T-ELEMENTS - A FINITE-ELEMENT APPROACH WITH ADVANTAGES OF BOUNDARY SOLUTION METHODS

Since their introduction in 1977, the so-called T-elements have consid erably evolved and have now become a highly efficient and well establi shed tool for the solution of complex boundary value problems. This cl ass of finite elements, associated with the Trefftz method, is based o n enforcement of interelement continuity and boundary conditions on as sumed displacement fields chosen so as to a priori satisfy the governi ng differential equations of the problem. Several alternative T-elemen t formulations are available which yield for a particular subdomain th e customary force-displacement relationship with a symmetric positive definite stiffness matrix which makes it possible for such elements to be implemented into the standard finite element (FE) codes. Owing to their nature, the T-elements may either be considered as a new FE mode l or as a non-conventional symmetric substructure-oriented form of the boundary element method (BEM). From the point of view of the latter, the outstanding features of the T-element approaches are the use of T- complete sets of non-singular solutions (rather than the singular Kelv in's type fundamental solutions) and the replacement of the customary integral equations form by a symmetric variational formulation. This p aper reviews and critically assesses the most important T-element form ulations developed over the past years. It shows that such elements no t only cumulate the advantages and discard the drawbacks of the conven tional finite element and boundary element methods, but also offer add itional advantages not available in the standard form of these methods .