Exudyn – A C++ based Python package for flexible multibody systems

Gerstmayr, Johannes

doi:10.21203/rs.3.rs-2693700/v1

Cited by 5 publications

(7 citation statements)

References 16 publications

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“…Therefore, to increase computational performance, we compute an update and factorization of the iteration matrix in the so called "modified Newton method" only if needed. Therein, the iteration matrix is computed at the beginning of the simulation and updated during the iteration process only if either a predefined maximum number of Newton iterations is reached or the error in each Newton iteration could not be reduced by a predefined tolerance [40,41].…”

Section: Modified Newton Methodsmentioning

confidence: 99%

“…In the classical formulation 2, Cardan/Tait-Bryan angles (123-Euler angles, cf. [40,43]) and Euler parameters are used as rotation parameters. However, Euler parameters are used only in the classical formulation 2 in combination with implicit integration and by imposing the Euler parameter unit length condition as an additional constraint equation on position level, cf.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…However, Euler parameters are used only in the classical formulation 2 in combination with implicit integration and by imposing the Euler parameter unit length condition as an additional constraint equation on position level, cf. [40]. Both the LGIM and the classical formulation 2 are used in combination with explicit and implicit time integration methods.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…If h opt ≥ h, the current step is accepted, otherwise the step is recomputed with h new . For more details, see [40].…”

Section: Acknowledgmentmentioning

confidence: 99%

“…Following [40], we estimate the error of a time step with current step size h by using an embedded Runge-Kutta formula, which includes two approximations of order p and p = p−1. The approximations are obtained by using two different integration formulas with common coefficients a ij , but two sets of weights b i and bi , leading to two approximations ξ and ξ.…”

Section: Appendix a Implementation Details A1 Tangent Operatorsmentioning

confidence: 99%

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Evaluation and Implementation of Lie Group Integration Methods for Rigid Multibody Systems

Holzinger

Arnold

Gerstmayr

2023

Preprint

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As commonly known, standard time integration of the kinematic equations of rigid bodies modelled with three rotation parameters is infeasible due to singular points. Common workarounds are reparameterization strategies or Euler parameters. Both approaches typically vary in accuracy depending on the choice of rotation parameters. To efficiently compute different kinds of multibody systems, one aims at simulation results and performance that are independent of the type of rotation parameters. As a clear advantage, Lie group integration methods are rotation parameter independent. However, few studies have addressed whether Lie group integration methods are more accurate and efficient compared to conventional formulations based on Euler parameters or Euler angles. In this paper, we close this gap using several typical rigid multibody systems. It is shown, that explicit Lie group integration methods outperform the conventional formulations in terms of accuracy. However, it turned out that the conventional Euler parameter-based formulation is the most accurate one in the case of implicit integration, while the average number of Newton iterations required per time step is most often smaller for the Lie group integration method. It also turns out, that Lie group integration methods can be implemented at almost no extra cost in an existing multibody simulation code if the Lie group method used to describe the configuration of a body is chosen accordingly.

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Section: Modified Newton Methodsmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

“…If h opt ≥ h, the current step is accepted, otherwise the step is recomputed with h new . For more details, see [40].…”

Section: Acknowledgmentmentioning

confidence: 99%

Section: Appendix a Implementation Details A1 Tangent Operatorsmentioning

confidence: 99%

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Evaluation and Implementation of Lie Group Integration Methods for Rigid Multibody Systems

Holzinger

Arnold

Gerstmayr

2023

Preprint

Self Cite

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Multibody Models Generated from Natural Language

Gerstmayr,

Manzl,

Pieber

2024

Multibody Syst Dyn

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Computational models are conventionally created with input data, script files, programming interfaces, or graphical user interfaces. This paper explores the potential of expanding model generation, with a focus on multibody system dynamics. In particular, we investigate the ability of Large Language Model (LLM), to generate models from natural language. Our experimental findings indicate that LLM, some of them having been trained on our multibody code Exudyn, surpass the mere replication of existing code examples. The results demonstrate that LLM have a basic understanding of kinematics and dynamics, and that they can transfer this knowledge into a programming interface. Although our tests reveal that complex cases regularly result in programming or modeling errors, we found that LLM can successfully generate correct multibody simulation models from natural-language descriptions for simpler cases, often on the first attempt (zero-shot).After a basic introduction into the functionality of LLM, our Python code, and the test setups, we provide a summarized evaluation for a series of examples with increasing complexity. We start with a single mass oscillator, both in SciPy as well as in Exudyn, and include varied inputs and statistical analysis to highlight the robustness of our approach. Thereafter, systems with mass points, constraints, and rigid bodies are evaluated. In particular, we show that in-context learning can levitate basic knowledge of a multibody code into a zero-shot correct output.

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Six-Bar Linkages With Compliant Mechanisms for Programmable Mechanical Structures

Pieber,

Gerstmayr

2023

Journal of Mechanisms and Robotics

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Programmable mechanical structures are formed by autonomous and adaptive cells and can reproduce meshes known from the finite element method. Furthermore, they can change their structure not only through morphing, but also by self-reconfiguration of the cells. A crucial component of the cells, which can preserve the underlying geometry of a triangular mesh, are six-bar linkages. The main part of the present contribution concerns the six-bar linkages as a fully 3D-printable compliant mechanism where each revolute joint of the six-bar linkage is replaced with a notch flexure hinge with circular contour. There are two key drawbacks associated with the use of notch flexure hinges, namely, compliance in the flexure hinges and the fact that the center of rotation is not maintained. For self-reconfiguration of the cells, an efficient model is needed to predict the positioning errors. Therefore, the flexure hinge is represented by three distinct models, namely a finite element model, a beam model, and a simplified linearized model based on translational and rotational spring elements. These models are compared and evaluated in succession first to identify the parameters of the simplified model and later on, the simplified model is used to show the deviations of a medium-scaled programmable structure with respect to the idealized behavior. The current work brings us closer to both the development of programmable mechanical structures and the prediction of positioning errors during self-reconfiguration.

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Exudyn – A C++ based Python package for flexible multibody systems

Cited by 5 publications

References 16 publications

Evaluation and Implementation of Lie Group Integration Methods for Rigid Multibody Systems

Evaluation and Implementation of Lie Group Integration Methods for Rigid Multibody Systems

Multibody Models Generated from Natural Language

Six-Bar Linkages With Compliant Mechanisms for Programmable Mechanical Structures

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