Construction of the equation of caustics in dynamic plane elasticity problems with the help of reduce

Abstract

The method of caustics has become a very efficient tool in crack, hole and many additional plane elasticity problems. Unfortunately, the fundamental equation of the caustics frequently requires complicated algebraic computations including that of a Jacobian determinant. Here we show that computer algebra software can prove very efficient in these computations, using as a vehicle for this illustration the already known fundamental equation of caustics in dynamic plane elasticity (both for crack problems in fracture mechanics as well as for hole and additional problems). We have used the programming capabilities of REDUCE, a very popular computer algebra system, for our algebraic computations. Moreover, we illustrate the ‘learning’ abilities of REDUCE especially for the derivation of the complex form of this equation. The case of static plane elasticity results simply as a special case of dynamic plane elasticity. Additional possibilities are suggested in brief.