Effect of geometrical nonlinearity

Geometrical nonlinearity due to in-plane stress should be considered when the deflection of the plate reaches the order of the plate thickness or that of the delaminated portions. This order of the deflection is often realized in composite materials when the propagation of multiple delaminations takes place. The clamped circular plate with multiple penny-shape delaminations of the same radius a is considered again. The boundary and the continuity conditions are the same as those in Section 2.1. Since no exact solution is available, the Rayleigh-Ritz approximation method is adopted. The total potential energy fl = f/- T is written as the sum of the total strain energy 

Considering the exact solution (Eq. (6)) of the linear case, the displacement field is assumed as 

Substituting Eq. (19) into Eq. (18) and considering the in-plane boundary conditions at r=0 and 1, we have the following expression of as a function of the generalized coordinates gg and q.  

The coefficients B, (/ = 0,l,---,4) are obtained by numerical integration. The equations derived by differentiating II by and q are numerically solved. The energy release rate is numerically obtained as 

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Chapter 16 Impact Damage in Composite Laminates 2.3 Effect of Geometrical Nonlinearity ... 

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