Case, Robert O.

This study presents the equations of motion for nine multiply separated precision point synthesis of coplanar four bar linkages. A computer program called NINEPT is introduced which employs the equations of motion to solve the problem of nine finitely separated precision point synthesis. The algorithms of NINEPT are described in detail and a program listing is provided.

The finite element method is a very powerful tool used to analyze a variety of problems in engineering. This thesis looks at the finite element method as a tool and several important modeling features of concern. A well known finite element software package, ANSYS, will be used to demonstrate a diverse number of its capabilities, and several procedures followed in solving a specific engineering problem. The subject matter involves a nonlinear contact analysis of a pressure vessel having a threaded closure. The choice of this application is prompted by an interest in better understanding how the finite element method is implemented in the design and analysis of different pressure vessel parameters. A parametric finite element analysis was performed. Load and stress distributions along the threaded region of the vessel were examined for parameters including number of threads, thread pitch, diameter ratio, closure plug length, and thread profile.

This thesis deals with the static analysis of a three dimensional underwater acoustic tower exclusively designed and fabricated by Harbor Branch Oceanographic Institution, Ft. Pierce, Florida. A commercial finite element package COSMOS/M was used for the finite element analysis. The structural modeling as well as processing of the results was performed using GEOSTAR Ver. 1.65 interactive graphics package. The analysis was concentrated on the main instrument pipe carrying the required instruments for data acquisition. Various environmental loading induced by ocean currents, hydrostatic pressure, buoyancy and self weight of the tower have been considered in the analysis. The construction aspects of the tower as well as the finite element analysis of tower substructures are also discussed. The deflection of the tower due to the imposed loading is studied and deflection profiles are drawn.

This paper studies the stress concentrations at the root of the threads of a cylinder. A photoelastic analysis using the stress freezing procedure is used to calculate the stress along the cylinder and the stress concentrations at the root of the threads. These values are compared to that of similar cylinders with different threaded configurations. A finite element model is built by using the photoelastic data to find a suitable load distribution along the threaded region. The finite element model predicted results similar to the photoelastic analysis and showed a method of reducing the stress concentrations on the threads by redesigning a pressure ring on the cylinder.

Three-dimensional photoelastic stress analysis techniques are used to determine the stress distribution in
a metal-to-metal contact bolted flange. The flange belongs
to a thin-walled stage support casing of a jet aircraft
engine. Of special interest is the state of stress
experienced at flange separation due to axial and bending
loads during severe in-flight maneuvering. Details of model
development, data collection and discussion of results for
the stresses in the bolts and in the vicinity of the flange
are presented.

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.

Equations of stress-difference elasticity, derived from the equations of equilibrium and compatibility for a two-dimensional stress field, are solved for arbitrarily digitized, singly and multiply connected domains. Photoelastic data determined experimentally along the boundary provide the boundary values for the solution of the three elliptic partial differential equations by the finite difference method. A computerized method is developed to generate grid mesh, weighting functions and nodal connectivity within the digitized boundary for the solution of these partial differential equations. A method is introduced to digitize the photoelastic fringes, namely isochromatics and isoclinics, and to estimate the values of sigma1 - sigma2, sigma x - sigma y and tau xy at each nodal point by an interpolation technique. Interpolated values of the stress parameters are used to improve the initial estimate and hence the convergence of the iterative solution of the system of equations. Superfluous boundary conditions are added from the digitized photoelastic data for further speeding up the rate of convergence. The boundary of the domain and the photoelastic fringes are digitized by physically traversing the cursor along the boundary, and the digitized information is scanned horizontally and vertically to generate internal and boundary nodal points. A linear search determines the nodal connectivity and isolates the boundary points for the input of the boundary values. A similar scanning method estimates the photoelastic parameters at each nodal point and also finds the points closest to the tint of passage of each photoelastic fringe. Stress values at these close points are determined without interpolation and are subsequently used as superfluous boundary conditions in the iteration scheme. Successive over-relaxation is applied to the classical Gauss-Seidel method for final enhancement of the convergence of the iteration process. The iteration scheme starts with an accelerating factor other than unity and estimates the spectral radius of the iteration matrix from the two vector norms. This information is used to estimate a temporary value of the optimum relaxation parameter, omega[opt], which is used for a fixed number of iterations to approximate a better value of the accelerating factor. The process is continued until two successive estimates differ by a given tolerance or the stopping criteria are reached. Detailed techniques of developing the code for mesh generation, photoelastic data collection and boundary value interpolation to solve the elliptic boundary value problems are presented. Three separate examples with varying stress gradients and fringe patterns are presented to test the validity of the code and the overall method. Results are compared with the analytical and experimental solutions, and the significant improvement in the rate of convergence is demonstrated.