ABSTRACT
Using both analytical and numerical approaches, this paper describes in detail the detection and classification of critical points in the primary equilibrium path of structural systems. The Total Lagrangian formulation is employed to describe the kinematics of a biarticulated prismatic 3D bar element. With this formulation, the internal force vector and the tangent stiffness matrix including the geometric nonlinearity effects are obtained. An elastic linear constitutive model is assumed for the uniaxial stress-strain state. Such model uses the Green-Lagrange strain tensor and the second Piola-Kirchhoff axial stress tensor which are energetically conjugate tensors. As a study case, the article presents a simple structural system with three degrees of freedom made up of two bi-articulated prismatic 3D bars and a linear spring. Finally, the geometrical and physical conditions for the coalescence between limit and bifurcation points are determined.
Keywords:
Total Lagrangian description; geometrical nonlinearity; critical points
