Author Type

Graduate Student

Date of Award

1989

Document Type

Thesis

Publication Status

Version of Record

Submission Date

October 2026

Thesis/Dissertation Advisor [Chair]

Case, Robert O.

Abstract

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.

Extent

167 p.

Comments

College of Engineering and Computer Science|Thesis (Ph.D.)--Florida Atlantic University, 1989.|FAU Electronic Theses and Dissertations Collection|College of Engineering and Computer Science

Identifier

FADT11934

Format

pdf

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