Material-smart analysis of textile-reinforced structures

A methodology of the material-smart structural analysis proposed in this paper links micromechanical modelling of a complex fibrous reinforcement to a three-dimensional analysis of a structural part. The geometry of the reinforcing textile varies throughout the entire volume of a part, thus its stiffness characteristics are dependent on the spatial coordinates. The methodology addresses this by determining elastic properties of the textile composite in a local region (a 'meso-volume') through a processing science model. The 'global' structural analysis incorporates a variational formulation of the three-dimensional elasticity problem for an inhomogeneous anisotropic body, a division of the body into meso-volumes having individual elastic properties, further partition of each meso-volume into sub-elements, and application of special deficient spline functions for a local approximation of displacements with respect to all three coordinates. All the necessary external and internal boundary conditions can be satisfied with any prescribed accuracy in the proposed numerical procedure. Several numerical examples for woven and braided composite plates are considered to illustrate the applicability of the methodology and the calculational procedure.