Symplectic system for analytical solutions of orthotropic foundation beam

Based on the two-dimensional theory of elasticity (2DET),Hamiltonian system is introduced to solve the bending of orthotropic BeamsResting on Pasternak Elastic Foundations and the original problems come downto solve the eigensolutions of zero eigenvalue and non-zeroes eigenvalue.Elastic foundation is treated as the side boundary conditions similar to theapplied load and their contributions to the solutions of beams areapproximated by linear expansion of all eigensolutions of zero. Thesymplectic concept makes no hypothesis of deformation along the thicknessdirection and shows a rational derivation. Thus, the current method canprecisely analyze foundation beams with arbitrary depth-to-length ratio, andcan deal with arbitrary end conditions. In additional, a new improvedboundary condition for fixed ends beam is presented. Numerical examples incomparison with other methods are given to illustrate the accuracy of thepresent symplectic approach.