Page 269 - Marine Structural Design

Chapter 12 A Theory of Nonlinear Finite Element Analysis 245

Figure A.9 Move Direction of Center for Yield Surface

The yield function for kinematic hardening rule is defined as,
f = f ((0) - 1) (A.25)
where, (a, } is the center of yield surface, and may be expressed as,

(A.26)

There are two ways to dennine (a, 1: Prager kinematic hardening rule and Ziegler kinematic
hardening rule.
@a, } = C{AP ] : Prager (A.27)

-
{da,} = ~p({o) {a,}) :Ziegler (A.28)
As shown in Figure A.9, Prager kinematic hardening rule moves in the direction perpendicular
to the yield surface; Ziegler kinematic hardening rule moves along the direction from the
}
center of yield surface {a, to the stress point (0).
From Eq. (A.25), the yield condition becomes,
-
f({a,))=a, -0, =o (A.29)

(A.30)
-
na is the equivalent stress which considers the movement of yield surface, and is expressed
as below,