Click here to access/download;Manuscript;Advances in Pantographic Structures.pdf Click here to view linked References Francesco dell'Isola et al.

The fundamental review article DIE ALLGEMEINEN ANSÄTZE DER MECHANIK DER KONTINUA in the Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Bd. IV‐4, Hft. 5 (1913) by Ernst Hellinger has not been translated into English so far. We believe that such a circumstance is really deprecative, as the insight reached by Hellinger in the mathematical structure of continuum mechanics seems, in some aspects, unsurpassed even nowadays. Hellinger's scientific manuscripts do not fill more than one and half boxes in library storage , but their impact on mathematics and mechanical sciences is profound. Indeed, the Hellinger‐Reissner variational principle is still a fundamental tool in theoretical and numerical mechanics. The intent of this paper is threefold: i) to allow to those who cannot understand German to enjoy the reading of a crystal‐clear and still topical article whose content has some enlightening parts, ii) to show that only one century ago the principle of virtual work (or virtual velocities) was regarded as the central principle in continuum mechanics and that Hellinger did forecast already then the main lines of its development, iii) to discuss some technical and conceptual aspects of the variational principles in continuum mechanics which some authors consider still controversial.

In the present work, a new director-based finite element formulation for geometrically exact beams is proposed. The new beam finite element exhibits drastically improved numerical performance when compared with the previously developed director-based formulations. This improvement is accomplished by adjusting the underlying variational beam formulation to the specific features of the director interpolation. In particular, the present approach does not rely on the assumption of an orthonormal director frame. The excellent performance of the new approach is illustrated with representative numerical examples. CopyrightIn this section, we treat the theory of the geometrically exact beam, also known as the special Cosserat beam, introduced by [2] and [1]. The theory is developed by restricting the kinematics of the three-dimensional continuum to a beam-like kinematic. By inserting the reduced kinematics DIRECTOR-BASED BEAM FINITE ELEMENTS IN SKEW COORDINATES 115with the surface element d 2  D d 1 d 2 . For the sake of clarity, the contributions due to external forces and inertia are developed in compact form in the Appendix.

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