tailieunhanh - ADVANCED MECHANICS OF COMPOSITE MATERIALS Episode 10

Tham khảo tài liệu 'advanced mechanics of composite materials episode 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 302 Advanced mechanics of composite materials the facings are made of one and the same material only the thicknesses are different Eqs. and yield h21 h3 h3 2h1 2h2 e -------------- --------- 2 hi h3 Returning to the general case we should emphasize that the reference plane providing Cmn 0 for all the mn values does not exist in this case only if the laminate structure is given. If the stacking-sequence of the layers is not pre-assigned and there are sufficient number of layers they can be arranged in such a way that Cmn 0. Indeed consider a laminate in Fig. and suppose that its structure is in general not symmetric . zi zi and k k. Using plane z 0 as the reference plane we can write the membranebending coupling coefficients as 1 k 2 1 k 2 Cm - y A i h z z y A i h z z Cmn 2 . Amnhi Zi Zi 1 2 Amnhi zi zi-1 i 1 i 1 where zi 0 and zi 0. Introduce a new layer coordinate zi zi zi-1 2 which is the distance between the reference plane of the laminate and the middle plane of the ith layer. Then the condition Cmn 0 yields k 2 k 2 Am nhizi Am 1 - i 1 i 1 Fig. . Layer coordinates with respect to the reference plane. Chapter 5. Mechanics of laminates 303 Now assume that we have a group of identical layers or plies with the same stiffness coefficients Amn and thicknesses. For example the laminate could include a mm thick 0 unidirectional layer which consists of 10 plies the thickness of an elementary ply is mm . Arranging these plies above zi and below zi the reference plane in such a way that 10 E zj - zj 0 1 j 1 we have no coupling for this group of plies. Doing the same with the other layers we arrive at a laminate with no coupling. Naturally some additional conditions following from the fact that the laminate is a continuous structure should be satisfied. However even with these conditions Eq. can be met with several systems of ply coordinates and symmetric arrangement of the plies zj zj is only one of these systems. The