Page 270 - Marine Structural Design

246 Part II Ultimate Strength

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UQ = +I{ kx - -QJ -ay)- c., -az)) (A.31)
[("y
+

By setting yield hnction f as the plastic potential, plastic strain increment may be expressed as,

(A.32)

(A.33)

12.5.5 Stress Increment - Strain Increment Relation in Plastic Region
Total strain increment is the sum of elastic strain increment and plastic strain increment,
{A€) = {A€')+ {/46P) (A.34)
On the other hand, the relationship between stress increment and elastic strain increment may
be expressed as below,
(do)= [Dqd€q (A.35)
Substituting this equation into Eq. (A.34), we obtain,
{do>= ~Dq(d€)-{d€p)) (A.36)
If the associated flow rule according with the yield function and plastic potential are used, the
plastic strain increment {AgP I can be expressed as,

(A.37)

In general, the yield function f is a fbnction of stress and plastic strain, and may be written as,
f = f (b), {EP 1) (A.38)

when plastic deformation occurs, the following equation may be obtained.

(A.39)

Substituting Eq. (A.37) into Eqs. (A.36), (A.39), we obtain,

(A.40)

(A.41)