p-Version Three Dimensional Solid Element for Heat Conduction

by Karan S. Surana, Univ of Kansas, Lawrence, United States,
Kuen W. Teong, Univ of Kansas, Lawrence, United States,

Document Type: Proceeding Paper

Part of: Mechanics Computing in 1990's and Beyond


This paper presents a finite element formulation for a three dimensional twenty-seven node hierarchical solid element for heat condition where the element temperature approximation can be of arbitrary polynomial orders pxi, peta and pζ in the ξ, η, and ζ directions. The element approximation functions and the corresponding nodal variables are derived directly from the one dimensional Lagrange interpolation functions of order pxi, peta and pζ and thus they automatically satisfy completeness requirement. The formulation ensures C° continuity. The element properties are derived using the weak formulation (or the quadratic functional) of the three dimensional Fourier heat conduction equation. Numerical examples are presented and comparisons are made with h-models using twenty node isoparametric solid elements.

Subject Headings: Finite element method | Heat transfer | Approximation methods | Lagrangian functions | Numerical methods | Temperature distribution | Temperature effects | Arbitration

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