Solution of the first biharmonic problem by the Trefftz method

The algorithm for the solution of the first biharmonic problem by the Trefftz method is presented. The solution is purely mathematical and follows Mikhlin [29] approach to the solution of the harmonic problem. As such it fills in the gap in the approximate methods of Mathematical Physics. Validity of the algorithm is demonstrated on two examples. The boundary values of the sought function and its normal derivative must be given explicitly to achieve correct results by the algorithm. For that reason, the presented algorithm is, however, not adequate for the plane problems of the theory of elasticity or for plates with free or simply supported edges.