Theory of Nonlinear Elastic Structures

The different sources of nonlinearity in elastic structures undergoing large displacements are identified, and a general matrix formulation of the theory of nonlinear elastic structures is developed. It is shown that the nonlinearity results from the nonlinearity of the transformations relating member deformations to joint displacements, from the necessity of formulating the joint equilibrium equations in the displaced configuration of the structure, and from the nonlinear action-deformation relationships of the structural members. Matrix expressions for the secant and tangent stiffnesses of members and structures are presented in a general form, and evaluated for the particular case of a beam element. The importance of selecting consistent tangent stiffnesses for solutions by methods of Newton type is emphasized.