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

Abstract:

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 p_xi, p_eta and p_ζ 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 p_xi, p_eta and p_ζ 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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