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At least 523 records · Page 29

Coupling CTH to Linear Acoustic Propagation across an Air-Earth Interface

The interface between the Earth and the atmosphere forms a strong contrast in material properties. As such, numerical issues can arise when simulating an elastic wavefield across such a boundary when using a numerical simulation scheme. This is exacerbated when two different simulation codes are coupled straddling that interface. In this report we document how we implement the coupling of CTH, a nonlinear shock physics code, to a linearized elastic/acoustic wave propagation algorithm, axiElasti, across the air-earth interface. We first qualitatively verify that this stable coupling between the two algorithms produces expected results with no visible effects of the coupling interface. We then verify the coupling interface quantitatively by checking consistency with results from previous work and with coupled acoustic-elastic seismo-acoustic source inversions in three earth materials.

58 GEOSCIENCES↗

Finite-element nonlinear transient response computer programs PLATE 1 and CIVM-PLATE 1 for the analysis of panels subjected to impulse or impact loads

Two computer programs are described for predicting the transient large deflection elastic viscoplastic responses of thin single layer, initially flat unstiffened or integrally stiffened, Kirchhoff-Lov ductile metal panels. The PLATE 1 program pertains to structural responses produced by prescribed externally applied transient loading or prescribed initial velocity distributions. The collision imparted velocity method PLATE 1 program concerns structural responses produced by impact of an idealized nondeformable fragment. Finite elements are used to represent the structure in both programs. Strain hardening and strain rate effects of initially isotropic material are considered.

Spilker, R. L.↗

Inelastic peridynamic model for molecular crystal particles

The peridynamic theory of solid mechanics is applied to modeling the deformation and fracture of micrometer-sized particles made of organic crystalline material. A new peridynamic material model is proposed to reproduce the elastic–plastic response, creep, and fracture that are observed in experiments. The model is implemented in a three-dimensional, meshless Lagrangian simulation code. In the small deformation, elastic regime, the model agrees well with classical Hertzian contact analysis for a sphere compressed between rigid plates. Under higher load, material and geometrical nonlinearity is predicted, leading to fracture. Finally, the material parameters for the energetic material CL-20 are evaluated from nanoindentation test data on the cyclic compression and failure of micrometer-sized grains.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Wind energy system time-domain (WEST) analyzers

A portable analyzer which simulates in real time the complex nonlinear dynamics of horizontal axis wind energy systems was constructed. Math models for an aeroelastic rotor featuring nonlinear aerodynamic and inertial terms were implemented with high speed digital controllers and analog calculation. This model was combined with other math models of elastic supports, control systems, a power train and gimballed rotor kinematics. A stroboscopic display system graphically depicting distributed blade loads, motion, and other aerodynamic functions on a cathode ray tube is included. Limited correlation efforts showed good comparison between the results of this analyzer and other sophisticated digital simulations. The digital simulation results were successfully correlated with test data.

Dreier, M. E.↗

Three-dimensional finite-element analysis of layered composite plates

Results are presented for an investigation of the three-dimensional, geometrically nonlinear, finite-element analysis of the bending of laminated anisotropic composite plates. The individual laminae are treated as homogeneous, transversely isotropic, and linearly elastic. A fully three-dimensional isoparametric finite element with eight modes (i.e., linear element) and 24 degrees of freedom (three displacement components per node) is used. The numerical results obtained using this linear analysis are compared with the exact solutions given in Pagano (1969, 1970). It is found that the results of the linear analysis converge to the exact solution as the mesh is refined.

Putcha, N. S.↗

Elastohydrodynamic lubrication calculations used as a tool to study scuffing

A new Reynolds equation was developed that takes into account the nonlinear viscous behavior of the fluid. The new Reynolds equation considers the nonlinear viscous fluid model of Eyring, the equilibrium equation, the constant mass flow, and the kinematic boundary condition. The new Reynolds equation and the elasticity equation are solved simultaneously by using a system approach and a Newton-Raphson technique. Comparisons are made with results obtained from the classical Reynolds equation. The effects of sliding speed and introducing a bump or a groove within the conjunction are studied. Results are shown for both moderate and heavy loads.

Houpert, L. G.↗

Aeroelastic Analysis of a Trimmed Generic Hypersonic Vehicle

The aeroelastic equations of motion governing a hypersonic vehicle in free flight are derived. The equations of motion for a translating and rotating flexible body using Lagrange's equations in terms of quasi-coordinates are presented. These equations are simplified for the case of a vehicle with pitch and plunge rigid body degrees of freedom and small elastic displacements. The displacements are approximated by a truncated series of the unrestrained mode shapes, which are obtained using equivalent plate theory. Subsequently, the nonlinear equations of motion are linearized about the trim state, which is obtained using a rigid body trim model and steady hypersonic aerodynamics. The appropriate flutter derivatives are calculated from piston theory. Results describing mode shapes, trim behavior, and aeroelastic stability of a generic hypersonic vehicle are presented.

Nydick, I.↗

Implementation of Fiber Substructuring Into Strain Rate Dependent Micromechanics Analysis of Polymer Matrix Composites

A research program is in progress to develop strain rate dependent deformation and failure models for the analysis of polymer matrix composites subject to impact loads. Previously, strain rate dependent inelastic constitutive equations developed to model the polymer matrix were incorporated into a mechanics of materials based micromechanics method. In the current work, the micromechanics method is revised such that the composite unit cell is divided into a number of slices. Micromechanics equations are then developed for each slice, with laminate theory applied to determine the elastic properties, effective stresses and effective inelastic strains for the unit cell. Verification studies are conducted using two representative polymer matrix composites with a nonlinear, strain rate dependent deformation response. The computed results compare well to experimentally obtained values.

Goldberg, Robert K.↗

Testing and Analyses of Advanced Composite Tow-Steered Shells with Cutouts

The structural response of two composite tow-steered shells with small cutouts in end compression is assessed using analyses and experimental measurements. The cylindrical shells were manufactured without cutouts using an automated fiber placement system, where the shells’ fiber orientation angles vary continuously around the shell circumference from ±10 degrees on the axially stiff crown and keel, to ±45 degrees on the shear-stiff sides. The first shell with overlaps has laminate thickness variations on the crown and keel that result from application of all 24 tows during each pass of the fiber placement system. The second shell without overlaps uses the fiber placement system’s tow drop/add capability to achieve a more uniform shell wall thickness. These shells without cutouts were tested in axial compression and buckled elastically. An unreinforced cutout representative of a passenger door on a commercial aircraft fuselage is machined into one side of each shell. Results from nonlinear finite element analysis are compared with their corresponding load, displacement, and strain measurements in prebuckling through stable postbuckling. Results from tests and analyses of shells with large cutouts are also discussed. The very good agreement observed in this study increases confidence in applying tow-steered composites to operational vehicles.

Tow-Steered↗

Numerical simulation of the nonlinear response of composite plates under combined thermal and acoustic loading

A time-domain study of the random response of a laminated plate subjected to combined acoustic and thermal loads is carried out. The features of this problem also include given uniform static inplane forces. The formulation takes into consideration a possible initial imperfection in the flatness of the plate. High decibel sound pressure levels along with high thermal gradients across thickness drive the plate response into nonlinear regimes. This calls for the analysis to use von Karman large deflection strain-displacement relationships. A finite element model that combines the von Karman strains with the first-order shear deformation plate theory is developed. The development of the analytical model can accommodate an anisotropic composite laminate built up of uniformly thick layers of orthotropic, linearly elastic laminae. The global system of finite element equations is then reduced to a modal system of equations. Numerical simulation using a single-step algorithm in the time-domain is then carried out to solve for the modal coordinates. Nonlinear algebraic equations within each time-step are solved by the Newton-Raphson method. The random gaussian filtered white noise load is generated using Monte Carlo simulation. The acoustic pressure distribution over the plate is capable of accounting for a grazing incidence wavefront. Numerical results are presented to study a variety of cases.

Mei, Chuh↗

Low-Velocity Impact Response of Sandwich Beams with Functionally Graded Core

The problem of low-speed impact of a one-dimensional sandwich panel by a rigid cylindrical projectile is considered. The core of the sandwich panel is functionally graded such that the density, and hence its stiffness, vary through the thickness. The problem is a combination of static contact problem and dynamic response of the sandwich panel obtained via a simple nonlinear spring-mass model (quasi-static approximation). The variation of core Young's modulus is represented by a polynomial in the thickness coordinate, but the Poisson's ratio is kept constant. The two-dimensional elasticity equations for the plane sandwich structure are solved using a combination of Fourier series and Galerkin method. The contact problem is solved using the assumed contact stress distribution method. For the impact problem we used a simple dynamic model based on quasi-static behavior of the panel - the sandwich beam was modeled as a combination of two springs, a linear spring to account for the global deflection and a nonlinear spring to represent the local indentation effects. Results indicate that the contact stiffness of thc beam with graded core Increases causing the contact stresses and other stress components in the vicinity of contact to increase. However, the values of maximum strains corresponding to the maximum impact load arc reduced considerably due to grading of thc core properties. For a better comparison, the thickness of the functionally graded cores was chosen such that the flexural stiffness was equal to that of a beam with homogeneous core. The results indicate that functionally graded cores can be used effectively to mitigate or completely prevent impact damage in sandwich composites.

Apetre, N. A.↗

Nonlinear Finite Element Analysis of Shells with Large Aspect Ratio

A higher order degenerated shell element with nine nodes was selected for large deformation and post-buckling analysis of thick or thin shells. Elastic-plastic material properties are also included. The post-buckling analysis algorithm is given. Using a square plate, it was demonstrated that the none-node element does not have shear locking effect even if its aspect ratio was increased to the order 10 to the 8th power. Two sample problems are given to illustrate the analysis capability of the shell element.

Chang, T. Y.↗

Inference of phase field fracture models

The phase field approach to modeling fracture uses a diffuse damage field to represent cracks. This representation mollifies singularities that arise in computations with sharp interface models and some of the resultant difficulties in the mathematical and numerical treatment of fracture. Phase field fracture models have proven effective at representing crack propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, lead to an array of possible models. There exists a large body of literature focusing on this class of models and on the impact of model form on the predicted crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here, we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used for the degradation of elastic response due to damage and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). Furthermore, in this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Void growth in an elastic-plastic medium.

The uniaxial deformation of an elastic-plastic medium containing a doubly periodic square array of circular cylindrical voids is studied under plane-strain conditions. Both the effects of geometrical nonlinearities resulting from large deformation and physical nonlinearities arising from plastic material behavior are included in formulating the problem. A variational principle is used as the basis for implementing a finite-element solution. Results are obtained for the change in void shape and size under increasing overall strain, the overall tensile behavior of the material with voids, and the development of the plastic zone about a void.

Needleman, A.↗

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Buttrill, Carey S.↗

A contact stress model for multifingered grasps of rough objects

The model developed utilizes a contact-stress analysis of an arbitrarily shaped object in a multifingered grasp. The fingers and the object are all treated as elastic bodies, and the region of contact is modeled as a deformable surface patch. The relationship between the friction and normal forces is nonlocal and nonlinear in nature and departs from the Coulomb approximation. The nature of the constraints arising out of conditions for compatibility and static equilibrium motivated the formulation of the model as a nonlinear constrained minimization problem. The model is able to predict the magnitude of the inwardly directed normal forces and both the magnitude and direction of the tangential (friction) forces at each finger-object interface for grasped objects in static equilibrium.

Sinha, Pramath Raj↗

Fracture mechanics parameters for small fatigue cracks

This paper presents a review of some common small-crack test specimens, the underlying causes of the small-crack effect, and the fracture-mechanics parameters that have been used to correlate or predict their growth behavior. This review concentrates on continuum mechanics concepts and on the nonlinear behavior of small cracks. The paper reviews some stress-intensity factor solutions for small-crack test specimens and develops some simple elastic-plastic J integral and cyclic J integral expressions that include the influence of crack-closure. These parameters were applied to small-crack growth data on two aluminum alloys, and a fatigue life prediction methodology is demonstrated. For these materials, the crack-closure transient from the plastic wake was found to be the major factor in causing the small-crack effect.

Newman, J. C., Jr.↗

Optimization of Car Body under Constraints of Noise, Vibration, and Harshness (NVH), and Crash

To be competitive on the today's market, cars have to be as light as possible while meeting the Noise, Vibration, and Harshness (NVH) requirements and conforming to Government-man dated crash survival regulations. The latter are difficult to meet because they involve very compute-intensive, nonlinear analysis, e.g., the code RADIOSS capable of simulation of the dynamics, and the geometrical and material nonlinearities of a thin-walled car structure in crash, would require over 12 days of elapsed time for a single design of a 390K elastic degrees of freedom model, if executed on a single processor of the state-of-the-art SGI Origin2000 computer. Of course, in optimization that crash analysis would have to be invoked many times. Needless to say, that has rendered such optimization intractable until now. The car finite element model is shown. The advent of computers that comprise large numbers of concurrently operating processors has created a new environment wherein the above optimization, and other engineering problems heretofore regarded as intractable may be solved. The procedure, shown, is a piecewise approximation based method and involves using a sensitivity based Taylor series approximation model for NVH and a polynomial response surface model for Crash. In that method the NVH constraints are evaluated using a finite element code (MSC/NASTRAN) that yields the constraint values and their derivatives with respect to design variables. The crash constraints are evaluated using the explicit code RADIOSS on the Origin 2000 operating on 256 processors simultaneously to generate data for a polynomial response surface in the design variable domain. The NVH constraints and their derivatives combined with the response surface for the crash constraints form an approximation to the system analysis (surrogate analysis) that enables a cycle of multidisciplinary optimization within move limits. In the inner loop, the NVH sensitivities are recomputed to update the NVH approximation model while keeping the Crash response surface constant. In every outer loop, the Crash response surface approximation is updated, including a gradual increase in the order of the response surface and the response surface extension in the direction of the search. In this optimization task, the NVH discipline has 30 design variables while the crash discipline has 20 design variables. A subset of these design variables (10) are common to both the NVH and crash disciplines. In order to construct a linear response surface for the Crash discipline constraints, a minimum of 21 design points would have to be analyzed using the RADIOSS code. On a single processor in Origin 2000 that amount of computing would require over 9 months! In this work, these runs were carried out concurrently on the Origin 2000 using multiple processors, ranging from 8 to 16, for each crash (RADIOSS) analysis. Another figure shows the wall time required for a single RADIOSS analysis using varying number of processors, as well as provides a comparison of 2 different common data placement procedures within the allotted memories for each analysis. The initial design is an infeasible design with NVH discipline Static Torsion constraint violations of over 10%. The final optimized design is a feasible design with a weight reduction of 15 kg compared to the initial design. This work demonstrates how advanced methodology for optimization combined with the technology of concurrent processing enables applications that until now were out of reach because of very long time-to-solution.

Kodiyalam, Srinivas↗