Sj. Pantazopoulou et Y. Ding, COLLOCATION IN FINITE-ELEMENT ANALYSIS OF CONSTRAINED PROBLEMS, Canadian journal of civil engineering, 22(1), 1995, pp. 1-14
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.