Question

An AS4/12K carbon fiber with Hexply 8551-7epoxy matrix has 55% fiber volume fraction for each ply. Assume fiber Poisson's ratio is 0.2 and matrix Poisson's ratio is 0.35. The layup used is [0/+-15/+-45/90]S Laminate and the laminate is 0.125" thick. If a plate that is 3 m long by 2 m wide and loaded with a uniformly distributed transverse load of 10 N/m², find the maximum mid-plane deflection.

Answer 1

To find the maximum mid-plane deflection of the plate, we need to calculate the effective modulus of elasticity and the bending stress. Using the plate theory, we can then find the maximum mid-plane deflection by substituting the values into the plate theory formula.

Step-by-step explanation:

To find the maximum mid-plane deflection of the plate, we need to calculate the bending stress and apply it to the plate's dimensions. First, we need to calculate the effective modulus of elasticity, which takes into account the fiber volume fraction and their respective properties.

Then, we can calculate the bending stress by considering the distributed load applied to the plate. Finally, we can use the bending stress to find the maximum mid-plane deflection using the plate's dimensions and the plate theory formula.

Calculate the effective modulus of elasticity (E_eff) using the fiber volume fraction and modulus of elasticity values for the carbon fiber and epoxy matrix.

Calculate the bending stress (σ) by dividing the transverse load by the moment of inertia (I).

Use the plate theory formula to find the maximum mid-plane deflection (δ) by substituting the values for the bending stress, plate length, plate width, and plate thickness.