TAILIEUCHUNG - The Behavior of Structures Composed of Composite Materials Part 6

Tham khảo tài liệu 'the behavior of structures composed of composite materials part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 139 Proceeding as before for the mid-plane symmetric rectangular plate of Section the resulting three coupled equations using classical plate theory . no transverse shear deformation have the following form 2 74 - P x dy Because of the bending-stretching coupling not only are lateral displacements w x y induced but in-plane displacements ỈÍ J and Y as well hence three coupled equations through . Governing Equations for a Composite Material Plate With Bending-Twisting Coupling Looking at Equation the moment curvature relations for a rectangular midplane symmetric plate with bending-twisting coupling are D KX D 2Ky My D12 CX D22K y 2D26 CXy M y D f K X D26Ky 2D66Kxy 140 Of course if transverse shear deformation is ignored . classical theory then the curvatures are given by and the moment curvature relations become . _ n d2w n 92wori 92w Mr -D. -7-2--7- -- 2D. 3-57- 11 3x2 12 dy2 16 dxdy _ n d2w n d2w d2w My D12 2 D22 2 2D26dxdy 3169 _ n d2w n 92W _on d2w 16 D26 2 2D66 Substituting these into provides the following governing differential equation. Z d4 -Hn b2Do d4 i1 11 3x4 Du y 3d 2dy2 26dxdy3 D22 4 p x y Comparing with it is seen that due to the presence of the t h and ỉ ọ bending-twisting coupling terms odd numbered derivatives appear in the governing differential equation. That precludes the use of both the Navier approach of Section and the use of the Levy approach of Section in obtaining solutions for plate with bending-twisting coupling. With these complications one may want to obtain solutions using the Theorem of Minimum Potential Energy discussed in Chapter 6 below. Concluding Remarks It appears that there is no end in trying to more adequately describe mathematically the behavior of composite materials utilized in structural components. Unfortunately the more sophisticated one gets in such descriptions the more difficult the mathematics becomes as is evidenced in the increasing .

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