Alexander Humer

HOTINT: A Script Language Based Framework for the Simulation of Multibody Dynamics Systems

The multibody dynamics and finite element simulation code has been developed since 1997. In the past years, more than 10 researchers have contributed to certain parts of HOTINT, such as solver, graphical user interface, element library, joint library, finite element functionality and port blocks. Currently, a script-language based version of HOTINT is freely available for download, intended for research, education and industrial applications. The main features of the current available version include objects like point mass, rigid bodies, complex point-based joints, classical mechanical joints, flexible (nonlinear) beams, port-blocks for mechatronics applications and many other features such as loads, sensors and graphical objects. HOTINT includes a 3D graphical visualization showing the results immediately during simulation, which helps to reduce modelling errors. In the present paper, we show the current state and the structure of the code. Examples should demonstrate the easiness of use of HOTINT.Copyright

Large Deflections of Beams with an Unknown Length of the Reference Configuration

The present paper deals with large deflections and deformations of beams. As a novel aspect in the non-linear theory of beams, we study a case, in which the length of the reference configuration is not known in advance, namely a one span beam, which is axially fixed at one end, but can be pulled out axially from a compartment at the other end by transverse external forces, the place of this end in the reference configuration thus being unknown. We do not adopt the assumption of axial inextensibility. For the sake of simplicity, we assume the beam to be slender, neglecting the influence of shear upon the deformation, and we restrict to the case of a plane static deformation. Without loss of generality, the ends of the beam are taken as clamped against bending, and the normal force is set to zero at that compartment, from which the beam is pulled out. A continuum mechanics based derivation of the field equations for large displacements of slender beams is presented, which allows us to determine constitutive relations between certain generalized structural quantities on the basis of a constitutive modeling at the stress-strain level. Boundary conditions are formulated for the unknown place of the beam end in the reference configuration, and an additional relation for determining the latter place is derived. We then present a coordinate transformation, which enables us to write the resulting boundary value-problem with respect to a domain of fixed length. The transformed boundary value problem together with the additional relation for the unknown place of the boundary in the reference configuration is solved with conventional numerical methods applied to classical problems in non-linear structural mechanics. The solutions are presented in a non-dimensional framework and a critical non-dimensional load factor is determined, above which equilibrium cannot be reached, i.e. about which the beam would be pulled out indefinitely.

A rational treatment of the relations of balance for mechanical systems with a time-variable mass and other non-classical supplies

This contribution intends to present a rational methodology for mechanical systems with a variable mass, represented by a supply of mass. Special emphasis is given to the relations of balance and jump for such systems. In these relations, we also allow for other types of additional, non-classical supplies, e.g., supplies of linear and angular momentum. In doing so, we aim at completing and substantially extending formulations laid down in the famous article by Truesdell and Toupin (1960), who stated local relations of balance of mass and linear momentum in the presence of sources of mass, and, among other formulations with relevance to the present article, gave fundamental formulations for the case that a flow of mass through the surface of the system is present in the global relations of balance.

Modeling of Piezoelectric Materials by Means of a Multiplicative Decomposition of the Deformation Gradient

The present article investigates a novel approach for the constitutive modeling of piezoelectric continua subjected to large deformation and strong electric fields, which is based on a multiplicative decomposition of the deformation gradient tensor, a concept frequently used in the description of inelastic processes. By splitting the total deformation into an inelastic and a purely elastic part, the notion of a stress-free intermediate configuration is introduced, which evolves from the referential undeformed state if an electric field is present. Considering large deformations, the field equations of electromechanics need to be written in a geometrically exact form, which requires the introduction of suitable electric field quantities that fit into the Lagrangian framework adopted in the proposed formulation. To give an example of constitutive equations, the behavior of piezoelectric materials according to Voigt’s linear theory is generalized to the nonlinear case. For this purpose, the piezoelectric part of the deformation gradient is identified by comparing the corresponding nonlinear strain measures with the electrically induced strains in the linear theory of piezoelectricity. The present article discusses the implications and the quantitative influence of the choice of different strain tensors on the material response within the discussed approach.

Energy-Momentum Conserving Time Integration of Modally Reduced Flexible Multibody Systems

Many conventional time integration schemes frequently adopted in flexible multibody dynamics fail to retain the fundamental conservation laws of energy and momentum of the continuous time domain. Lack of conservation, however, in particular of angular momentum, may give rise to unexpected, unphysical results. To avoid such problems, a scheme for the consistent integration of modally reduced multibody systems subjected to holonomic constraints is developed in the present paper. As opposed to the conventional approach, in which the floating frame of reference formulation is combined with component mode synthesis for approximating the flexible deformation, an alternative, recently proposed formulation based on absolute coordinates is adopted in the analysis. Owing to the linear relationship between the generalized coordinates and the absolute displacement, the inertia terms in the equations of motion attain a very simple structure. The mass matrix remains independent of the current state of deformation and the velocity dependent term known from the floating frame approach vanishes due to the absence of relative coordinates. These advantageous properties facilitate the construction of an energy and momentum consistent integration scheme. By the mid-point rule, algorithmic conservation of both linear and angular momentum is achieved. In order to consistently integrate the total energy of the system, the discrete derivative needs to be adopted when evaluating the strain energy gradient and the derivative of the algebraic constraint equations.Copyright

The Absolute Nodal Coordinate Formulation

The key idea of the absolute nodal coordinate formulation (ANCF) is to use slope vectors in order to describe the orientation of the cross-section of structural mechanics components, such as beams, plates or shells. This formulation relaxes the kinematical assumptions of Bernoulli–Euler and Timoshenko beam theories and enables a deformation of the cross-sections. The present contribution shows how to create 2D and 3D structural finite elements based on the ANCF by employing different sets of slope vectors for approximating the cross-sections’ orientation. A specific aim of this chapter is to present a unified notation for structural mechanics and continuum mechanics ANC formulations. Particular focus is laid on enhanced formulations for such finite elements that circumvent severe issues like Poisson or shear locking. The performance of these elements is evaluated and a detailed assessment comprising the convergence order, the number of iterations, and Jacobian updates for large deformation benchmark problems is provided.

Enhancement of the stability of beams with piezoelectric transducers

Subject of the present work is the stability control of beam-type structures under a compressive force. Main scope of this article is to increase the critical buckling load by means of active feedback control. The compressive force is applied with the help of a cable which is fixed at the tip of the free end and passes through a point at the fixation of the beam. The structural displacement of the column is controlled by a constant gain feedback algorithm, with strain sensors used as input and piezoelectric actuators. A consistent theoretical formulation of this nonconservative system based on the Bernoulli–Euler beam theory is presented. The formulation takes into account the complete mechatronic system, including the influence of the controller with discrete strain measurements as well as distributed piezoelectric patches. The analytical results are compared to numerical simulations. The influence of the controller on the buckling load, the appearance of flutter instability and the limits of the controller’s operation range are highlighted.

Generalized Component Mode Synthesis for the Spatial Motion of Flexible Bodies With Large Rotations About One Axis

By far the most common approach to describe flexible multi-body systems in industrial practice is the floating frame of reference formulation (FFRF) very often combined with the component mode synthesis (CMS) in order to reduce the number of flexible degrees of freedom. As a result of the relative formulation of the flexible deformation with respect to the reference frame, the mass matrix and the quadratic velocity vector are state-dependent, i.e. non-constant. This requires an evaluation of both the mass matrix and the quadratic velocity vector in every integration step, representing a considerable numerical cost. One way to avoid the state-dependency is to use an absolute formulation as proposed in [2], which was extended in [4] for the use of the same shape functions as used in the classical CMS approach. In this approach, referred to as generalized component mode synthesis (GCMS), the total absolute displacements are approximated directly. Consequently, the mass matrix is constant, there is no quadratic velocity vector and the stiffness matrix is a co-rotated constant matrix. However, it was shown that when using the same shape functions as in the classical CMS approach, nine times the number of degrees of freedom are necessary to describe the same deformation shapes as in the CMS. Even though the integration times of the CMS and GCMS are of the same order, as presented in [5], in technical systems the majority of components are constrained to motions with only one single large rotation. Therefore, in this work the GCMS is formulated for large rotations around a fixed spatial axis. This allows to reduce the number of necessary flexible shape functions to three times the number of CMS shape functions and, consequently, further increases numerical efficiency compared to the GCMS for arbitrary large rotations. A piston engine composed of three flexible bodies, two of which rotate, is used as a test example for the planar formulation. It is compared to the GCMS and a classical FFRF with CMS. The results agree very well, while the GCMS for planar rotations is about three times faster than the other formulations.Copyright

Modeling of Dielectric Elastomers Accounting for Electrostriction by Means of a Multiplicative Decomposition of the Deformation Gradient Tensor

Nonlinear modeling of inelastic material behavior by a multiplicative decomposition of the deformation gradient tensor is quite common for finite strains. The concept has proven applicable in thermoelasticity, elastoplacticity, as well as for the description of residual stresses arising in growth processes of biological tissues. In the context of advanced materials, the multiplicative decomposition of the deformation gradient tenser has been introduced within the fields of electroelastic elastomers, shape-memory alloys as well as piezoelastic materials. In the present paper we apply this multiplicative approach to the special case of dielectric elastomers in order to account for the electrostrictive effect. Therefore, we seek to include the two main sources of electro-mechanical coupling in dielectric elastomers. These are elastostatic forces acting between the electric charges and electrostriction due to intramolecular forces of the material. In particular we intend to study the significance of electrostriction for the particular case of dielectric elastomers, in the form of a thin layer with two compliant electrodes.

Smoothed particle hydrodynamics and modal reduction for efficient fluid–structure interaction

ABSTRACT From wind turbines to capillary blood flow, problems of fluid–structure interaction occur across different scales of length and time. Owed to the multiple scales involved, the inherent complexity of coupled fluid and structural dynamics requires advanced numerical methods for the computational analysis. The proposed method relies on the coupling of modally reduced flexible multibody systems with fluids represented by the smoothed particle hydrodynamics method. A reduced-order basis is employed to describe small flexible deformation of a structural component relative to its large rigid body motion that is represented by a body-fixed frame. An efficient evaluation of the surface deformation of the bodies involved is a vital ingredient for the coupling. Conventional approaches suffer from the drawback of flexible deformation being represented in a body-fixed local frame. The generalized component mode synthesis, in which the total displacement is interpolated, mitigates this computational limitation. The linear relation between generalized coordinates and the total displacement allows the coupling forces to be evaluated within the parallel fluid framework. Only the reduced set of equations of motion is solved on the solid side using an implicit time integration scheme with possibly large time-steps, whereas the particle-based fluid simulation relies on a fast explicit scheme.