Finite element method

The development of a parallel data structure and an associated elemental decomposition algorithm for explicit finite element analysis for massively parallel SIMD computer, the DECmpp 12000 (MasPar MP-1) machine, is presented, and then extended to implementation on the MIMD computer, Cray-T3D. The new parallel data structure and elemental decomposition algorithm are discussed in detail and is used to parallelize a sequential Fortran code that deals with the application of isoparametric elements for the nonlinear dynamic analysis of shells of revolution. The parallel algorithm required the development of a new procedure, called an 'exchange', which consists of an exchange of nodal forces at each time step to replace the standard gather-assembly operations in sequential code. In addition, the data was reconfigured so that all nodal variables associated with an element are stored in a processor along with other element data. The architectural and Fortran programming language features of the MasPar MP-1 and Cray-T3D computers which are pertinent to finite element computations are also summarized, and sample code segments are provided to illustrate programming in a data parallel environment. The governing equations, the finite element discretization and a comparison between their implementation on Von Neumann and SIMD-MIMD parallel computers are discussed to demonstrate their applicability and the important differences in the new algorithm. Various large scale transient problems are solved using the parallel data structure and elemental decomposition algorithm and measured performances are presented and analyzed in detail. Results show that Cray-T3D is a very promising parallel computer for finite element computation. The 32 processors of this machine shows an overall speedup of 27-28, i.e. an efficiency of 85% or more and 128 processors shows a speedup of 70-77, i.e. an efficiency of 55% or more. The Cray-T3D results demonstrated that this machine is capable of outperforming the Cray-YMP by a factor of about 10 for finite element problems with 4K elements, therefore, the method of developing the parallel data structure and its associated elemental decomposition algorithm is recommended for implementation on other finite element code in this machine. However, the results from MasPar MP-1 show that this new algorithm for explicit finite element computations do not produce very efficient parallel code on this computer and therefore, the new data structure is not recommended for further use on this MasPar machine.

The response of fluid-loaded plates has been extensively studied in the past.
However, most of the work deals with either infinite plates or finite plates with particular
boundary conditions and the results are generally presented only in the limit of small
wavelengths compared with the dimensions of the plates. Furthermore, the problem of
coupled finite plates where both the acoustic interaction and structural interaction are
included in the solution has not been considered. In this dissertation the response of two
coupled finite plates set in two alternative configurations is considered. The plates are
simply supported on two edges, with arbitrary boundary conditions on the remaining two
edges. The solutions obtained for the response of the plates include both the structural
interaction at the common junction and the acoustic interaction due to the scattered
pressure from each of the two plates. The results are presented in terms of the vibrational
power flow into and out of each plate component. The solution is based on a formulation developed in the wavenumber domain
combined with the Mobility Power Flow method. Using this approach, different
substructural elements coupled under different boundary conditions to form a complex
global structure can be considered. The detailed spatial and temporal scales of the structure response are not lost when using this method.
In obtaining the solution for the scattering from the fluid-loaded plates, a modal
decomposition in the direction normal to the simply supported edge is used. A spatial
Fourier-transform decomposition is used in the other direction. Due to the finiteness of
the plate, eight unknowns parameters are obtained in the transformed result. The solution
for these eight unknown parameters is obtained from the boundary conditions and the
condition that the response must remain finite. Two analytical approaches are used to
solve the final plate integral equation. The first approach consists of an approximation
method which obtains a solution based on the solution of the corresponding infinite plate
problem. The second approach is a more accurate solution based on the Projection
Method for the solution of integral equations.
Both of the approaches used in the solution provide accurate predictions at high
frequencies. At low frequencies especially for low structural damping or for heavy fluid
loading, only the Projection Method gives reliable results. This is attributed to the fact
that at low frequencies, the influence of the edges of the plates on the scattering is
significant.
The overall results obtained from this analysis indicate that the fluid loading and
the plate characteristics have a significant influence on the acoustic scattering properties,
especially in the case of heavy fluid loading.
The application of the method to coupled fluid-loaded plates indicates that the junction
enhances the scattering properties. The acoustical interaction between the coupled plates
increases the contribution to scattering from subsonic wavenumber components. In the
absence of the interaction, only supersonic wavenumbers contribute to the scattering.
Inclusion of acousticlal interaction requires both supersonic and subsonic components.
The significance of the contribution from the subsonic wavenumber components is
dependent on the type of the fluid loading.

This dissertation is concerned with modal analysis of plates with properties which vary over the structures. The uncertain geometric and material parameters are treated as random fields which are discretized over individual regions by using a local averaging technique. These discretized properties are then combined with a random perturbation procedure based upon traditional finite element methods. The result is a stochastic finite element method (SFEM) program for modal analysis of plates. This SFEM method is applied to two problems areas. The first application is to provide a new approach for modal analysis of printed circuit boards wherein the circuit board is modeled as an elastic plate with random spatial variation of its properties. The SFEM program is used to predict the effect of this variation on the natural frequencies and mode shapes of the board. Predicted results are compared with those obtained from modal testing of a circuit board. It is shown that variations between the measured and predicted modal parameters can be accounted for by small random variations in the board properties. This approach offers a simple, realistic, and cost-effective way for prediction of board modal properties. The second application is on vibration control of plates by application of surface viscoelastic damping treatments. Existing works generally treat the geometric and material properties of the damping layer as deterministic parameters, although uncertainties in the values of these parameters are commonplace. No work has been done regarding surface damping treatments with uncertain properties. In this thesis, the modal properties of plates with random spatial variation of the damping layer properties are investigated. The effects of this variation on the system natural frequencies, modal loss factors, and mode shapes are calculated by the SFEM program developed. Results are presented for a cantilever aluminum plate with complete PVC surface damping treatment with uncertain properties. In the SFEM modeling of both PC boards and plates with surface damping treatments, the effects on the system eigenvalues/eigenvectors of the correlation distance of the random property field, the correlation constant between the random fluctuations, and the magnitude of the random property variations, are investigated.

Two-dimensional and three-dimensional methodologies are developed to determine the dislocation multiplication in microelectronic and optoelectronic devices/circuits. A two-dimensional finite element code is developed to simulate the dislocation multiplication in microelectronic and optoelectronic devices/circuits. Example two-dimensional analyses are performed and analysis results are presented. The three-dimensional methodology is successfully implemented using ANSYS APDL Language within the ANSYS program. A three dimensional heterojunction bipolar transistor model is generated. CFD-thermal and structural analyses are performed to determine temperature fields and dislocation densities, which are calculated as functions of time, thickness of the thermal shunt, and heat generation rates.

The artificial ankle joint implant has been developed since 1970 after the relatively successful total hip and knee arthroplasty. The main goal of ankle replacement is to eliminate pain and preserve joint motion. Unfortunately, total ankle replacement (TAR) has not been effective as implant of other joints. Recently, published studies of early series showed that the newer second-generation ankle prosthesis have been improved with time. However, only one of the three current ankle designs is allowed by FDA to be used widely in the U.S. This study provides a new ankle design with an advanced approach in designs, biomechanical rationale, and implantation using finite element method (FEM). The new ankle prosthesis in designed to be optimal in terms of ultimate stress, implant parameter that correlating with minimal bone removal using finite element model created from CT scan. In addition, its implantation is less invasive and traumatic compared to the current TAR with longer expecting service life time. Case study showed that the thickness meniscus of the new ankle design obtained from FEM is well within the recommendation ranges by the expert in the ankle joint implantation field.

The Center for Ocean Energy Technology at Florida Atlantic University is developing an ocean energy turbine system to investigate the feasibility of harnessing Florida's Gulf Stream current kinetic energy and transforming it into a usable form. The turbine system has components which are prone to marine corrosion given the materials they are made of and to the harsh environment they will be exposed to. This study assumes a two-part system composed of a coating system acting as a barrier and sacrificial anode cathodic protection which polarizes the metal structures to a potential value where corrosion is significantly reduced. Several configurations (varying in anode quantity, size and location) were considered in order to cathodically protect the structures with various coating qualities (poor, good and excellent). These cases were modeled and simulated via Boundary Element Method software and analyzed so as to assess the most appropriate design.

Preventing bad things from happening to engineered systems, demands improvements to how we model their operation with regard to safety. Safety-critical and fiscally-critical systems both demand automated and exhaustive verification, which is only possible if the models of these systems, along with the number of scenarios spawned from these models, are tractably finite. To this end, this dissertation ad dresses problems of a model's tractability and usefulness. It addresses the state space minimization problem by initially considering tradeoffs between state space size and level of detail or fidelity. It then considers the problem of human interpretation in model capture from system artifacts, by seeking to automate model capture. It introduces human control over level of detail and hence state space size during model capture. Rendering that model in a manner that can guide human decision making is also addressed, as is an automated assessment of system timeliness. Finally, it addresses state compression and abstraction using logical fault models like fault trees, which enable exhaustive verification of larger systems by subsequent use of transition fault models like Petri nets, timed automata, and process algebraic expressions. To illustrate these ideas, this dissertation considers two very different applications - web service compositions and submerged ocean machinery.

The main objective of the thesis is to carry out a rigorous hydrodynamic analysis of ocean current turbines and determine power for a range of flow and geometric parameters. For the purpose, a computational tool based on the vortex lattice method (VLM) is developed. Velocity of the flow on the turbine blades, in relation to the freestream velocity, is determined through induction factors. The geometry of trailing vortices is taken to be helicoidal. The VLM code is validated by comparing its results with other theoretical and experimental data corresponding to flows about finite-aspect ratio foils, swept wings and a marine current turbine. The validated code is then used to study the performance of the prototype gulfstream turbine for a range of parameters. Power and thrust coefficients are calculated for a range of tip speed ratios and pitch angles. Of all the cases studied, the one corresponding to tip speed ratio of 8 and uniform pitch angle 20 produced the maximum power of 41.3 [kW] in a current of 1.73 [m/s]. The corresponding power coefficient is 0.45 which is slightly less than the Betz limit power coefficient of 0.5926. The VLM computational tool developed for the research is found to be quite efficient in that it takes only a fraction of a minute on a regular laptop PC to complete a run. The tool can therefore be efficiently used or integrated into software for design optimization.

We discuss piezoelectric and piezoceramic material as well as ultrasound transducers. We study the analytical methods for calculating the impedance of a simple bar of piezoceramic material and a simple ultrasound transducer, and discuss the methodology behind the numerical technique (Finite Element Method) to model a complex ultrasound transducer. With a simple ultrasound transducer model created in the software program PZex, we find out how the impedance is aected when the scale of the relative permittivity is varied. We then create a working model of a complex ultrasound transducer and learn how impedance is affected by varying the size of the electrode driven and adding a propagation layer. We saw that there was not a direct relationship between varying the relative permittivity and the change in impedance as we expected. We saw that varying the size of the electrode and adding a propagation layer created expected impedances.