A unit-cell model of textile composite beams for predicting stiffness properties

Flexural stiffness properties of a textile composite beam are obtained from a finite-element model of the unit cell. Three linearly independent deformations, namely, pure extension, pure bending and pure shear, are applied to the unit cell. The top and bottom surfaces of the beam are assumed to be traction free. Periodic boundary conditions on the lateral boundaries of the unit cell are enforced by multi-point constraint elements. From the forces acting on the unit cell, the flexural stiffness coefficients of the composite beam are obtained. The difficulties in determining the transverse shear stiffness are discussed, and a modified approach is presented. The methods are first verified by applying them to isotropic and bimaterial beams for which the results are known, and then illustrated for a simple plain-weave textile composite.