Programmable structures are formed by autonomous and adaptive triangular cells. However, they are composed of a large number of parts, specifically bearings, which make them laborious to manufacture and expensive. An essential part of these programmable structures are six-bar linkages, which allow to build cells that can preserve the underlying geometry of a triangular mesh. A major improvement, which is the main part of this paper, is to replace the joints of the six-bar-linkage by a compliant mechanism, which allows to manufacture them as one 3D printable part. A multibody system formulation is setup with the model of the compliant mechanisms, treating every joint either ideal or compliant with the given stiffness parameters. The multi-body formulation furthermore allows to include friction as well as an actuator model in a straight-forward manner. The overall stiffness parameter of the real system is then identified from a comparison with an experimental setup of a real compliant triangular cell. Finally, the model is used to show the deviations of a medium-scaled programmable structure with respect to the idealized behavior. The present paper marks a relevant step towards the realization of larger programmable structures as well as the development of 3D programmable structures.
The present work addresses pipes conveying fluid and axially moving beams undergoing large deformations. A novel two dimensional beam finite element is presented, based on the Absolute Nodal Coordinate Formulation (ANCF) with an extra Eulerian coordinate to describe axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used to model axially moving beams and pipes conveying fluid. The proposed approach, which is derived from an extended version of Lagrange's equations of motion, allows for the investigation of the stability of pipes conveying fluid and axially moving beams for a certain axial velocity and stationary state of large deformation. Additionally, a multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations, we show that axially moving beams and a larger number of discrete masses behave similarly as the case of (continuously) distributed mass.
The present paper addresses axially moving beams with co-moving concentrated masses while undergoing large deformations. For the numerical modeling, a novel beam finite element is introduced, which is based on the absolute nodal coordinate formulation extended with an additional Eulerian coordinate to represent the axial motion. The resulting formulation is well known as Arbitrary Lagrangian Eulerian (ALE) method, which is often used for axially moving beams and pipes conveying fluids. As compared to previous formulations, the present formulation allows us to introduce the Eulerian part by an independent coordinate, which fully incorporates the dynamics of the axial motion, while the shape functions remain independent of the beam coordinates and are thus constant. The proposed approach, which is derived from an extended version of Lagrange’s equations of motion, allows for the investigation of the stability of axially moving beams for a certain axial velocity and stationary state of large deformation. A multibody modeling approach allows us to extend the beam formulation for co-moving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations we show that a larger number of discrete masses behaves similarly as the case of (continuously) distributed mass along the beam.
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