Composite Materials Design and Applications Part 17

Tham khảo tài liệu 'composite materials design and applications part 17', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | in which both go and Gi dgo dy are continuous as one crosses from material 1 to material 2. Taking into account the antisymmetry of the function go with respect to variable y one obtains H2 2 y H1 2 -H2 2 y H2 2 -H1 2 y -H2 2 E1 a. .3 . n go1 - - r -y A1y B1 G1 6 E2 a 3 . _ go2 - y A2y G26 E1 a 3 . go3 - jjy A1y - B1 G1 6 with -GSÒ - 12 G 2 H G 1 H1 - H2 EIZ E2 h3 E1 H - H2 E1 aH -- G12 4 a A1 B1 _ h2 1 1 V ÊE1 -E2 2 ÊE2 E1 h2 - a Ì E1H1 H 2 16 GJ 11 I G2 J 2 GJ 3 Az _ A 2B1 aH2 E2 E1 A 1 H2 3 8 I. G2 G1J 2. Shear stresses due to bending These are given by the relation see Equation T - Gi -Gs grad go then T - G - o T. - G -A-- - 0 Gi G S dy T Gi GSÒ dz 0 One obtains 0 y H2 T .xy 1 Gy 2 EIZ E 2 -y E1 4 H2 2 y H1 2 T . y 1G 1y 2 Eo E1 2003 by CRC Press LLC The corresponding distribution is illustrated below for two distinct designs of the components 1 and 3. Shear coefficient The calculation of k is done without difficulty starting from Equation k dõ LEa dS One obtains k a_ 8 E2 H E1 H3 - H3 E1 Ê 4rr5 G1 4 H Í r5 3 bE1 H12 - H2 2 - H with G2 H2 G1 H1 - H2 a 12 E2 h2 E1 H3 - E2 h2 E1 H3 - h2 5 b E1 I H 77 h2 16 G1 - H22 Ơ2 2E2 3E1 a The evolution of the shear coefficient k is represented in the following figure for different values of the ratios E1 E2 and with the same Poisson coefficient when varying thickness of the skins. 47 Observation of the evolution of ty for the beam with thin skins justifies the simplification proposed in Application Sandwich Beam Simplified Calculation of the Shear Coefficient. 2003 by CRC Press LLC Remarks The limiting cases E2 E1 H2 H1 H2 0 correspond to a homogeneous beam with rectangular cross section for which one finds again the classical value k 6 5 or . The expression for the k coefficient written above is long. One can obtain a more simplified expression for easier manipulation if the skins are thin relative to the total thickness of the beam. One can refer to Application .