Constitutive relation error estimator for transient finite element analysis

The concept of error in the constitutive relation allows defining a consist ent error measurement for dynamic finite element simulations. A solution wh ich satisfies exactly the kinematic constraints, the initial conditions and the equilibrium equation is built from the solution to the discretised pro blem. This construction utilizes, as best as possible, the properties of th e integration scheme used to obtain a satisfactory effectivity index. The q uality of the numerical solution is assessed by the way in which the consti tutive relations are satisfied. Results from various tests conducted on a o ne degree-of-freedom problem and on a 1D example display the estimator's go od behaviour. The effectivity index remains at a reasonable value and, on t he basis of the first test, a comparison of the error in the constitutive r elation with different estimators drawn from the literature, is presented. (C) 1999 Elsevier Science S.A. All rights reserved.