J. Jirousek et al., MESH DESIGN AND RELIABILITY ASSURANCE IN HYBRID-TREFFTZ P-ELEMENT APPROACH, Finite elements in analysis and design, 22(3), 1996, pp. 225-247
This paper is concerned with the reliability of a uniform p-extension
process based on the hybrid-Trefftz (HT) finite element model. In this
model, introduced more than fifteen years ago, the assumed displaceme
nt field of the element a priori satisfies the governing differential
equations of the problem, while the interelement continuity and the bo
undary conditions are enforced in an average weighted residual sense.
One of the most important advantages of this concept is the existence,
inside each element, of a large internal zone of super convergence wh
ere the errors are currently one to two orders of magnitude lower than
those in the narrow perturbed zone along its boundary. The final aim
of this paper is to present a very simple and efficient way of produci
ng reliable results (displacement, internal forces) in the form of con
tour lines or other suitable graphical representation. To take full ad
vantage of the HT elements, only the results of a regular grid of inte
rnal sampling points in the super convergent zone of the elements are
used along with a post-processing approach known as 'krigeing'. The as
sessment of reliability is based on the control of undesired displacem
ent and traction jumps along the element interfaces rather than checki
ng the smallness of any kind of global error measure. Special attentio
n is paid to singularities associated with angular corners. In contras
t to the traditional HT singularity calculation, involving the use of
very accurate but costly to implement special purpose functions, use i
s made of a local mesh refinement. For a practical application of the
HT p-element approach, general guidelines for prior design of the elem
ent meshes and the choice of the grids of internal sampling points are
presented. The efficiency of the approach is illustrated on a series
of examples of thin (Kirchhoff) plates in bending. In the last part of
the paper some further possible improvements of the basic approach pr
esented are briefly discussed. They include in particular the automati
c identification of corner singularities and the quantitative reliabil
ity assessment of the smoothed results at nodes of the FE mesh.