Geometrically exact initially curved Kirchhoff

In this paper we present geometrically exact Kirchhoff\'s initially curved planar beam model. The theoretical formulation of the proposed model is based upon Reissner\'s geometrically exact beam formulation presented in classical works as a starting point, but with imposed Kirchhoff\'s constraint in the rotated strain measure. Such constraint imposes that shear deformation becomes negligible, and as a result, curvature depends on the second derivative of displacements. The constitutive law is plasticity with linear hardening, defined separately for axial and bending response. We construct discrete approximation by using Hermite\'s polynomials, for both position vector and displacements, and present the finite element arrays and details of numerical implementation. Several numerical examples are presented in order to illustrate an excellent performance of the proposed beam model.