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Transient one-dimensional heat conduction problems solved by finite element. (English) Zbl 1192.74094
Summary: This paper establishes a solution method for the one-dimensional (1D) transient temperature and thermal stress fields in non-homogeneous materials. Finite-element method is used to space discretization, which results in a system of first-order differential equations. Transient solutions of these differential equations are obtained via either direct numerical difference or mode superposition. The formulation and system of equations are established in a very concise way. For 1D plates, axially symmetric cylinders and rotationally symmetric spheres, explicit expressions are given and the corresponding finite-element formulations are easily programmed. Moreover, stress analysis can be made from the calculated temperature field. Some sample examples are provided to show the applicability and effect of the proposed method.

MSC:
74F05 Thermal effects in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74S20 Finite difference methods applied to problems in solid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
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