Problem 2.1

Derive (2.5) in detail.

Problem 2.2

Discuss the validity of the reciprocity relations given in (2.6).

Problem 2.3

Write the 6 6 compliance matrix for a transversely isotropic material directly in terms of the five independent material constants E ₁, E ₂, v ₁₂, v ₂₃, and G ₁₂.

Problem 2.4

Derive expressions for the elements C _ij of the stiffness matrix for a transversely isotropic material directly in terms of the five independent material constants E ₁ , E ₂, v ₁₂, v ₂₃, and G ₁₂.

Problem 2.5

Write the 6 6 compliance matrix for an isotropic material directly in terms of the two independent material constants E and v.

Problem 2.6

Write the 6 6 stiffness matrix for an isotropic material directly in terms of the two independent material constants E and v.

MATLAB Problem 2.7

Consider a 40-mm cube made of glass-reinforced polymer composite material that is subjected to a compressive force of 150 kN perpendicular to the fiber direction, directed along the 3-direction. The cube is free to expand or contract. Use MATLAB to determine the changes in the 40-mm dimensions of the cube. The material constants for glass-reinforced polymer composite material are given as follows [1]:

MATLAB Problem 2.8

Repeat Problem 2.7 if the cube is made of aluminum instead of glass-reinforced polymer composite material. The material...