LEAST-SQUARES T-ELEMENTS - EQUIVALENT FE AND BE FORMS OF A SUBSTRUCTURE-ORIENTED BOUNDARY SOLUTION APPROACH

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.