TY - JOUR

T1 - On consistent discretization of inertia terms for C0 structural elements with modified stiffness matrices

AU - Stolarski, Henryk K.

AU - D'Costa, Joseph F.

PY - 1997

Y1 - 1997

N2 - In the existing finite element calculations of dynamic problems using C0 structural elements, the inertia terms are evaluated without any reference 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 on the following two observations. First, as shown in this work (at least for the beam problems), the modified stiffness matrix for a given C0 element can be obtained by standard, unmodified approach, in which degrees of freedom remain unchanged, but the shape functions are different. Those modified functions are of higher order and define the translational 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 the displacement field used in the unmodified evaluation of the stiffness terms should also be used in discretization of the inertia terms. This implies that the modified higher-order functions should be employed when evaluating the element mass matrix for the C0 elements with modified stiffness matrices. As a consequence of this approach, consistency 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 dynamic computations.

AB - In the existing finite element calculations of dynamic problems using C0 structural elements, the inertia terms are evaluated without any reference 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 on the following two observations. First, as shown in this work (at least for the beam problems), the modified stiffness matrix for a given C0 element can be obtained by standard, unmodified approach, in which degrees of freedom remain unchanged, but the shape functions are different. Those modified functions are of higher order and define the translational 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 the displacement field used in the unmodified evaluation of the stiffness terms should also be used in discretization of the inertia terms. This implies that the modified higher-order functions should be employed when evaluating the element mass matrix for the C0 elements with modified stiffness matrices. As a consequence of this approach, consistency 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 dynamic computations.

KW - Assumed strain

KW - Consistent

KW - Decomposition

KW - Mass matrix

KW - Mode

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U2 - 10.1002/(SICI)1097-0207(19970930)40:18<3299::AID-NME213>3.0.CO;2-G

DO - 10.1002/(SICI)1097-0207(19970930)40:18<3299::AID-NME213>3.0.CO;2-G

M3 - Article

AN - SCOPUS:0031234882

VL - 40

SP - 3299

EP - 3312

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 18

ER -