safety assessment. A parametric analysis of an exemplary model is used to demonstrate the simulation capabilities.
As a net shape process, die casting is intrinsically efficient and improvements in energy efficiency are strongly dependent on design and process improvements that reduce scrap rates so that more of the total consumed energy goes into acceptable, usable castings. A casting that is distorted and fails to meet specified dimensional requirements is typically remelted but this still results in a decrease in process yield, lost productivity, and increased energy consumption. This work focuses on developing, and expanding the use of, computer modeling methods that can be used to improve the dimensional accuracy of die castings and produce die designs and machine/die setups that reduce rejection rates due to dimensional issues. A major factor contributing to the dimensional inaccuracy of the casting is the elastic deformations of the die cavity caused by the thermo mechanical loads the dies are subjected to during normal operation. Although thermal and die cavity filling simulation are widely used in the industry, structural modeling of the die, particularly for managing part distortion, is not yet widely practiced. This may be due in part to the need to have a thorough understanding of the physical phenomenon involved in die distortion and the mathematical theory employed in the numerical models to efficiently model the die distortion phenomenon. Therefore, two of the goals of this work are to assist in efforts to expand the use of structural modeling and related technologies in the die casting industry by 1) providing a detailed modeling guideline and tutorial for those interested in developing the necessary skills and capability and 2) by developing simple meta-models that capture the results and experience gained from several years of die distortion research and can be used to predict key distortion phenomena of relevance to a die caster with a minimum of background and without the need for simulations. These objectives were met. A detailed modeling tutorial was provided to NADCA for distribution to the industry. Power law based meta-models for predicting machine tie bar loading and for predicting maximum parting surface separation were successfully developed and tested against simulation results for a wide range of machines and experimental data. The models proved to be remarkably accurate, certainly well within the requirements for practical application. In addition to making die structural modeling more accessible, the work advanced the state-of-the-art by developing improved modeling of cavity pressure effects, which is typically modeled as a hydrostatic boundary condition, and performing a systematic analysis of the influence of ejector die design variables on die deflection and parting plane separation. This cavity pressure modeling objective met with less than complete success due to the limits of current finite element based fluid structure interaction analysis methods, but an improved representation of the casting/die interface was accomplished using a combination of solid and shell elements in the finite element model. This approximation enabled good prediction of final part distortion verified with a comprehensive evaluation of the dimensions of test castings produced with a design experiment. An extra deliverable of the experimental work was development of high temperature mechanical properties for the A380 die casting alloy. The ejector side design objective was met and the results were incorporated into the metamodels described above. This new technology was predicted to result in an average energy savings of 2.03 trillion BTU's/year over a 10 year period. Current (2011) annual energy saving estimates over a ten year period, based on commercial introduction in 2009, a market penetration of 70% by 2014 is 4.26 trillion BTU's/year by 2019. Along with these energy savings, reduction of scrap and improvement in casting yield will result in a reduction of the environmental emissions associated with the melting and pouring of the metal which will be saved as a result of this technology. The average annual estimate of CO2 reduction per year through 2020 is 0.085 Million Metric Tons of Carbon Equivalent (MM TCE).
The functional, structural adequacy of a 20 meter long generic space truss (Mini-Mast), subjected to fatigue loading, was examined with respect to the failure modes which are most likely to occur during services. The space truss is made of thin-walled tubes having unidirectional, zero degree layups of Celanese G50 graphite fibers/Narmco 5217 epoxy composites. The approach used to investigate the most probable failure mode of the truss under fatigue loading is to determine the stress level, including the types of stress, in the member first, then followed by failure mode analysis based on the stress level just determined. To begin, an approximate beam-parameter truss (BPT) model is analyzed first, followed by a detailed analysis of the truss using a finite element model (FEM) run with NASTRAN code. The response results of the BPT model are used to compare FEM results and to check any major deviation of trend derived from the FEM. The purpose of the work was to search available fatigue data of the tube material, to conduct approximate dynamical stress analysis of the BPT model, to run detailed dynamical stress analysis of the FEM model using NASTRAN code, and to predict the fatigue life of the truss member based on limited fatigue data.
A NASA Langley-sponsored rotorcraft structural dynamics program, known as Design Analysis Methods for VIBrationS (DAMVIBS), has been under development since 1984. The objective of this program was to establish the technology base needed by the industry to develop an advanced finite-element-based dynamics design analysis capability for vibrations. Under the program, teams from the four major helicopter manufacturers have formed finite-element models, conducted ground vibration tests, made test/analysis comparisons of both metal and composite airframes, performed 'difficult components' studies on airframes to identify components which need more complete finite-element representation for improved correlation, and evaluated industry codes for computing coupled rotor-airframe vibrations. Studies aimed at establishing the role that structural optimization can play in airframe vibrations design work have also been initiated. Five government/industry meetings were held in connection with these activities during the course of the program. Because the DAMVIBS Program is coming to an end, the fifth meeting included a brief assessment of the program and its benefits to the industry.
A NASA Langley-sponsored rotorcraft structural dynamics program, known as Design Analysis Methods for VIBrationS (DAMVIBS), has been under development since 1984. The objective of this program was to establish the technology base needed by the industry to develop an advanced finite-element-based dynamics design analysis capability for vibrations. Under the program, teams from the four major helicopter manufacturers have formed finite-element models, conducted ground vibration tests, made test/analysis comparisons of both metal and composite airframes, performed 'difficult components' studies on airframes to identify components which need more complete finite-element representation for improved correlation, and evaluated industry codes for computing coupled rotor-airframe vibrations. Studies aimed at establishing the role that structural optimization can play in airframe vibrations design work have also been initiated. Five government/industry meetings were held in connection with these activities during the course of the program. Because the DAMVIBS Program is coming to an end, the fifth meeting included a brief assessment of the program and its benefits to the industry.
Modeling and simulation of structural impacts into soil continue to challenge analysts to develop accurate material models and detailed analytical simulations to predict the soil penetration event. This paper discusses finite element modeling of a series of penetrometer drop tests into soft clay. Parametric studies are performed with penetrometers of varying diameters, masses, and impact speeds to a maximum of 45 m/s. Parameters influencing the simulation such as the contact penalty factor and the material model representing the soil are also studied. An empirical relationship between key parameters is developed and is shown to correlate experimental and analytical results quite well. The results provide preliminary design guidelines for Earth impact that may be useful for future space exploration sample return missions.
This paper presents high fidelity Navier-Stokes simulations of the Boeing Subsonic Ultra Green Aircraft Research truss-braced wing wind-tunnel model and compares the results to linear MSC. Nastran flutter analysis and preliminary data from a recent wind-tunnel test of that model at the NASA Langley Research Center Transonic Dynamics Tunnel. The simulated conditions under consideration are zero angle of attack, so that structural nonlinearity can be neglected. It is found that, for Mach number greater than 0.78, the linear flutter analysis predicts flutter onset dynamic pressure below the wind-tunnel test and that predicted by the Navier-Stokes analysis. Furthermore, the wind-tunnel test revealed that the majority of the high structural dynamics cases were wing limit cycle oscillation (LCO) rather than flutter. Most Navier-Stokes simulated cases were also LCO rather than hard flutter. There is dip in the wind-tunnel test flutter/LCO onset in the Mach 0.76-0.80 range. Conditions tested above that Mach number exhibited no aeroelastic instability at the dynamic pressures reached in the tunnel. The linear flutter analyses do not show a flutter/LCO dip. The Navier-Stokes simulations also do not reveal a dip; however, the flutter/LCO onset is at a significantly higher dynamic pressure at Mach 0.90 than at lower Mach numbers. The Navier-Stokes simulations indicate a mild LCO onset at Mach 0.82, then a more rapidly growing instability at Mach 0.86 and 0.90. Finally, the modeling issues and their solution related to the use of a beam and pod finite element model to generate the Navier-Stokes structure mode shapes are discussed.
The fatigue damage of a space propulsion system component is computed using probabilistic structural analysis methods. The analysis takes into account the variations in static and dynamic loads, the uncertainty in structural damping, and the scatter in material fatigue resistance. The key elements of the probabilistic approach include: (1) a numerical engine model for describing the global component interface loads consistent with engine balance, (2) models for computing the local mode boundary conditions on the component, (3) a static structural analysis model that captures the strains at a damage critical location as a function of engine performance variables, (4) a finite element model for assessment of the random amplitude stress response due to random base and pressure excitations with uncertain power and correlation length, and (5) advanced first order reliability methods for computing the probabilities associated with the fatigue damage.
Hydrodynamic, computational fluid dynamics, and finite-element modeling were performed for a novel floating membrane reservoir system design for closed-loop pumped storage hydropower application. The conceptual design, which is now protected under an invention disclosure with a patent pending, offers a potential low-cost, low-impact solution to address the high costs, long investment return periods, and environmental disruptions encountered with traditional pumped storage development while offering modularity to enable replication at many locations. Prior to physical tests on a prototype, this paper documents the response analysis and modeling completed to simulate hydraulic and structural performance under different reservoir deployment and alignment arrangements, evaluate system stability, and refine the conceptual design. The results indicate that the excitation frequency from vortex shedding is at least an order of magnitude lower than the water sloshing frequencies in the reservoir, the structural natural frequency of the entire reservoir, and the vibrational frequencies of the side membranes, although excitation frequencies from other sources could cause mechanical resonance under certain conditions. To control destabilizing effects and prevent rocking motion and vibration, the authors conclude that the design could be improved by including a support structure around the floating reservoir, which could also provide floating-membrane containment, improve safety, and facilitate vertical reservoir movement. These conclusions, based on hydrodynamic and structural response modeling, help define specifications for upcoming full-scale prototype construction, deployment, and testing. This study demonstrates standard modeling technique application to an innovative design for which similar applications have not been previously evaluated. As a result, the refined design is capable of improving the scalability and feasibility of pumped storage hydropower in the United States and will be considered for commercialization following prototype testing.
This report provides basic documentation of information used to create a BSDS finite element model using NuMAD. The model is intended for use as a structural model. Use of this model for aerodynamic analyses is to be performed with caution. The BSDS project successfully demonstrated the design and manufacturing of a wind turbine blade integrating several innovations including flatback airfoils on inboard blade stations, a carbon fiber spar cap and an iterative blade design process. Refer to the References at the end of this report for full and in-depth information on the BSDS blade project.
Virtual prototyping in engineering design relies today on modern numerical models of contacting structures with accurate resolution of interface mechanics, which strongly affect the system-level stiffness and energy dissipation due to frictional losses. High-fidelity modeling within the localized interfaces is required to resolve local quantities of interest that may drive design decisions. The high-resolution finite element meshes necessary to resolve inter-component stresses tend to be computationally expensive, particularly when the analyst is interested in response time histories. The Hurty/Craig-Bampton (HCB) transformation is a widely used method in structural dynamics for reducing the interior portion of a finite element model while having the ability to retain all nonlinear contact degrees of freedom (DOF) in physical coordinates. These models may still require many DOF to adequately resolve the kinematics of the interface, leading to inadequate reduction and computational savings. This study proposes a novel interface reduction method to overcome these challenges by means of system-level characteristic constraint (SCC) modes and properly orthogonal interface modal derivatives (POIMDs) for transient dynamic analyses. Both SCC modes and POIMDs are computed using the reduced HCB mass and stiffness matrices, which can be directly computed from many commercial finite element analysis software. Comparison of time history responses to an impulse-type load in a mechanical beam assembly indicate that the interface-reduced model correlates well with the HCB truth model. Localized features like slip and contact area are well-represented in the time domain when the beam assembly is loaded with a broadband excitation. The proposed method also yields reduced-order models with greater critical timestep lengths for explicit integration schemes.
The trend towards nanomechanical resonator sensors with increasing sensitivity raises the need to address challenges encountered in the modeling of their mechanical behavior. Selecting the best approach in mechanical response modeling amongst the various potential computational solid mechanics methods is subject to controversy. A guideline for the selection of the appropriate approach for a specific set of geometry and mechanical properties is needed. In this study, geometrical limitations in frequency response modeling of flexural nanomechanical resonators are investigated. Deviation of Euler and Timoshenko beam theories from numerical techniques including finite element modeling and Surface Cauchy-Born technique are studied. The results provide a limit beyond which surface energy contribution dominates the mechanical behavior. Using the Surface Cauchy-Born technique as the reference, a maximum error on the order of 50 % is reported for high-aspect ratio resonators.