9.3 BEAM ELEMENT 397 9.2 Plate Element In the absence of shear deformation,the force-strain relationships for a thin-plate element are (Eq.3.21) A A1 A6 B11 B12 B16 A12 2 A26 B12 B22 B N A6 A26 A66 B16 B26 B66 Bu (9.8) B12 B16 Du D12 D16 B12 B22 B26 D12 D2 D26 Ky B16 B26 B66 D16 D26 D66 Kxy [E where [E]is the stiffness matrix for a plate element without shear deformations.In the presence of shear deformation,the force-strain relationships are (Eqs.5.13- 5.15) N A A2 A16 B11 B12 B16 0 0 A2 An 6 B12 B22 B26 0 A6 6 A66 B6 B26 B6 0 0 M Bu1 B12 B16 D11 D12 D 0 0 Kx M B12 B22 B26 D12 D22 D26 0 B16 B26 B66 D16 D26 D66 0 0 Kxy 0 0 0 0 0 0 0 0 0 0 0 0 s Yyz [目 (9.9) where [E]is the stiffness matrix for a plate element with shear deformations. Frequently,the behavior of shells can be described by replacing the curved surface with small,flat elements.The stiffness matrices above are applicable to such flat shell elements. 9.3 Beam Element For a beam element,the force-strain relationships are arbitrary layup,no shear deformation,no restrained warping (Eq.6.2) N P P2 P3 P4 P2 P2 P2s P24 Pi3 P2s P33 (9.10) 4 P2a P P 11 [可9.3 BEAM ELEMENT 397 9.2 Plate Element In the absence of shear deformation, the force–strain relationships for a thin-plate element are (Eq. 3.21)    Nx Ny Nxy Mx My Mxy    =          A11 A12 A16 B11 B12 B16 A12 A22 A26 B12 B22 B26 A16 A26 A66 B16 B26 B66 B11 B12 B16 D11 D12 D16 B12 B22 B26 D12 D22 D26 B16 B26 B66 D16 D26 D66          % &' ( [E]    o x o y γ o xy κx κy κxy    , (9.8) where [E] is the stiffness matrix for a plate element without shear deformations. In the presence of shear deformation, the force–strain relationships are (Eqs. 5.13– 5.15)    Nx Ny Nxy Mx My Mxy Vx Vy    =               A11 A12 A16 B11 B12 B16 0 0 A12 A22 A26 B12 B22 B26 0 0 A16 A26 A66 B16 B26 B66 0 0 B11 B12 B16 D11 D12 D16 0 0 B12 B22 B26 D12 D22 D26 0 0 B16 B26 B66 D16 D26 D66 0 0 000000 S11 S12 000000 S12 S22               % &' ( [E]    o x o y γ o xy κx κy κxy γxz γyz    , (9.9) where [E] is the stiffness matrix for a plate element with shear deformations. Frequently, the behavior of shells can be described by replacing the curved surface with small, flat elements. The stiffness matrices above are applicable to such flat shell elements. 9.3 Beam Element For a beam element, the force–strain relationships are arbitrary layup, no shear deformation, no restrained warping (Eq. 6.2)    N
M
y M
z T
   =      P11 P12 P13 P14 P12 P22 P23 P24 P13 P23 P33 P34 P14 P24 P34 P44      % &' ( [E]    o x 1 ρy 1 ρz ϑ    (9.10)