Utilizing discretized cauchy integrals for the trefftz method

For several problems in mechanics the solution for the displacements, strains and stresses can be expressed in terms of complex valued functions. With the use of the complex valued functions the satisfaction of the governing differential equations is guaranteed a priori. Here different types of approximation functions are derived using discretized Cauchy integrals. The boundary of the Cauchy integrals can be the boundary of the solution domain or the boundary of a finite element domain. The computation of the real approximation functions for the displacements and stresses involve complex logarithmic terms which are multiplied by powers of the complex variable z=x+iy. The constructed approximation functions are used for finite element computations and for simulations involving only the boundary of the solution domain. For a variety of numerical examples high accuracy for displacements and stresses could be obtained.