104 3-D textile reinforcements in composite materials 27 4.3 Definition of a local axis. z(w) z(w) y(v) wo'ssaudmau'peaypoow/:dny x (u) ZEL'8SI 4.4 Definition of plate displacements. When this theory is applied,the following stiffness properties are needed: Ex,Ey,Gxy and Vxy. Irons theory This theory is based on the following assumptions: The perpendicular line to the mid-surface of the laminated plate remains straight after deformation. The strain energy corresponding to the stresses perpendicular to the mid-surface is neglected. However,the assumption that the perpendicular line to the mid-surface remains perpendicular after deformation is not imposed.Therefore,inter- laminar shear stresses are accounted for in this case.Irons theory consid- ers in-plane and shear stresses for each ply of the laminate. The relationship between stresses and strains proceeds from a three- dimensional approach.The local axis and the definition of the displace- ments of the plate are represented in Fig.4.4.The displacement fields are:104 3-D textile reinforcements in composite materials When this theory is applied, the following stiffness properties are needed: EX, EY, GXY and nXY. Irons theory This theory is based on the following assumptions: • The perpendicular line to the mid-surface of the laminated plate remains straight after deformation. • The strain energy corresponding to the stresses perpendicular to the mid-surface is neglected. However, the assumption that the perpendicular line to the mid-surface remains perpendicular after deformation is not imposed. Therefore, inter￾laminar shear stresses are accounted for in this case. Irons theory consid￾ers in-plane and shear stresses for each ply of the laminate. The relationship between stresses and strains proceeds from a three￾dimensional approach. The local axis and the definition of the displace￾ments of the plate are represented in Fig. 4.4. The displacement fields are: 4.3 Definition of a local axis. 4.4 Definition of plate displacements. RIC4 7/10/99 7:43 PM Page 104 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:21 AM IP Address: 158.132.122.9