ABSTRACT
Computation of strains requires expressions for displacement derivatives. The strain– displacement relations are definitions and remain unchanged with the adoption of the isoparametric 4-node quadrilateral. However, the displacement interpolation functions that are needed in x, y coordinates are only available in a, b coordinates. Displacement derivatives required for the strains in x, y coordinates must then be obtained through coordinate transformation and the chain rule for differentiation. Programming for the B-matrix is then straightforward. Programming the B-matrix quadrilateral for stress analysis requires somewhat greater effort than the triangle. Communication between other parts of a complete finite element program would be through a suitable common block and to some extent through subroutine arguments. Division by the determinant formed in computing the inverse of the Jacobian calls for a trap to warn of a division by zero. The B-matrix is organized by displacement components.
