ISSN:
0029-5981
Keywords:
spurious mechanism
;
spurious pressure
;
hybrid element
;
stabilization
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
In two-dimensional penalty finite element analysis of incompressible materials, Q9/3P, the 9-node quadrilateral with three assumed quasi-pressure modes, is the most popular element not bothered by spurious pressure. In constructing the penalty matrix of Q9/3P, it is necessary to form a 3×18 matrix and a 3×3 symmetric matrix. The inverse of the symmetric matrix is then post- and pre-multiplied by the 3×18 matrix and its transpose, respectively. By employing a rank subtraction technique, a new and more efficient implementation scheme is devised for the penalty matrix. Same as the conventional Q9 element, when Q9/3P is fully integrated, it becomes expensive and too stiff. On the other hand, there are two spurious kinematic modes should the element be sub-integrated. In the proposed Q9/3P element, the two mechanisms will be annihilated by judiciously chosen higher-order assumed stress modes in conjunction with a modified Hellinger-Reissner functional. It will be demonstrated that the element is of good accuracy and high efficiency.
Additional Material:
9 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620382302
Permalink