Numerical methods and computers used in elastohydrodynamic lubrication

Some of the methods of obtaining approximate numerical solutions to boundary value problems that arise in elastohydrodynamic lubrication are reviewed. The highlights of four general approaches (direct, inverse, quasi-inverse, and Newton-Raphson) are sketched. Advantages and disadvantages of these approaches are presented along with a flow chart showing some of the details of each. The basic question of numerical stability of the elastohydrodynamic lubrication solutions, especially in the pressure spike region, is considered. Computers used to solve this important class of lubrication problems are briefly described, with emphasis on supercomputers

Computational Methods for Nonlinear Systems Analysis With Applications in Mathematics and Engineering

An investigation into current methods and new approaches for solving systems of nonlinear equations was performed. Nontraditional methods for implementing arc-length type solvers were developed in search of a more robust capability for solving general systems of nonlinear algebraic equations. Processes for construction of parameterized curves representing the many possible solutions to systems of equations versus finding single or point solutions were established. A procedure based on these methods was then developed to identify static equilibrium states for solutions to multi-body-dynamic systems. This methodology provided for a pictorial of the overall solution to a given system, which demonstrated the possibility of multiple candidate equilibrium states for which a procedure for selection of the proper state was proposed. Arc-length solvers were found to identify and more readily trace solution curves as compared to other solvers making such an approach practical. Comparison of proposed methods was made to existing methods found in the literature and commercial software with favorable results. Finally, means for parallel processing of the Jacobian matrix inherent to the arc-length and other nonlinear solvers were investigated, and an efficient approach for implementation was identified. Several case studies were performed to substantiate results. Commercial software was also used in some instances for additional results verification

Aircraft interior noise reduction by alternate resonance tuning

Existing interior noise reduction techniques for aircraft fuselages perform reasonably well at higher frequencies, but are inadequate at lower, particularly with respect to the low blade passage harmonics with high forcing levels found in propeller aircraft. A method is being studied which considers aircraft fuselages lines with panels alternately tuned to frequencies above and below the frequency to be attenuated. Adjacent panels would oscillate at equal amplitude, to give equal source strength, but with opposite phase. Provided these adjacent panels are acoustically compact, the resulting cancellation causes the interior acoustic modes to become cut off and therefore be non-propagating and evanescent. This interior noise reduction method, called Alternate Resonance Tuning (ART), is currently being investigated both theoretically and experimentally. This new concept has potential application to reducing interior noise due to the propellers in advanced turboprop aircraft as well as for existing aircraft configurations. This program summarizes the work carried out at Duke University during the third semester of a contract supported by the Structural Acoustics Branch at NASA Langley Research Center

A modeling framework for contact, adhesion and mechano-transduction between excitable deformable cells

Cardiac myocytes are the fundamental cells composing the heart muscle. The propagation of electric signals and chemical quantities through them is responsible for their nonlinear contraction and dilatation. In this study, a theoretical model and a finite element formulation are proposed for the simulation of adhesive contact interactions between myocytes across the so-called gap junctions. A multi-field interface constitutive law is proposed for their description, integrating the adhesive and contact mechanical response with their electrophysiological behavior. From the computational point of view, the initial and boundary value problem is formulated as a structure-structure interaction problem, which leads to a straightforward implementation amenable for parallel computations. Numerical tests are conducted on different couples of myocytes, characterized by different shapes related to their stages of growth, capturing the experimental response. The proposed framework is expected to have impact on the understanding how imperfect mechano-transduction could lead to emergent pathological responses.Comment: 31 pages, 17 figure

An adaptive learning control system for aircraft

A learning control system and its utilization as a flight control system for F-8 Digital Fly-By-Wire (DFBW) research aircraft is studied. The system has the ability to adjust a gain schedule to account for changing plant characteristics and to improve its performance and the plant's performance in the course of its own operation. Three subsystems are detailed: (1) the information acquisition subsystem which identifies the plant's parameters at a given operating condition; (2) the learning algorithm subsystem which relates the identified parameters to predetermined analytical expressions describing the behavior of the parameters over a range of operating conditions; and (3) the memory and control process subsystem which consists of the collection of updated coefficients (memory) and the derived control laws. Simulation experiments indicate that the learning control system is effective in compensating for parameter variations caused by changes in flight conditions

Effects of finite strains in fully coupled 3D geomechanical simulations

Numerical modeling of geomechanical phenomena and geo-engineering problems often involves complex issues related to several variables and corresponding coupling effects. Under certain circumstances, both soil and rock may experience a nonlinear material response caused by, for example, plastic, viscous, or damage behavior or even a nonlinear geometric response due to large deformations or displacements of the solid. Furthermore, the presence of one or more fluids (water, oil, gas, etc.) within the skeleton must be taken into account when evaluating the interaction between the different phases of the continuum body. A multiphase three-dimensional (3D) coupled model of finite strains, suitable for dealing with solid-displacement and fluid-diffusion problems, is described for assumed elastoplastic behavior of the solid phase. Particularly, a 3D mixed finite element was implemented to fulfill stability requirements of the adopted formulation, and a permeability tensor dependent on deformation is introduced. A consolidation scenario induced by silo filling was investigated, and the effects of the adoption of finite strains are discusse

Aircraft interior noise reduction by alternate resonance tuning

Model problem development and analysis continues with the Alternate Resonance Tuning (ART) concept. The various topics described are presently at different stages of completion: investigation of the effectiveness of the ART concept under an external propagating pressure field associated with propeller passage by the fuselage; analysis of ART performance with a double panel wall mounted in a flexible frame model; development of a data fitting scheme using a branch analysis with a Newton-Raphson scheme in multiple dimensions to determine values of critical parameters in the actual experimental apparatus; and investigation of the ART effect with real panels as opposed to the spring-mass-damper systems currently used in much of the theory

Automatic implementation of material laws: Jacobian calculation in a finite element code with TAPENADE

In an effort to increase the versatility of finite element codes, we explore the possibility of automatically creating the Jacobian matrix necessary for the gradient-based solution of nonlinear systems of equations. Particularly, we aim to assess the feasibility of employing the automatic differentiation tool TAPENADE for this purpose on a large Fortran codebase that is the result of many years of continuous development. As a starting point we will describe the special structure of finite element codes and the implications that this code design carries for an efficient calculation of the Jacobian matrix. We will also propose a first approach towards improving the efficiency of such a method. Finally, we will present a functioning method for the automatic implementation of the Jacobian calculation in a finite element software, but will also point out important shortcomings that will have to be addressed in the future.Comment: 17 pages, 9 figure