A parametric cubic modelling system for general solids of composite material

Abstract

SUMMARYA new approach to modelling solids that are anisotropic and heterogeneous is presented with applications to structures of composite material. A parametric cubic modelling system is presented for lines, surfaces, volumes, and physical data that uses construction-in-context to generate numerical data. This system automates the construction of discrete element models and can reduce input data requirements by more than an order of magnitude. A tricubic isoparametric discrete element is presented that does not require displacement derivatives to define connectivity. This element is capable of exact displacement and strain continuity over a surface while permitting strain discontinuities at heterogeneous material interfaces. The shape of an element can be any hexahedron, pentahedron, or tetrahedron and the material properties are allowed to vary over the volume. Evaluation of modelling error with respect to closed-form solutions for curved geometries indicate a single element can model up to 90-degree segments with stresses accurate to 1 per cent. Applications of the system to composite structures are presented for interlaminar edge effects and attachment stresses in a sandwich panel.

Global-Local Laminate Variational Model

“…al. [4] used a global representation based upon a three dimensional laminate model developed by Pagano [51 which is based upon the assumption that the stress field is only a function of one space coordinate. This is a generalization and improvement of the material model given in [3], however, this approach is not convenient for coupling with the model presented earlier [1].…”

Stress Fields in Composite Laminates

“…, R ybicki [ 19], utilizes larger elements that possess a more complex s t r e s s field . Stanton , Crane , and Neu [20 ] employ a tricubic isoparametric discrete element and a system to automate the construction of finite element models. The latter approach effects an appreciable reduction in data input requirements.…”

Multiprocessing On Supercomputers for Computational Aerodynamics

“…These are differenced as needed: first partials at each corner of the interpolation cell (24), second mixed partials at each corner (24), and third mixed partials at each corner (8). These 56 partial derivatives, along with the 8 corner function values, are placed into a 4 x 4 x 4 tensor B according to the arrangement of Stanton, Crain, and Neu (1977):…”