ABSTRACT
The shear force V0 and the moment M0 act at L. The interpolation model, incorporating the constraints w(0, t)=−w′ (0, t)=0 a priori, is
(10.6)
The stiffness and mass matrices, due to the domain, are readily shown to be
(10.7)
The stiffness and mass contributions from the boundary conditions are
(10.8)
The governing equation is now
(10.9)
10.2 THERMAL COUNTERPART OF THE PRINCIPLE OF VIRTUAL WORK
For our purposes, we focus on the equation of conductive heat transfer as
(10.10)
Multiplying by the variation of T−T0, integrating by parts, and applying the divergence theorem furnishes
(10.11)
Now suppose that the interpolation models for temperature in the current element furnish a relation of the form
(10.12)
The terms on the left in Equation 10.11 can now be written as
(10.13)
KT and MT can be called the thermal stiffness (or conductance) matrix and thermal mass (or capacitance) matrix, respectively.
