Given a Square Composite Laminate Having a Stacking Sequence of 302/-303 , Draw the Deformed

Given a Square Composite Laminate Having a Stacking Sequence of 302/-303 , Draw the Deformed

HW1: due 1/26/06

  1. Given a square composite laminate having a stacking sequence of [302/-303], draw the deformed shape of the laminate if it is subjected to (a) uniaxial tension along 0o-direction, (b) bending with respect to 0o-direction and (c) a temperature rise. Also provide statements to enhance your drawings.
  1. Draw the deformed shape of the following composite material combining two square unidirectional laminas together and loaded by uniaxial tension. Justify your answer.

HW2: due 2/1/06

  1. Given a solid circular shaft made of a steel with Young’s modulus E = 207 GPa, strength GPa and specific gravity . The length of the shaft is L and the radius is r. If the steel shaft is to be replaced by a hollow tube having an inner radius r and made of a nano-composite based on carbon nanotubes, find the weight saving percentage if both torsional rigidity and strength are to be maintained.
  1. A composite shaft is manufactured by shrink-fitting a steel sleeve over a brass core so that the two parts act as a single solid bar in torsion. The outer diameters of the two parts are d1= 1.6” for the brass core and d2= 2.0” for the steel sleeve. The shear moduli of elasticity are Gb= 5400 ksi for the brass and Gs= 12,000 ksi for the steel. Assuming that the allowable shear stresses in the brass and steel are psi and psi, respectively, determine the maximum permissible torque Tmax that may be applied to the shaft.

HW3: due 2/8/06

  1. Given two fibers, one has a diameter three times the other. Compare the necessary mechanical properties of them to justify that the smaller fiber is better than the larger one for making composite materials.
  2. A composite shaft is manufactured by shrink-fitting () a steel sleeve over a brass core so that the two parts act as a single solid shaft. The outer diameters of the two parts are d1= 40mm for the brass core and d2= 50mm for the steel sleeve. (1) Calculate the axial thermal residual stress in each part using the following material properties: = 21 x 10-6/oC and Eb = 100 GPa, 10 x 10-6/oC and Es= 200 GPa. (2) Explain the radial stress state (tension or compression) in each part.
  3. A cylindrical pressure vessel is manufactured by filamentary winding with three identical fiber yarns; one of them is along the circumferential direction. For optimal design, what should be the orientations of the remaining two fiber yarns.

HW4: due 2/15/06

  1. Plot curves of E1, E2, v12 and G12 versus Vf for a unidirectional carbon/epoxy composite with the following constituent properties:E1f= 235GPa, E2f= 15GPa, G12f= 27GPa, v12f= 0.2, Em= 3.45GPa, vm= 0.36 and Gm= 1.27GPa, using (a) the rule of mixtures and (b) the Halpin-Tsai equation with .
  2. The longitudinal modulus of a unidirectional glass/epoxy composite containing short aligned fibers is E1=39.1GPa. Use Halpin-Tsai equation to determine the length of the fibers for the properties: Vf= 0.6, df= 10, Ef= 70GPa, Em= 3.5GPa and vm= 0.36.
  3. Use Halpin-Tsai equation to determine the fiber volume fraction Vf of two different composites having the same matrix and the same longitudinal modulus E1equal to ten times the matrix modulus. The first is a nanocomposite consisting of parallel carbon nanotubes dispersed in the matrix; the second is a continuous-fiber Kevlar/epoxy composite. The following properties are given:

Carbon nanotubes: E1f= 1000GPa, l= 1and d= 1nm

Kevlar fibers: E1f= 130GPa

Matrix: Em= 3.33GPa

HW5: due 2/22/06

  1. Identify a composite material and a core material (other than those used in the classroom demonstration) for building a composite violin. In order to justify your design, present a complete analysis including (1) matching the dimensions, (2) matching the ratio of anisotropy (3) matching the vibration frequencies and (4) meeting the requirement of the maximum allowable mass.
  2. Identify an engineering design (other than any of those cases discussed in the classroom) based on biomimetics. Present the important details of the engineering design and its biological origin and explain their similarity. Use diagrams and photos to enhance your comparison.

HW6: due 2/27/06

  1. Given the engineering constants of a unidirectional carbon/epoxy AS4/3501-6 as follows: E1= 147GPa, E2= 10.3GPa, G12= 7GPa and = 0.27, present Ex, Gxy, , and as functions of from 0o to 90o.
  2. Shown below is a [45] composite lamina loaded by a uni-axial stress of 10GPa. If the composite is made of the properties given in A, sketch the deformed shape and dimensions.

HW7: due 3/22/06

  1. Determine the longitudinal modulus E1 and the longitudinal tensile strength F1t of a unidirectional carbon/epoxy composite with the following properties:

Vf=0.65, E1f=235GPa, Em=4.14GPa, Fft=3450MPa, Fmt=104MPa

  1. Given below are the engineering constants and strengths of a composite material: E11= 19.4Msi, E22= 1.22Msi, v12= 0.3, G12= 0.47Msi, Xt= 175ksi, Yt = 6ksi and S =10ksi. If off-axis composite laminates are made of the composite material and loaded with uniaxial tension, draw the strengths of the composite laminates as a function of fiber orientation with respect to the loading direction from 0o to 90o based on (a) maximum stress criterion, (b) maximum strain criterion and (c) Tsai-Hill criterion.

HW8: due 3/29/06

A composite laminate is made of a material having the following engineering constants: E11= 181 GPa, E22= 10.3 GPa, and G12= 7.17 GPa. The composite laminate has a stacking sequence of [0/45/-45/90]s and the thickness of each ply is 0.5 mm.

A. Verify that this composite laminate has an isotropic extensional stiffness matrix [A], i.e. [A] is constant in all directions.

B. If the composite laminate is loaded by the following in-plane forces:

Nxx= 1000N/m, Nyy=500N/m and Nxy= 200N/m (where x-axis coincides with 0o-direction), draw the stress distributions ply by ply through the thickness. The following matrices must be included in your report: [Q], , [A], [A]-1, {} and {}.

HW9: due 4/5/06

A composite laminate is made of a material having the following engineering constants: E11= 181 GPa, E22= 10.3 GPa, and G12= 7.17 GPa. The composite laminate has a stacking sequence of [0/45/-45/90]s and the thickness of each ply is 0.5 mm.

A. Use graph to present the bending stiffness D11, or Dxx, as a function of angle from 0o to 90o.

B. If the composite laminate is loaded by the following out-of-plane moments: Mxx=1000N, Myy=500N and Mxy=200N, draw the stress distributions through the thickness in every ply. The following matrices must be included in your report: [Q], , [D], [D]-1, {}, {} and {}.

Top View