ABSTRACT

Substituting Eqs. (12.124) and (12.125) into Eqs. (12.122) and (12.123), respectively, gives

(I2.126a)

(12.126b)

Equation (12.126) requires the functions y(x) ,y'(x), NF)(x), and N;~I (x), which are given by Eqs. (12.121), (12.86), and (12.120). Substituting all of these expressions into Eq. (12.126), evaluating Q(x) and F(x) as average values for each element as done in Eqs. (12.90) and (12.191), integrating, and evaluating the results at the limits of integration yields the two element equations:

y(_1 + gil tu;) _ Y I (_I _(P tu;) _ PU) tu; = 0 1 tu; 6 ,+ tu; 3 2

(12.127a)

(12.I27b)

Equation (12.127) is valid for nonuniform tu. Letting tu; = tu = constant and multiplying through by tu yields

( Q(il tu2) (QUl tu2) PU) tu2-y. 1 - +y. I 1+ - -- = 01 3 1+ 6 2 ( QU) tu

(I2.128a)

(12.128b)