J. Jirousek et A. Wroblewski, LEAST-SQUARES T-ELEMENTS - EQUIVALENT FE AND BE FORMS OF A SUBSTRUCTURE-ORIENTED BOUNDARY SOLUTION APPROACH, Communications in numerical methods in engineering, 10(1), 1994, pp. 21-32
An efficient solution to boundary-value problems may be based on the a
pplication of a suitably truncated T-complete set of Trefftz functions
over individual subdomains and on linking the fields by a least-squar
es procedure. Although it yields a symmetric system of linear equation
s, this approach as originally presented by Zielinski and Zienkiewicz
is not suited for implementation into FE codes. The present paper pres
ents two equivalent formulations, which take respectively the form of
the finite (FE) and nonconventional boundary-element (BE) approach. Bo
th allow the resulting simultaneous equations to be assembled followin
g the standard direct stiffness methods and can readily be implemented
into existing FE codes. As in the conventional p-method, the accuracy
may be controlled within large limits without increasing the number o
f elements. The present approach allows substantial saving in computer
time in comparison with the so-called hybrid-Trefftz (HT) elements, t
hough the assumed displacement fields are identical. The practical eff
iciency of the new T-element approach is assessed on the problem of st
ress concentration in a symmetrically compressed perforated panel.