J. Jirousek et A. Wroblewski, T-ELEMENTS - A FINITE-ELEMENT APPROACH WITH ADVANTAGES OF BOUNDARY SOLUTION METHODS, Advances in engineering software, 24(1-3), 1995, pp. 71-88
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
.