PARAMETRIC CONTINUOUS CRACK TIP BOUNDARY ELEMENTS IN LINEAR ELASTIC FRACTURE MECHANICS By HAROLD GRAYSON }"ALTERS' Bachelor of Science in Mechanical Engineering Louisiana State University Baton Rouge, Louisiana 1984 Master of Science in Mechanical Engineering Louisiana State University Baton Rouge, Louisiana 1986 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requiremep.ts for the Degree of DOCTOR OF PHILOSOPHY May, 1990