Masters Theses

Date of Award

6-1973

Degree Type

Thesis

Degree Name

Master of Science

Major

Mechanical Engineering

Major Professor

D. L. Fenton

Abstract

The purpose of this thesis is to produce and document TRAX, an improved finite element transient heat conduction program for axisymmetric or plane bodies. A finite element solution of the transient axisymmetric body heat conduction equation is demonstrated using the Euler Theorem from the calculus of variations. The basic element is chosen to be triangular in cross-section with a linear internal temperature distribution. Anisotropic conductivity at any orientation in the plane of the cross-section is included in the element formulation. Heat generation within the element is considered in the element derivation, but not included in the final formulation. A quadrilateral element is defined to be a combination of two triangular elements. Lumped heat capacity matrices are formulated for both types of element. Element conductivity matrices are formulated as derived for the triangular element. Plane body elements are allowed by assigning a value of one to the axisymmetric element centroid radius. The system matrix equation is derived. It includes boundary conditions for convection and radiation to the body surfaces, and specified temperature at any point in the body. The transient time period must be divided into a finite number of time steps in any finite element transient heat conduction analysis. In TRAX the transient time period iii is first broken into time intervals of variable length. Each time interval is then divided into an even number of time steps. iv Changes in boundary conditions, material properties, and the time parameters are allowed in TRAX at every time interval. Variation in the external fluid temperature for convection is allowed at every time step. Steady-state cases are assumed to be solutions for a particular type of time interval. A Gauss-Cholesky solution routine is used to solve the system matrix equation for the body being analyzed. Computer time requirements are minimized because factoring, the most time consuming part of this solution routine, is only required at the first time step in an interval. Object time dimensioning and overlay techniques are applied to minimize core storage requirements. Various features are included to make data input and output interpretation easy and convenient. Two example problems are solved using TRAX on an IBM 370-155 computer. The first problem verifies the validity of the solution procedure by comparison with published data. The second problem demonstrates the application of many program features.

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