C0 Zigzag Kinematic Displacement Models for the Analysis of Laminated Composites

Abstract

Three new theories for analysis of laminated composite and sandwich structures are presented and assessed for accuracy and for suitability for finite-element analysis. These theories are based on assumed displacement fields that consist of a smooth polynomial expansion (quadratic, fully cubic, and partly cubic) in the thickness coordinate with a piecewise (layerwise) linear field superposed upon them. Interlaminar transverse shear continuity is enforced to make the number of degrees of freedom in the theories independent of the number of layers (plies) in the structure. In the case of the quadratic and partly cubic theories, a special formulation is developed that yields a theory in which all variables are C0continuous. In addition, a new transverse normal strain field is derived by assuming the transverse normal stress to be constant through the thickness of the laminate. The final form of the model uses only engineering-type degrees of freedom-displacements and rotations. To verify the accuracy of the proposed theories, Navier-type solutions are developed for a simply supported beam subjected to a sinusoidally varying transverse load and the results are compared with an analytical elasticity solution. The results show that all the proposed theories predict local stresses very accurately compared to the first-order shear deformation theory.