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By Baur F.

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10) at node 3 SOME BASIC DISCRETE SYSTEMS 21 where h is the heat transfer coefficient and Ta is the ambient temperature. 13 gives the unknown temperatures T1 , T2 and T3 . In the case of heat conduction, there is only one degree of freedom at each node as temperature is a scalar. 13 should be observed. 14) • where Q is the total heat flow and is constant. • The global stiffness matrix [K] can be obtained by assembling the stiffness matrices of each layer and the result is a symmetric and positive definite matrix.

Also, from the following data, calculate the temperature distribution in the composite wall. 0 m2 . 5 W/mK. 0 ◦ C. 10. The inner and outer radii of the pipe are r1 and r2 respectively. The thickness of the insulating material is r2 − r3 . Assume appropriate conditions and form the discrete system equations. 11. The flow rate at the entrance is Qm3 /s. Neglecting any loss of mass, construct a system of simultaneous equations to calculate the pressure distribution at selected points using a discrete system analysis.

1 Introduction The finite element method is a numerical tool for determining approximate solutions to a large class of engineering problems. The method was originally developed to study the stresses in complex air-frame structures (Clough 1960) and was later extended to the general field of continuum mechanics (Zienkiewicz and Cheung 1965). There have been many articles on the history of finite elements written by numerous authors with conflicting opinions on the origins of the technique (Gupta and Meek 1996; Oden 1996; Zienkiewicz 1996).

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2-summing operators and L (2)(2)-systems by Baur F.

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