@Article{cmes.2008.038.217,
AUTHOR = {X.Y.  Cui, G. R.  Liu, G. Y.  Li, G.  Zheng},
TITLE = {A rotation free formulation for static and free vibration analysis of thin beams using gradient smoothing technique},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {38},
YEAR = {2008},
NUMBER = {3},
PAGES = {217--230},
URL = {http://www.techscience.com/CMES/v38n3/25255},
ISSN = {1526-1506},
ABSTRACT = {In this paper, a gradient smoothed formulation is proposed to deal with a fourth-order differential equation of Bernoulli-Euler beam problems for static and dynamic analysis. Through the smoothing operation, the C<sup>1</sup> continuity requirement for fourth-order boundary value and initial value problems can be easily relaxed, and C<sup>0</sup> interpolating function can be employed to solve C<sup>1</sup> problems. In present thin beam problems, linear shape functions are employed to approximate the displacement field, and smoothing domains are further formed for computing the smoothed curvature and bending moment field. Numerical examples indicate that very accurate results can be yielded when a reasonable number of nodes are used.},
DOI = {10.3970/cmes.2008.038.217}
}