Finite Element Analysis of Beams with Nonlocal Foundations
Lei, Y., Friswell, M. I. and Adhikari, S.,
47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics
& Materials Conference, Newport, Rhode Island, USA, May 2006.
In this paper, a nonlocal viscoelastic foundation model is
proposed and used to analyse the dynamics of beams with different
boundary conditions using the finite element method. Unlike local
foundation models the reaction of the nonlocal model is obtained
as weighted average of state variables over a spatial domain via
convolution integrals with spatial kernel functions that depend on
a distance measure. In the finite element analysis, the
interpolating shape functions of the element displacement field
are identical to those of standard two-node beam elements.
However, for nonlocal elasticity or damping, nodes remote from the
element do have an effect on the energy expressions, and hence the
damping and stiffness matrices. The expressions of these direct
and cross stiffness and damping matrices may be obtained
explicitly for some common spatial kernel functions. Alternatively
numerical integration may be applied to obtain solutions.
Numerical results for eigenvalues and associated eigenmodes of
Euler-Bernoulli beams are presented and compared (where possible)
with results in literature using exact solutions, Galerkin
approximations or the transfer matrix approach. The examples
demonstrate that the finite element technique is efficient for the
dynamic analysis of beams with nonlocal viscoelastic foundations.
BiBTeX Entry
@INPROCEEDINGS{cp21,
AUTHOR={Y. Lei and M. I. Friswell and S. Adhikari},
TITLE={Finite element analysis of beams with nonlocal foundations},
BOOKTITLE={47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics \& Materials Conference},
YEAR={2006},
Address={Newport, Rhode Island, USA},
Month={May},
Note={}
}
by Sondipon Adhikari