2.3 Bending deformation of isotropic layer classical lamination
theory
2.3 Bending deformation of isotropic layer classical lamination
theoryBending response of a single layer
Assumption of linear variation is far from reality, but gives
reasonable results.Kirchoff-Love plate theory corresponds to Euler
Bernoulli beam theory.
Basic kinematicsNormals to mid-plane remain normal
Bending strains proportional to curvatures
Hookes lawMoment resultants
D-matrix (EI per unit width)
Bending of symmetrically laminated layers
The power of distance from mid-plane
Bending-extension coupling of unsymmetrical laminatesWith
unsymmetrical laminates, mid-plane is not neutral surface when only
moment is applied.Conversely pure bending deformation require both
force and moment.
B-matrixForce resultants needed to produce pure bending
How can we see that is B zero for symmetrical laminate?
Under both in-plane strains and curvatures
Under in-plane strains
Example 2.3.1
A MatrixA=0.2Qal+0.05Qbr
Checks:Ratios of diagonal terms.Ratios of diagonals to off
diagonals.Diagonal terms approximately average moduli times total
thickness (+10% correction due to Poissons ratio)
B-Matrix
11D-matrixFor all-aluminumFor all brass, 1.5 times
larger.Calculated D
Is it reasonable? Other checks?
Strains