VARIATIONAL FORMULATION OF 2 COMPLEMENTARY HYBRID-TREFFTZ FE MODELS

The paper presents two complementary variational formulations of Treff tz-type elements wherein the piece-wise assumed displacement approxima tions a priori fulfil the governing differential equations over the el ement subdomain. The two formulations are such that either the displac ement conformity or the reciprocity of the conjugate tractions is enfo rced at the element interfaces, one more strongly than the other. This is achieved through linking the piece-wise approximations either thro ugh an auxiliary displacement or a boundary traction frame. The two fo rmulations concern solid mechanics and structures. Although for hybrid elements monotonic convergence in energy cannot be warranted, in prac tice the two presented formulations yield opposite bounds on the energ y provided that the number of internal Trefftz functions is sufficient ly large.