Hk. Stolarski et Jf. Dcosta, ON CONSISTENT DISCRETIZATION OF INERTIA TERMS FOR C-0 STRUCTURAL ELEMENTS WITH MODIFIED STIFFNESS MATRICES, International journal for numerical methods in engineering, 40(18), 1997, pp. 3299-3312
In the existing finite element calculations of dynamic problems using
C-0 structural elements, the inertia terms are evaluated without any r
eference to the modifications such as reduced integration, projections
etc., typically needed in the discretization of the stiffness terms.
A different discretization of inertia is discussed here. It is based o
n the following two observations. First, as shown in this work (at lea
st for the beam problems), the modified stiffness matrix for a given C
-0 element can be obtained by standard, unmodified approach, in which
degrees of freedom remain unchanged, but the shape functions are diffe
rent. Those modified functions are of higher order and define the tran
slational field within the element in terms of both translational and
rotational parameters. Second, if standard consistent approach to the
formulation of dynamic problems is to be followed, approximation of th
e displacement field used in the unmodified evaluation of the stiffnes
s terms should also be used in discretization of the inertia terms. Th
is implies that the modified higher-order functions should be employed
when evaluating the element mass matrix for the C-0 elements with mod
ified stiffness matrices. As a consequence of this approach, consisten
cy between formulation of the inertia and stiffness terms is restored.
This leads to inertial coupling between rotational and translational
degrees of freedom, which is absent in standard evaluation of inertia.
It is demonstrated that this approach tends to improve accuracy of dy
namic computations. (C) 1997 by John Wiley & Sons, Ltd.