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Compute the [Q] matrix of a lamina reinforced with a balanced bidirectional fabric selected from Table
Compute the curvature of the bimetallic in Problem 1 when it is subjected to a change of temperature ?T = 10 °C.
Plot the strain and stress distribution (?x and sy) through the thickness of the bimetallic analyzed in Problem.
For each of the following laminates, specify the laminate type. Note that a laminate may have more than one characteristic.
For each of the laminates described in Table, specify if they are balanced and/or specially orthotropic.
Compute the laminate moduli (Ex, Ey, Gxy, and ?xy) and the laminate bending moduli (Ex, Ey, Gxy, and ?bxy) for the laminate .
How much does the load need to be increased/ decreased to avoid first ply failure, assuming all components are increased/ decreased proportionally?
Determine the strength ratio R at the bottom surface of the laminate.
The minimum value of strength ratio R thus obtained corresponds to the last ply failure (LPF), i.e., RLP F .
Determine the value of the forces Nx, Ny, Nxy, Mx, My, Mxy required to produce a curvature ?x = 0.00545 mm-1, ?y = -0.00486 mm-1.
Compute the [A], and [D] matrices (neglect shear deformations) for the intact laminate. Each lamina is 2.5 mm thick.
Nx = -1000 N/mm all other zero. Why is the strength ratio different from case(a) ?
Make a sketch (not to scale) of the deformed shape of a beam subject to a positive bending moment Mx and positive axial load Nx.
Compute the reduced stiffness and compliance matrices, and the intralaminar shear stiffness and compliance matrices .
Compute the stress vector at x = y = z = 60/47 using Cauchy's law.
Make a sketch (not to scale) of the deformed shape of a beam subject to a positive bending moment Mx. Make sure your drawing shows the thickness of the beam.
Compute the extensional [A], coupling [B], and bending stiffness [D] matrices of a bimetallic (copper and aluminum) strip.
Derive the middle-surface strains and curvatures. Derive the strain functions as a function of x, y, and z.
Derive the seven stress resultants integrating over the thickness of a laminated plate with N = 3, t1 = t2 = t3.
All laminae are 1.0 mm thick. Comment on the coupling of the constitutive equations for each case.
Comment on the relative magnitude of the coefficients as the number of laminae increases.
Compute the middle-surface strains ?0x, ?0y, ?0xy, and the curvatures ?x, ?y, ?xy for the following load cases.
Demonstrate that an angle-ply laminate has A16 = A26 = 0 using an example laminate of your choice.
Indicate why some values are continuous or discontinuous and state which locations through the thickness this occurs.
Given e0x = e0y = ?0xy = 0 and ?x = 1.0 m-1, ?y = 0.5 m-1, ?xy = 0.25 m-1, compute the strains (in laminate coordinates) at z = -1.27 mm in the laminate.