@Article{cmes.2008.030.001,
AUTHOR = {Chein-Shan Liu},
TITLE = {A Lie-Group Shooting Method for Post Buckling Calculations of Elastica},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {30},
YEAR = {2008},
NUMBER = {1},
PAGES = {1--16},
URL = {http://www.techscience.com/CMES/v30n1/25149},
ISSN = {1526-1506},
ABSTRACT = {In this paper we propose a new numerical integration method of second-order boundary value problems (BVPs) resulting from the elastica of slender rods under different loading conditions and boundary conditions. We construct a compact space shooting method for finding unknown initial conditions. The key point is based on the construction of a one-step Lie group element <i>G(T)</i> and the establishment of a generalized mid-point Lie group element <i>G(r)</i> by using the mean value theorem. Then, by imposing <i>G(T) = G(r)</i> we can search the missing initial condition through a closed-form solution in terms of the weighting factor <i>r</i> ∈ (0,1). The Lie-group shooting method is very effective for large deflection problems of elastica even exhibiting multiple solutions.},
DOI = {10.3970/cmes.2008.030.001}
}