COLLOCATION IN FINITE-ELEMENT ANALYSIS OF CONSTRAINED PROBLEMS

The concept of three-field displacement finite element formulations of constrained problems is explored in this paper. The approach studied uses collocation within the element domain to enforce the constraints of the problem and resembles mixed formulations because in addition to the approximation of the displacement field, all other auxiliary defo rmation variables that enter the constraint conditions are interpolate d independently. Plate-bending as described by the Reissner-Mindlin th eory is used as a model problem for the development of the approach. T wo triangular plate elements are formulated based on this methodology, and their performance is investigated using several patch tests. Nume rical examples are also considered to study the element behavior under locking conditions (which occur with the classical displacement appro ach at the thin plate limit). The ability of the elements to overcome locking is established using mathematical arguments and practical exam ples. The influence of the position of collocation points on the compu ted results is evaluated through sensitivity studies, with the aim to identify the optimal set. Results are compared with those obtained fro m the exact solutions and the associated classical displacement model with selective reduced integration of the constrained energy terms.