Abstract

Stress, strain and displacement in two-dimensional regions can be calculated by computerized techniques. In the x-y plane, a region is discretized into four-node finite elements such as quadrilaterals and triangles with side nodes. Each such element has eight distinct deformation modes. These correspond to three rigid-body displacements, three uniform strain profiles for compressible materials or two deviatoric strain fields accompanied by an isotropic pressure for incompressible materials, and two flexures. Pointwise equilibrium requires the bending shapes to be functions of Poisson's ratio. Nodal equilibrium and compatibility are satisfied for prescribed loads implementing exact differentiation and integration. Element volume change parameters for compressible materials or isotropic pressure for incompressible materials are eliminated, and a linear system of equations is formed in terms of the seven remaining unknowns per element employing a neural-network solution strategy to pass simultaneously the patch and zero-locking tests. The strain and stress distributions including isotropic pressure for incompressible materials, and displacement profiles are solved as x-y polynomials. This technique, Tessellica, can be used in computer-aided design, and can be integrated in subsequent manufacture or construction of buildings, bridges, dams, ships, aircraft and automobiles, for example, and in bioengineering applications.