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Several time-stepping schemes for incompressibility problems are presented which can be solved directly for steady state or iteratively through the time domain. The difficulty of mixed interpolation is avoided by using these schemes. The schemes are applicable to problems of fluid and solid mechanics.
Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensive. The methods from the second group (local ABC's) are, as a rule, algorithmically simple, numerically cheap, and geometrically universal; however, they usually lack accuracy of computations. In this paper we first present a survey and provide a comparative assessment of different existing methods for constructing the ABC's. Then, we describe a relatively new ABC's technique of ours and review the corresponding results. This new technique, in our opinion, is currently one of the most promising in the field. It enables one to construct such ABC's that combine the advantages relevant to the two aforementioned classes of existing methods. Our approach is based on application of the difference potentials method attributable to V. S. Ryaben'kii. This approach allows us to obtain highly accurate ABC's in the form of certain (nonlocal) boundary operator equations. The operators involved are analogous to the pseudodifferential boundary projections first introduced by A. P. Calderon and then also studied by R. T. Seeley. The apparatus of the boundary pseudodifferential equations, which has formerly been used mostly in the qualitative theory of integral equations and PDE'S, is now effectively employed for developing numerical methods in the different fields of scientific computing.
This chapter describes three studies on the surface design, surface engineering, and tribology of chemical-vapor-deposited (CVD) diamond films and coatings toward wear-resistant, self-lubricating diamond films and coatings. Friction mechanisms and solid lubrication mechanisms of CVD diamond are stated. Effects of an amorphous hydrogenated carbon on CVD diamond, an amorphous, nondiamond carbon surface layer formed on CVD diamond by carbon and nitrogen ion implantation, and a materials combination of cubic boron nitride and CVD diamond on the adhesion, friction, and wear behaviors of CVD diamond in ultrahigh vacuum are described. How surface modification and the selected materials couple improved the tribological functionality of coatings, giving low coefficient of friction and good wear resistance, is explained.
This research has been concerned with load diffusion in composite structures. Fundamental solid mechanics studies were carried out to provide a basis for assessing the complicated modeling necessary for large scale structures used by NASA. An understanding of the fundamental mechanisms of load diffusion in composite subcomponents is essential in developing primary composite structures. Analytical models of load diffusion behavior are extremely valuable in building an intuitive base for developing refined modeling strategies and assessing results from finite element analyses. The decay behavior of stresses and other field quantities provides a significant aid towards this process. The results are also amendable to parameter study with a large parameter space and should be useful in structural tailoring studies.
Recent progress in distributed object technology has enabled software applications to be developed and deployed easily such that objects or components can work together across the boundaries of the network, different operating systems, and different languages. A distributed object is not necessarily a complete application but rather a reusable, self-contained piece of software that co-operates with other objects in a plug-and-play fashion via a well-defined interface. The Common Object Request Broker Architecture (CORBA), a middleware standard defined by the Object Management Group (OMG), uses the Interface Definition Language (IDL) to specify such an interface for transparent communication between distributed objects. Since IDL can be mapped to any programming language, such as C++, Java, Smalltalk, etc., existing applications can be integrated into a new application and hence the tasks of code re-writing and software maintenance can be reduced. Many scientific applications in aerodynamics and solid mechanics are written in Fortran. Refitting these legacy Fortran codes with CORBA objects can increase the codes reusability. For example, scientists could link their scientific applications to vintage Fortran programs such as Partial Differential Equation(PDE) solvers in a plug-and-play fashion. Unfortunately, CORBA IDL to Fortran mapping has not been proposed and there seems to be no direct method of generating CORBA objects from Fortran without having to resort to manually writing C/C++ wrappers. In this paper, we present an efficient methodology to integrate Fortran legacy programs into a distributed object framework. Issues and strategies regarding the conversion and decomposition of Fortran codes into CORBA objects are discussed. The following diagram shows the conversion and decomposition mechanism we proposed. Our goal is to keep the Fortran codes unmodified. The conversion- aided tool takes the Fortran application program as input and helps programmers generate C/C++ header file and IDL file for wrapping the Fortran code. Programmers need to determine by themselves how to decompose the legacy application into several reusable components based on the cohesion and coupling factors among the functions and subroutines. However, programming effort still can be greatly reduced because function headings and types have been converted to C++ and IDL styles. Most Fortran applications use the COMMON block to facilitate the transfer of large amount of variables among several functions. The COMMON block plays the similar role of global variables used in C. In the CORBA-compliant programming environment, global variables can not be used to pass values between objects. One approach to dealing with this problem is to put the COMMON variables into the parameter list. We do not adopt this approach because it requires modification of the Fortran source code which violates our design consideration. Our approach is to extract the COMMON blocks and convert them into a structure-typed attribute in C++. Through attributes, each component can initialize the variables and return the computation result back to the client. We have tested successfully the proposed conversion methodology based on the f2c converter. Since f2c only translates Fortran to C, we still needed to edit the converted code to meet the C++ and IDL syntax. For example, C++/IDL requires a tag in the structure type, while C does not. In this paper, we identify the necessary changes to the f2c converter in order to directly generate the C++ header and the IDL file. Our future work is to add GUI interface to ease the decomposition task by simply dragging and dropping icons.
We analyze the onset of "necking" and subsequent filament failure during the transient uniaxial elongation of viscoelastic fluid samples in extensional rheometers. In the limit of rapid elongation (such that no molecular relaxation occurs), the external work applied is all stored elastically and the Considere criterion originally developed in solid mechanics can be used to quantitatively predict the critical Hencky strain to failure. By comparing the predictions of the Doi-Edwards model for linear homopolymer melts with those of the "Pom-Pom" model for prototypical branched melts we show that the critical strain to failure in rapid elongation of a rubbery material is intimately linked to the molecular topology of the chain, especially the degree of chain branching. The onset of necking instability is monotonically shifted to larger Hencky strains as the number of branches is increased. Numerical computations at finite Deborah numbers also show that there is an optimal range of deformation rates over which homogeneous extensions can be maintained to large strain. We also consider other rapid homogeneous stretching deformations, such as biaxial and planar stretching, and show that the degree of stabilization afforded by inclusion of material with long-chain branching is a sensitive function of the imposed mode of deformation.
A method has been developed for modeling structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with an equivalent-continuum model. It has been shown that this substitution may be accomplished by equating the vibrational potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As an important example with direct application to the development and characterization of single-walled carbon nanotubes, the model has been applied to determine the effective continuum geometry of a graphene sheet. A representative volume element of the equivalent-continuum model has been developed with an effective thickness. This effective thickness has been shown to be similar to, but slightly smaller than, the interatomic spacing of graphite.
Many scientific applications in aerodynamics and solid mechanics are written in Fortran. Refitting these legacy Fortran codes with distributed objects can increase the code reusability. The remote variable scheme provided in NPSS/CCDK helps programmers easily migrate the Fortran codes towards a client-server platform. This scheme gives the client the capability of accessing the variables at the server site. In this paper, we review and enhance the remote variable scheme by using the operator overloading features in C++. The enhancement enables NPSS programmers to use remote variables in much the same way as traditional variables. The remote variable scheme adopts the lazy update approach and the prefetch method. The design strategies and implementation techniques are described in details. Preliminary performance evaluation shows that communication overhead can be greatly reduced.
The objective of the First MIT Conference on Computational Fluid and Solid Mechanics (June 12-14, 2001) is to bring together industry and academia (and government) to nurture the next generation in computational mechanics. The objective of the current talk, 'High-End Computing for Incompressible Flows', is to discuss some of the current issues in large scale computing for mission-oriented tasks.
The research carried out here builds on our previous NASA supported research on the general topic of edge effects and load diffusion in composite structures. Further fundamental solid mechanics studies were carried out to provide a basis for assessing the complicated modeling necessary for large scale structures used by NASA. An understanding of the fundamental mechanisms of load diffusion in composite subcomponents is essential in developing primary composite structures. Specific problems recently considered were focussed on end effects in sandwich structures and for functionally graded materials. Both linear and nonlinear (geometric and material) problems have been addressed. Our goal is the development of readily applicable design formulas for the decay lengths in terms of non-dimensional material and geometric parameters. Analytical models of load diffusion behavior are extremely valuable in building an intuitive base for developing refined modeling strategies and assessing results from finite element analyses. The decay behavior of stresses and other field quantities provides a significant aid towards this process. The analysis is also amenable to parameter study with a large parameter space and should be useful in structural tailoring studies.
The theory of strain compatibility of the solid mechanics discipline was incomplete since St. Venant's 'strain formulation' in 1876. We have addressed the compatibility condition both in the continuum and the discrete system. This has lead to the formulation of the Integrated Force Method. A dual Integrated Force Method with displacement as the primal variable has also been formulated. A modest finite element code (IFM/Analyzers) based on the IFM theory has been developed. For a set of standard test problems the IFM results were compared with the stiffness method solutions and the MSC/Nastran code. For the problems IFM outperformed the existing methods. Superior IFM performance is attributed to simultaneous compliance of equilibrium equation and compatibility condition. MSC/Nastran organization expressed reluctance to accept the high fidelity IFM solutions. This report discusses the solutions to the examples. No inaccuracy was detected in the IFM solutions. A stiffness method code with a small programming effort can be improved to reap the many IFM benefits when implemented with the IFMD elements. Dr. Halford conducted a peer-review on the Integrated Force Method. Reviewers' response is included.
A method has been proposed for developing structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with equivalent-continuum models. It has been shown that this substitution may be accomplished by equating the vibrational potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As important examples with direct application to the development and characterization of single-walled carbon nanotubes and the design of nanotube-based devices, the modeling technique has been applied to determine the effective-continuum geometry and bending rigidity of a graphene sheet. A representative volume element of the chemical structure of graphene has been substituted with equivalent-truss and equivalent continuum models. As a result, an effective thickness of the continuum model has been determined. This effective thickness has been shown to be significantly larger than the interatomic spacing of graphite. The effective thickness has been shown to be significantly larger than the inter-planar spacing of graphite. The effective bending rigidity of the equivalent-continuum model of a graphene sheet was determined by equating the vibrational potential energy of the molecular model of a graphene sheet subjected to cylindrical bending with the strain energy of an equivalent continuum plate subjected to cylindrical bending.
The work presented here concerns the numerical development and simulation of the flow, pressure patterns and motion of a pair of fingers arranged behind each other and axially aligned in-line. The fingers represent the basic elemental component of a Finger Seal (FS) and form a tight seal around the rotor. Yet their flexibility allows compliance with rotor motion and in a passive-adaptive mode complies also with the hydrodynamic forces induced by the flowing fluid. While the paper does not treat the actual staggered configuration of a finger seal, the inline arrangement represents a first step towards that final goal. The numerical 2-D (axial-radial) and 3-D results presented herein were obtained using a commercial package (CFD-ACE+). Both models use an integrated numerical approach, which couples the hydrodynamic fluid model (Navier-Stokes based) to the solid mechanics code that models the compliance of the fingers.
In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.
Within NASA's Aviation Safety Program, NASA GRC participates in the Modeling and Simulation Project called ASMM. NASA GRC s focus is to characterize the propulsion systems performance from a fleet management and maintenance perspective by modeling and through simulation predict the characteristics of two classes of commercial engines (CFM56 and GE90). In prior years, the High Performance Computing and Communication (HPCC) program funded, NASA Glenn in developing a large scale, detailed simulations for the analysis and design of aircraft engines called the Numerical Propulsion System Simulation (NPSS). Three major aspects of this modeling included the integration of different engine components, coupling of multiple disciplines, and engine component zooming at appropriate level fidelity, require relatively tight coupling of different analysis codes. Most of these codes in aerodynamics and solid mechanics are written in Fortran. Refitting these legacy Fortran codes with distributed objects can increase these codes reusability. Aviation Safety s modeling and simulation use in characterizing fleet management has similar needs. The modeling and simulation of these propulsion systems use existing Fortran and C codes that are instrumental in determining the performance of the fleet. The research centers on building a CORBA-based development environment for programmers to easily wrap and couple legacy Fortran codes. This environment consists of a C++ wrapper library to hide the details of CORBA and an efficient remote variable scheme to facilitate data exchange between the client and the server model. Additionally, a Web Service model should also be constructed for evaluation of this technology s use over the next two- three years.
Using automated and standardized computer tools to calculate the pertinent test result values has several advantages such as: 1. allowing high-fidelity solutions to complex nonlinear phenomena that would be impractical to express in written equation form, 2. eliminating errors associated with the interpretation and programing of analysis procedures from the text of test standards, 3. lessening the need for expertise in the areas of solid mechanics, fracture mechanics, numerical methods, and/or finite element modeling, to achieve sound results, 4. and providing one computer tool and/or one set of solutions for all users for a more "standardized" answer. In summary, this approach allows a non-expert with rudimentary training to get the best practical solution based on the latest understanding with minimum difficulty.Other existing ASTM standards that cover complicated phenomena use standard computer programs: 1. ASTM C1340/C1340M-10- Standard Practice for Estimation of Heat Gain or Loss Through Ceilings Under Attics Containing Radiant Barriers by Use of a Computer Program 2. ASTM F 2815 - Standard Practice for Chemical Permeation through Protective Clothing Materials: Testing Data Analysis by Use of a Computer Program 3. ASTM E2807 - Standard Specification for 3D Imaging Data Exchange, Version 1.0 The verification, validation, and round-robin processes required of a computer tool closely parallel the methods that are used to ensure the solution validity for equations included in test standard. The use of automated analysis tools allows the creation and practical implementation of advanced fracture mechanics test standards that capture the physics of a nonlinear fracture mechanics problem without adding undue burden or expense to the user. The presented approach forms a bridge between the equation-based fracture testing standards of today and the next generation of standards solving complex problems through analysis automation.
Motivation: (1) The activation of pyroshock devices such as explosives, separation nuts, pin-pullers, etc. produces high frequency transient structural response, typically from few tens of Hz to several hundreds of kHz. (2) Lack of reliable analytical tools makes the prediction of appropriate design and qualification test levels a challenge. (3) In the past few decades, several attempts have been made to develop methodologies that predict the structural responses to shock environments. (4) Currently, there is no validated approach that is viable to predict shock environments overt the full frequency range (i.e., ~100 Hz to 10 kHz). Scope: (1) Model, analyze, and interpret space structural systems with complex interfaces and discontinuities, subjected to shock loads. (2) Assess the viability of a suite of numerical tools to simulate transient, non-linear solid mechanics and structural dynamics problems, such as shock wave propagation.