PSI - Issue 28

Paolo S. Valvo et al. / Procedia Structural Integrity 28 (2020) 2350–2369 / Structural Integrity Procedia 00 (2020) 000–000 P.S. Valvo

2357

8

(a)

(b)

Fig. 4: Flexibility coe ffi cients: (a) unit force loads in the x -direction; (b) unit force loads in the z -direction.

3.3. Matrix notation

It is useful to introduce a more compact matrix notation. We define the crack-tip force vector,

F x F z

F =

(9)

,

the crack-tip relative displacement vector,

∆ u x ∆ u z

∆ u =

(10)

,

and the crack-tip flexibility matrix (symmetric and positive definite),

c xx c xz c zx c zz

C =

(11)

.

Equation (7) becomes simply

∆ u = C F .

(12)