ABSTRACT
Marguerre-von Kármán’s (MvK) theory for large deflection of thin isotropic elastic shells leads to two coupled nonlinear fourth-order partial differential equations. This chapter presents four propositions for the symmetry groups of the homogeneous MvK equations which imply the two group classification results. Both the time-independent and the time-dependent MvK equations constitute self-adjoint systems and are Euler-Lagrange equations. In the static case, the balance laws provide a set of path-independent integrals inherent to Marguerre’s shell theory. Among them are the counterparts of the well-known and widely used in fracture mechanics J-, L-, and M-integrals.
