Symmetry’s Applications to Bihamonic Equation and the Generalized Solution of Elasticity Problem
The generalized elasticity solutions are obtained in this paper by symmetries from Lie transformations. The symmetries of the bihamonic equation are obtained by mathematica package SYM. The several invariant solutions are found by solving the corresponding ordinary differential equations from Lie transformations. The superposition of invariant solutions, corresponding to an eigenfunction expansion, could yield the generalized elasticity solutions in rectangular coordinates and polar coordinates, where the eigenvalues arises from the invariance of bihamonic equation.
J. Qin and K. F. Huang, "Symmetry’s Applications to Bihamonic Equation and the Generalized Solution of Elasticity Problem", Applied Mechanics and Materials, Vols. 52-54, pp. 899-904, 2011