Symplectic Solutions in Singularity Problems of Anisotropic Beams
Based on the two-dimensional elasticity,the symplectic method is applied to study analytically the stress distributions of anisotropic beam.Using variation principle and introducing separation of variables, dual equations were presented.Then in the symplectic space which consists of the original variables and their dual variables,the problem can be solved via effective mathematical physics methods such as the method of sepatation of variables and eigenfunction vector expansion.So the original problems come down to solve the eigensolutions of zero eigenvalue and non-zeroes eigenvalue that describe the exponentially decaying localized solutions usually ignored by Saint-Venant's principle. Completed numerical examples are newly given to compare with established results.
Brendan Gan, Yu Gan and Y. Yu
Y. Z. Yang "Symplectic Solutions in Singularity Problems of Anisotropic Beams", Advanced Materials Research, Vols. 378-379, pp. 90-93, 2012