Tham khảo tài liệu 'advanced mechanics of materials (1993-john willey) episode 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 522 13 FLAT PLATES I The second term in Eq. is integrated similarly. For the integral of the third term we obtain p 2 a apaxz dz afỉơxz1 h l2 J -h 2 ữz The fourth integral obtained from Eq. is p 2 ayơxydz J-h 2 Similarly the other terms can be integrated. To obtain the moment equilibrium equations we multiply Eqs. by z and then integrate through the thickness and employ the definitions of Eq. . The complete set of equilibrium equations obtained is thus Mx odVxy ayNxy - fixNyy x 3Px aphBx 0 PNXy Ệ Nyy P NXy - yN X PPy PhBy 0 ỉ ey afipz afihB 0 ox oy - - 0MXX daMxy aMxy - pxM - ơfjRy 0 ox Oy pMXy aAy PxMxy - yM - aPQy - rJPR 0 Nxy -Nyx For rectangular coordinates a p 1. Then Eqs. yield ÔNXX . dNxv n n OX oy y Pz hBz 0 ÔX oy dMxx t dMxv si - 0 ox oy Nxy Nyx Equations are exact relations provided that x y z are orthogonal curvilinear plate coordinates for the deformed plate. They are approximations for the small-displacement theory of plates if x y z are orthogonal curvilinear plate STRESS-STRAIN-TEMPERATURE RELATIONS 523 coordinates in the undeformed plate since Eqs. are approximations for such axes. Therefore we shall use them as the equilibrium relations for the smalldisplacement theory of plates relative to orthogonal curvilinear plate axes in the undeformed plate. The last of Eqs. is an identity that follows from Eqs. . Often Rx and Ry are zero in any case they may usually be discarded from Eqs. . However if they are retained we obtain from the third fourth and fifth of Eqs. by the elimination of Qx and Qy _0_ ÔX ayM y P Myy aVRy X uJyf JJ Ô Ô fl ra a z Mxy dy Myy ayMxx xMxy appz 0 Equation is called the moment equilibrium equation of plates. For rectangular axes a 1 and Eq. reduces to if we discard Rx and Ry d2 W _ ổ2M_ ổ2AC hBz Pz Q ổx2 ôxôy dy STRESS-STRAIN-TEMPERATURE RELATIONS FOR ISOTROPIC ELASTIC PLATES The preceding .
