Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Aerospace Engineering


Mechanical and Aerospace Engineering

First Advisor

Kent L. Lawrence


This research is concerned with the development and implementation of a family of tetrahedral elements through the fourth order. The straight-sided tetrahedral elements are developed in closed-form. This work investigates the efficiency of closed-form implementation of stiffness matrices and error estimators compared to numerical implementation. An additional objective is the compaction of closed-form source-code files which require as little storage space as possible, a more pronounced requirement at high p-levels. For the straight-sided elements through p-level 4, the stiffness matrix, equivalent nodal load vectors, and error estimators (based on nodal averaging) are developed using closed-form equations obtained through the use of a computer algebra system. The stiffness matrix and error estimators are also implemented using numerical integration so that a timing comparison between the numerical and the closed-form approaches could be performed. The curved-sided elements, including the stiffness matrix, equivalent nodal load vectors, and error estimators are also implemented using Gaussian quadrature only. A test conducted on a model of all curved-sided elements is used to verify that the elements are working correctly. Results indicate that the closed-form implementation solutions are comparable to the numerical solutions. For all p-levels the closed-form stiffness matrix is more efficient by a factor of at least 4 when compared with numerically integrated elements.


Aerospace Engineering | Engineering | Mechanical Engineering


Degree granted by The University of Texas at Arlington