  The development of a nonlinear structural theory (model) for isotropic
linear-elastic finite continua is the main objective of the study. To derive
the theory, we used Taylor's multivariable expansion and Bubnov-Galerkin's weak
formulation. The resulting formulation is consistent with elasticity theory. As
a special case, we consider second order theory, resulting in 30 internal
degrees of freedom (IDF). A set of 30 ordinary differential equations (ODE) is
derived and must be solved to determine the deformation field. ODEs depend on
the initial and actual geometry of the structure, loads and material
properties. Our theory can be used to derive analytical or numerical solutions.
Aspects of generalization of the method to solids with nonlinear constitutive
relations are presented.
