Transient Heat Conduction Problem Using Constant Strain Triangle

2 Transient Heat Conduction Problem Using Constant Strain Triangle 

Following the procedure used with the one-dimensional FEM model and using the constant strain triangle element developed in the previous section, we can now formulate the finite element equations for a transient conduction problem with internal heat generation rate per unit volume of Q. The governing equation is given by 

If we use an implicit finite difference time stepping procedure, we must evaluate the spatial derivatives in the next time step j +1. In order to arrive at a linear set of algebraic equations that can be solved using standard matrix routines, we would the like the final set of equation to be of the form 

The element force vector (fe) is formed by the internal heat generation term and the temperatures in the previous time steps as 

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