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ACCEPTED MANUSCRIPT in their plate theories. Some examples for theories of even higher order â including not only the shear deformation eï¬ects but also, e. g., warping of crossections â can be found in [15]. With the kinematic assumption (2) the strain-displacement relationships for small displacements can be written in the form â¡ â¡ â¤ â¤ â¡ â¤ â¡ â¤ â¡ â¤ âÏx âu0 0 â¢ â¥ â¢ Îµx â¥ â¢ â¥ â¢ Îµx â¥ â¢ Îºx â¥ âx âx â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ âÏy â¢ â¥ âv 0 0 â¢Îµ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ Îµ Îº â¢ yâ¥ â¢ â¥ â¢ â¥ â¢ â¥ y y ây â¢ â¥ ây â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¥ âÏ âÏ âu âv y â¢Î³ â¥ = â¢ â¢ â¥ â¢ â¥ â¢ â¥ 0 x 0 0 â¢ â¥+zâ¢ =: + z + Î³ Îº + â¢ xy â¥ â¥ â¢ â¥ â¢ xy â¥ . xy â¢ ây â¥ âx ây âx â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ âw â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ â¥ 0 0 â¢ â¥ Î³ 0 â¢Î³xz â¥ â¢ â¥ â¢ â¥ â¢ â¥ + Ï 0 xâ¥ xz â¥ â¢ âx â¢ â¥ â¢ â¥ â¢ â¢ â¥ â¢ â¥ â£ â¦ â£ â¦ â£ â¦ â£ â¦ â£ âw â¦ 0 0 +Ï Î³yz Î³ 0 0 y yz ây (3) Based on the strain-displacement-relations (3) and Hookeâs deformation law (1), ï¬nally the structural law for thick-walled multilayered laminates according to the ï¬rst-order shear deformation theory is derived â¡ â¤ â¢ Nx â¥ â¢ â¥ â¢ â¥ â¢N â¥ â¢ y â¥ â¢ â¥ â¢ â¥ â¢N â¥ â¢ xy â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ Mx â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ My â¥ â¢ â¥ â£ â¦ â¡ = â¢A11 A12 A16 B11 B12 â¢ â¢ â¢ A22 A26 B22 â¢ â¢ â¢ â¢ A66 symm. â¢ â¢ â¢ â¢ D11 D12 â¢ â¢ â¢ â¢ â¢ symm. D22 â¢ â£ Mxy â¡ Qy B16 â¥ â¡ = â¤ 2 â¢âk2 A55 â¢ â£ symm. âk1 k2 A45 â¥ âk12 A44 â¥ â¦ Îµ0x â¤ â¢ â¥ â¢ â¥ â¢ â¥ â¢ Îµ0 â¥ â¢ yâ¥ â¢ â¥ â¢ â¥ â¢Î³ 0 â¥ â¢ xy â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ Îºx â¥ â¢ â¥ â¢ â¥ â¢ â¥ â¢ Îºy â¥ â¢ â¥ â£ â¦ â¥ â¥ B26 â¥ â¥ â¥ â¥ B66 â¥ â¥ â¥ â¥ D16 â¥ â¥ â¥ â¥ â¥ D26 â¥ â¥ â¦ D66 â¤ â¢Qx â¥ â¢ â¥ â£ â¦ â¡ â¤ , (4) Îºxy â¤ â¡ 0 â¢âÎ³xz â¥ â¢ â£ 0 âÎ³yz â¥ â¦ , with the shear correction factors 2 k1 , k2 , the stress resultants and moment 2 For details on the shear correction factors see e. g. [16] 5