Tham khảo tài liệu 'mechanics analysis composite materials episode 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Chapter 5. Mechanics of laminates 231 Fig. . Reduction of transverse shear stresses to stress resultants transverse shear forces . Because the particular distribution of Tr- and rK does not influence the displacements we can introduce some average stresses having the same resultants as the actual ones . However according to Eqs. shear strains are linear combinations of shear stresses. So we can use the same law to introduce average shear strains as Average shear strains yx and y can be readily expressed in terms of displacements if we substitute Eqs. into Eqs. . 1 X . Ỉ dUz h .v -0 - r -e J dz - e _ 1 h M .v - w -e y dz _ e . These equations in contrast to Eqs. do not include derivatives with respect to z. So we can substitute Eqs. and to get the final result 8w ỠX Sw ộỹ 232 Mechanics and analysis of composite materials Consider Eqs. and . Integrating them over the layer thickness and using Eqs. and we get vx j J55yt J56 vz dz Vy j Absyx Abby dz yx I i a55Tx 56 02 Yy l I 66 dz . Because the actual distribution of stresses and strains according to the foregoing reasoning is not significant we can change them for the corresponding average stresses and strains vx Sssyx Ssbyy Vy Sbsyx Sbb y yx sssK ssbVy yy SbsK SbbVy where 5 mn im Ị Amndz e s Sfttn Snm Tf I Qntn dz . It should be emphasized that Eqs. are not the inverse form of Eqs. . Indeed solving Eqs. using Eqs. and taking into account that ass Ãbb asb Ãsb 66 Ãss 7 _ Amn__ m AssAbb - A256 we arrive at Eqs. in which 777 .7 7 2 A ÃSS dz 66 dz - e j56 dz 2 These expressions in general do not coincide with Eqs. . Thus the constitutive equations for transverse shear are specified by Eqs. and there exist two in general different approximate forms of stiffness coefficients -Eqs. and . The fact that equations obtained in this way are approximate is quite natural because the .
