A Trefftz approach to computational mechanics

This paper presents a Tre tz method for solving structural elasticity problems and ow problems of incompressible viscous uids. The problem of unilateral contact is also dealt with. For each type of problem, Tre tz polynomials and associated variational formulations are given. Complex structures are studied by a sub-structuring technique. This method requires the resolution of a non-symmetrical linear system. It is shown that it is possible to take advantage of this Tre tz approximation in two ways: (i) the approach presented can be considered as a simpli ed method which enables a solution to be evaluated quickly; (ii) this approach also makes it possible to obtain a good quality solution associated with high degree polynomial bases. This method is adapted to optimization processes because the discretization of the structure requires only very few sub-domains to build a good approximation and o ers a great exibility in use