(3 pts) d. Write down the integral expression for the A (stiffness matrix) for the heat problem for this element in terms of global x derivatives. (3 pts) e. Put the integral into a form with the integrand as a function of the local coordinate only. (3 pts) f. Indicate the matrix size of each term in that expression. (For example 2x2, 3x2, 1x1, etc.) (3 pts) g. For a constant body force term b (force per unit length) over the element, indicate how you would get the element force matrix F. 4. The "capacitance" matrix used for 2 dimensional transient heat problems will be shown next quarter to have the general form C= [[ N'Nda arru in terms of the basis functions for any 2D element. a. (3 pts) What are the basis functions for a three-noded triangle element ? b. (4 pts) Calculate the Cn and Cia components of this matrix for a three-noded triangle element. 5. (3 points each) a. Why is it not possible to have a three-noded one-dimensional element with nodes at x=0, x=0.2, x=1 ? b. State what the "0-1" property is in finite element problems. c. Why is it useful? d. What is the name of the variational principle that is the basis for the majority of FEM solutions in linear elasticity