Browsing by Author "Capobianco, Giuseppe"

Now showing 1 - 5 of 5

Open Access
Finite element formulations for constrained spatial nonlinear beam theories
(2021) Harsch, Jonas; Capobianco, Giuseppe; Eugster, Simon R.
A new director-based finite element formulation for geometrically exact beams is proposed by weak enforcement of the orthonormality constraints of the directors. In addition to an improved numerical performance, this formulation enables the development of two more beam theories by adding further constraints. Thus, the paper presents a complete intrinsic spatial nonlinear theory of three kinematically different beams which can undergo large displacements and which can have precurved reference configurations. Moreover, the hyperelastic constitutive laws allow for elastic finite strain material behavior of the beams. Furthermore, the numerical discretization using concepts of isogeometric analysis is highlighted in all clarity. Finally, all presented models are numerically validated using exclusive analytical solutions, existing finite element formulations, and a complex dynamical real-world example.
Open Access
Mechanical systems with frictional contact : geometric theory and time discretization methods
(2021) Capobianco, Giuseppe; Leine, Remco I. (Prof. Dr. ir. habil.)
This dissertation deals with the mathematical description and the simulation of mechanical systems with frictional contact. First, a geometric theory for the description of smooth mechanical systems is developed, which is then extended to allow for nonsmooth motions, i.e., motions with discontinuous velocities. The developed nonsmooth theory of mechanics is used to describe mechanical systems with frictional contact. Finally, two numerical schemes for the simulation of such systems are derived by using a time finite element method and the generalized-alpha approach, respectively.
Open Access
A nonsmooth generalized‐alpha method for mechanical systems with frictional contact
(2021) Capobianco, Giuseppe; Harsch, Jonas; Eugster, Simon R.; Leine, Remco I.
In this article, the existing nonsmooth generalized‐α method for the simulation of mechanical systems with frictionless contacts, modeled as unilateral constraints, is extended to systems with frictional contacts. On that account, we complement the unilateral constraints with set‐valued Coulomb‐type friction laws. Moreover, we devise a set of benchmark systems, which can be used to validate numerical schemes for mechanical systems with frictional contacts. Finally, this set of benchmarks is used to numerically assert the properties striven for during the derivation of the presented scheme. Specifically, we show that the presented scheme can reproduce the dynamics of the frictional contact adequately and no numerical penetration of the contacting bodies arises - a big issue for most popular time‐stepping schemes such as the one of Moreau. Moreover, we demonstrate that the presented scheme performs well for multibody systems containing flexible parts and that it allows general parametrizations such as the use of unit quaternions for the rotation of rigid bodies.
Open Access
On the divergence theorem for submanifolds of Euclidean vector spaces within the theory of second-gradient continua
(2022) Capobianco, Giuseppe; Eugster, Simon R.
In the theory of second-gradient continua, the internal virtual work functional can be considered as a second-order distribution in which the virtual displacements take the role of test functions. In its easiest representation, the internal virtual work functional is represented as a volume integral over a subset of the three-dimensional Euclidean vector space and involves first and second derivatives of the virtual displacements. In this paper, we show by an iterative integration by parts procedure how an alternative representation of such a functional can be obtained when the integration domain is a subset that contains also edges and wedges. Since this procedure strongly relies on the divergence theorem for submanifolds of a Euclidean vector space, it is a main goal to derive this divergence theorem for submanifolds starting from Stokes’ theorem for manifolds. To that end, results from Riemannian geometry are gathered and applied to the submanifold case.
Open Access
Stability of rigid body motion through an extended intermediate axis theorem : application to rockfall simulation
(2021) Leine, Remco I.; Capobianco, Giuseppe; Bartelt, Perry; Christen, Marc; Caviezel, Andrin
The stability properties of a freely rotating rigid body are governed by the intermediate axis theorem, i.e., rotation around the major and minor principal axes is stable whereas rotation around the intermediate axis is unstable. The stability of the principal axes is of importance for the prediction of rockfall. Current numerical schemes for 3D rockfall simulation, however, are not able to correctly represent these stability properties. In this paper an extended intermediate axis theorem is presented, which not only involves the angular momentum equations but also the orientation of the body, and we prove the theorem using Lyapunov’s direct method. Based on the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints. In particular, we show how this scheme is incorporated in an existing 3D rockfall simulation code. Simulations results reveal that the stability properties of rotating rocks play an essential role in the run-out length and lateral spreading of rocks.