Document Type
Thesis
Date of Award
5-31-1984
Degree Name
Master of Science in Mechanical Engineering - (M.S.)
Department
Mechanical Engineering
First Advisor
Rong-Yaw Chen
Second Advisor
Sachio Nakamura
Third Advisor
Jui Sheng Hsieh
Abstract
The finite element formulation of plane elasticity and plate bending is presented and is employed in the development of the formulation of element stiffness equations and structural stiffness equations. The basic relations used to derive the finite element equations for a solid continuum are also presented. The programming organization is summarized.
The computer program cited from TAYLOR has been used to solve the deep beam problem with triangular and rectangular elements and the SAP IV program has been used to solve the plate bending problems with quadrilateral elements. Problems solved are: (1) stress distribution at the midspan of a simply supported deep beam with uniform load, (2) deflections and stresses in a rectangular plate with uniform load throughout the plate, with uniform load on the central rectangular area of the plate, and with linearly increasing load over the rectangular plate and (3) deflections and stresses in a rectangular plate with all edges clamped under uniform load condition.
Finally, the results obtained from the finite element solutions are compared with those obtained from exact solutions for the rectangular plate. Then, the effect of the number of elements on convergence to the analytical solution is investigated. As the number of elements is increased from 9 to 144, the error in deflection was reduced from 35-40% to 1-3% and the error in stress was reduced from 20-25% to 1-5%. These examples have clearly shown that as the number of elements is increased, the results converge to the exact solutions.
Recommended Citation
Jen, Yao-Zong, "The application of the finite element method to plate stress analysis" (1984). Theses. 3569.
https://digitalcommons.njit.edu/theses/3569
