# I need help with question 6.18 Macromechanics 215 N, 1000 N/m; all remaining components are equal to

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I need help with question 6.18

Macromechanics 215 N, 1000 N/m; all remaining components are equal to zero b) Mry 1 Nm/m; all remaining components are equal to sero ) Comment on the coupling efects obsereed 6.12 Compute the strains ( (y, and ry at the interface between the 459 and laminae above the middle surface by using the results of case (b) of Ezercise 6.11 and -45 /a.e3 6.23). cise 6.13 Compute the stresses ơz and σ1 in the 45° and in the-45° laminae right to the interface based on the strains computed in Exercise 6.12 using (6.24). Discuss the results Exercise 6.14 Cross-ply, and (d) Specially orthotropic. Write those terms that are equal to zero in the constitutive equations (A, B and D) for the following special laminates: (a) Symmetric, (b) Balanced antisymmetric, (e) Exercise 6.15 Define and erplain the following: (a) Regular laminate, (b) Balanced lami- Exercise 6.16 Indicate whether the following are continuous or discontinuous functions nate, and (c) Specially orthotropic laminate. through the thickness. Also, indicate why some values are continuous or discontinuous and state which locations through the thickness this occurs. (a) Strains er, Ey, and ey (b) Stresses ơndy, and ơry Exercise 6.17 Demonstrate that an angle-ply laminate has A16-A26-0 using an erample laminate of your choice. In which case Dio 0? In which case Dio0 Exercise 6.18 Given e:-ε:-า, = 0 and K,-1.0 m-1, Ky = 0.5 m,-1, Kr, 0.2s in-l , compute the strains (in laminate coordinates) at :1.27 mm in the laminate of Exereise 6.7 Exercise 6.19 Compute the stresses (laminate coordinates) at-1.27 mm using the results of Exercise 6.18. Note that θ-30°. Exercise 6.20 Show that a balanced laminate, not necessarily symmetric, has Ae-Au 0. In which case Di6-0? Exercise 6.21 Compute the (Q) matriz of a lamina reinforced with a balanced bidirectional fabric selected from Table 2.8. Use Vs -0.37, E-glass jibers, and isophthalic polyester resin. Exercise 6.22 Compute (A], [Bl, and ID) matrices of the lamina in Erercise 6.21. Also ur the (in-plane) laminate moduli Es, E, Gey and vy Introduction to Composite Materials Desig 214 Exercise 6.6 Given the following stresses o, A*: sin(ox) sin(By) Oy B”: sin(az) sin(31) ary-0 Oy. = Qk sin(az) cos(dy) ơr.-R” cos(ar) sin(3y) where k = 1 N, N is the number of laminae, and Ak, Bk,Q', and Re are constants erive the seven stress resultants integrating over the thickness of a laminated plate ith Exercise 6.7 Find σι, σ2, and σ6 at z = 0, on both laminae of a laminate 1£30/r subject to N-1 N/m (all remaining forces and moments equal to zero), with t1 t2-1.27 mm, E1 = 137.8 GPa, E2 = 9.6 GPa, G12-5.2 GPa, v12-0.3. Exercise 6.8 Compute the (A), [B], [D], and [H] matrices for the following laminates. All laminae are 1.0 mm thick. Comment on the coupling of the constitutive equations for case. (a) one lamina of aluminum (E- 71 GPa, v 0.3) (b) one lamina (O]; carbon-epory (AS4-3501-6). (c) [30]; carbon-epory (d) [o/90)r; carbon-epory (e) [0/90 s; carbon-epory (f) [±30]s, carbon-epory Exercise 6.9 Compute the녜 [B], [D], and [团 the follouing lami equations for each case. Comment on the relative magnitude of the corfficirn cases, the total laminate thickness is 4.0 mm. Comment on the coupling of th be number matrices jor laminates. In al of laminae increases. Macromechanics 215 N, 1000 N/m; all remaining components are equal to zero b) Mry 1 Nm/m; all remaining components are equal to sero ) Comment on the coupling efects obsereed 6.12 Compute the strains ( (y, and ry at the interface between the 459 and laminae above the middle surface by using the results of case (b) of Ezercise 6.11 and -45 /a.e3 6.23). cise 6.13 Compute the stresses ơz and σ1 in the 45° and in the-45° laminae right to the interface based on the strains computed in Exercise 6.12 using (6.24). Discuss the results Exercise 6.14 Cross-ply, and (d) Specially orthotropic. Write those terms that are equal to zero in the constitutive equations (A, B and D) for the following special laminates: (a) Symmetric, (b) Balanced antisymmetric, (e) Exercise 6.15 Define and erplain the following: (a) Regular laminate, (b) Balanced lami- Exercise 6.16 Indicate whether the following are continuous or discontinuous functions nate, and (c) Specially orthotropic laminate. through the thickness. Also, indicate why some values are continuous or discontinuous and state which locations through the thickness this occurs. (a) Strains er, Ey, and ey (b) Stresses ơndy, and ơry Exercise 6.17 Demonstrate that an angle-ply laminate has A16-A26-0 using an erample laminate of your choice. In which case Dio 0? In which case Dio0 Exercise 6.18 Given e:-ε:-า, = 0 and K,-1.0 m-1, Ky = 0.5 m,-1, Kr, 0.2s in-l , compute the strains (in laminate coordinates) at :1.27 mm in the laminate of Exereise 6.7 Exercise 6.19 Compute the stresses (laminate coordinates) at-1.27 mm using the results of Exercise 6.18. Note that θ-30°. Exercise 6.20 Show that a balanced laminate, not necessarily symmetric, has Ae-Au 0. In which case Di6-0? Exercise 6.21 Compute the (Q) matriz of a lamina reinforced with a balanced bidirectional fabric selected from Table 2.8. Use Vs -0.37, E-glass jibers, and isophthalic polyester resin. Exercise 6.22 Compute (A], [Bl, and ID) matrices of the lamina in Erercise 6.21. Also ur the (in-plane) laminate moduli Es, E, Gey and vy

Introduction to Composite Materials Desig 214 Exercise 6.6 Given the following stresses o, A*: sin(ox) sin(By) Oy B”: sin(az) sin(31) ary-0 Oy. = Qk sin(az) cos(dy) ơr.-R” cos(ar) sin(3y) where k = 1 N, N is the number of laminae, and Ak, Bk,Q', and Re are constants erive the seven stress resultants integrating over the thickness of a laminated plate ith Exercise 6.7 Find σι, σ2, and σ6 at z = 0, on both laminae of a laminate 1£30/r subject to N-1 N/m (all remaining forces and moments equal to zero), with t1 t2-1.27 mm, E1 = 137.8 GPa, E2 = 9.6 GPa, G12-5.2 GPa, v12-0.3. Exercise 6.8 Compute the (A), [B], [D], and [H] matrices for the following laminates. All laminae are 1.0 mm thick. Comment on the coupling of the constitutive equations for case. (a) one lamina of aluminum (E- 71 GPa, v 0.3) (b) one lamina (O]; carbon-epory (AS4-3501-6). (c) [30]; carbon-epory (d) [o/90)r; carbon-epory (e) [0/90 s; carbon-epory (f) [±30]s, carbon-epory Exercise 6.9 Compute the녜 [B], [D], and [团 the follouing lami equations for each case. Comment on the relative magnitude of the corfficirn cases, the total laminate thickness is 4.0 mm. Comment on the coupling of th be number matrices jor laminates. In al of laminae increases.

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