关键词: 薄板弯曲, 有限元, 广义协调元

Abstract: In this paper, three generalized conforming elements for thin plate bending based on generalized compatibility conditions are derived: a triangular element with 9 d.o.f.(LT9 element) and two rectangular elements with 12 d.o.f.(LR12-1 and LR12-2). Their formulation is as simple as the conventional non-conforming element and they can be implemented in routine manner. By satisfying the generalized compatibility condition under constant moments, these new elements can always pass the patch test. Numerical examples show that high accurate result is obtained with fewer degrees of freedom by using these new elements of thin plate. They are respectively the most accurate 9-d.o.f. triangular element and the most accurate 12-d.o.f.rectan-gular element for thin plant bending currently available.

Key words: plate bending, finite element, generalized conforming element