Issue 29

D. Addessi et al., Frattura ed Integrità Strutturale, 29 (2014) 178-195; DOI: 10.3221/IGF-ESIS.29.16

Figure 1 : FE global reference system: nodal displacement vector components.

is the translation of node J parallel to the local axis x ,

are the rotations at node I / J around

U

Φ

Φ

where

and

, x J

z,I/J

y,I/J

x, J Φ is the rotation at node J around x axis (Fig. 2). The corresponding basic force vector Q

z and y axis, respectively, and

is defined as:

} T

, x J y J P M M M M M  Q , x J P is the force parallel to the local axis x at node J , , z I , z J , x J , y I , {    

(4)

M

M

are the moments at node I / J around z and

where

and

z,I/J

y,I/J

M

y axis, respectively, and

is the moment at node J around x axis.

x, J

Figure 2 : FE basic reference system: nodal displacement vector components. The element deformation D is derived from the global nodal displacement U , using the following transformation:  D T U (5) where the kinematic matrix is introduced as: 1 0 0 0 0 0 1 0 0 0 0 0 0 1/ 0 0 0 1 0 1/ 0 0 0 0 0 1/ 0 0 0 0 0 1/ 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 L L L L               T (6)

    

    

0 0 1/ 0 1 0 0 0 1/ 0 0 0 0 0 1/ 0 0 0 0 0 1/ 0 1 0 L L L L  

180