Are the terms stiffening/softening structures mechanically unambiguous?

Abstract

The purpose of this paper is to give a conditionally affirmative answer to the question posed in its title. The tool that enables such an answer is a mechanically objective arc-length in the form of a representative displacement of the structure. In this context, mechanical objectivity is defined as the independence of model parameters, such as the chosen finite element or the discretization of the investigated structure in the framework of a consistent mesh refinement. It guarantees, e.g., the mechanical objectivity of the transition from a stiffening to a softening structure and vice versa. It is shown numerically that at this point some characteristic degrees of freedom (d.o.f.) of the investigated structure are stiffening while others are softening. Hence, individual d.o.f. are, in general, unsuitable for marking extreme values of the stiffness of structures. A global quantity, alternative to the suggested stiffness in this work, is the extreme value of the determinant of the tangent stiffness matrix. It is shown numerically that, in general, this value depends on arbitrary model parameters and, therefore, does not have a physical meaning. An oblate rotational ellipsoidal shell, subjected to internal pressure, serves as an example for buckling of a stiffening shell, contradicting the widespread misconception of buckling being restricted to non-stiffening structures.