A numerical replacement of computer algebra methods for the derivation of polynomial equations in mechanics

The classical computer algebra methods of Grobner bases and characteristic sets have been already used for the derivation of polynomial formulae, mainly in classical geometry. Here we derive analogous formulae in applied mechanics by using a completely different approach: the numerical determination of the coefficients in the required polynomial formulae without the use of computer algebra techniques. Two compatibility equations for the stress components in plane elasticity and the equation of caustics in fracture mechanics are used as the vehicle for illustration of the present elementary numerical approach. Beyond the simplicity of the present method, its powerfulness consists mainly is the fact that the well-known disadvantages of computer algebra methods (in the required computer memory and, mainly, computer time) are now avoided. Generalizations of the present approach follow easily (e.g. from polynomial to differential equations). (C) 1997 Elsevier Science Limited.