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Efficient Implementation Strategies for the Absolute Nodal Coordinate Formulation with Linear and Hyperelastic Material Laws.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Efficient Implementation Strategies for the Absolute Nodal Coordinate Formulation with Linear and Hyperelastic Material Laws./
Author:	Taylor, Michael E.
Description:	1 online resource (347 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-06, Section: B.
Contained By:	Dissertations Abstracts International84-06B.
Subject:	Mechanical engineering. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30242138click for full text (PQDT)
ISBN:	9798363500992

Efficient Implementation Strategies for the Absolute Nodal Coordinate Formulation with Linear and Hyperelastic Material Laws.
Taylor, Michael E.

Efficient Implementation Strategies for the Absolute Nodal Coordinate Formulation with Linear and Hyperelastic Material Laws. - 1 online resource (347 pages)

Source: Dissertations Abstracts International, Volume: 84-06, Section: B.

Thesis (Ph.D.)--The University of Wisconsin - Madison, 2022.

Includes bibliographical references

The Absolute Nodal Coordinate Formulation (ANCF) enables the inclusion of flexible bodies with geometric and material nonlinearities within a multibody dynamics simulation. Since the mass matrix for this nonlinear finite element formulation is generally constant, evaluating the element's generalized internal force and its Jacobian matrix are this formulation's most computationally expensive components. Several different calculation strategies for evaluating the generalized internal force and its Jacobian for continuum mechanics-based ANCF elements with linear elastic material laws can be found in the existing literature. However, based on these papers alone, it is unclear which computational strategy is the most efficient.To address this question, this thesis presents a detailed comparison of different computational strategies for the generalized internal force and its Jacobian using both hand calculations and timing studies on two computers. Four existing methods with additional enhancements were implemented alongside variations of a newly proposed method. While the new generalized internal force calculation is based on an existing strategy with modifications to improve memory transactions and instruction level-parallelism, the analytical expression for the Jacobian matrix is new. Although these different strategies calculate the same generalized internal force vector and its Jacobian, their execution performance is significantly different. While there are cases where some of the existing strategies have the advantage, in general, the new generalized internal force and Jacobian calculation strategy developed in this thesis proved to be the most efficient. Previous research has primarily focused on implementing linear elastic material laws within ANCF, with far less attention given to hyperelastic material laws within ANCF. This thesis partially addresses this gap by demonstrating how the new generalized internal force and Jacobian calculation strategy for linear elastic materials can be extended to the class of hyperelastic materials based on the principal invariants of the right Cauchy-Green deformation tensor. A two-term Mooney-Rivlin material law is compared with a linear material law to provide context for the relative execution performance of this proposed computational strategy.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798363500992Subjects--Topical Terms:

649730
Mechanical engineering.
Subjects--Index Terms:

Absolute nodal coordinate FormulationIndex Terms--Genre/Form:

542853
Electronic books.

Efficient Implementation Strategies for the Absolute Nodal Coordinate Formulation with Linear and Hyperelastic Material Laws.
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502 $a Thesis (Ph.D.)--The University of Wisconsin - Madison, 2022.
504 $a Includes bibliographical references
520 $a The Absolute Nodal Coordinate Formulation (ANCF) enables the inclusion of flexible bodies with geometric and material nonlinearities within a multibody dynamics simulation. Since the mass matrix for this nonlinear finite element formulation is generally constant, evaluating the element's generalized internal force and its Jacobian matrix are this formulation's most computationally expensive components. Several different calculation strategies for evaluating the generalized internal force and its Jacobian for continuum mechanics-based ANCF elements with linear elastic material laws can be found in the existing literature. However, based on these papers alone, it is unclear which computational strategy is the most efficient.To address this question, this thesis presents a detailed comparison of different computational strategies for the generalized internal force and its Jacobian using both hand calculations and timing studies on two computers. Four existing methods with additional enhancements were implemented alongside variations of a newly proposed method. While the new generalized internal force calculation is based on an existing strategy with modifications to improve memory transactions and instruction level-parallelism, the analytical expression for the Jacobian matrix is new. Although these different strategies calculate the same generalized internal force vector and its Jacobian, their execution performance is significantly different. While there are cases where some of the existing strategies have the advantage, in general, the new generalized internal force and Jacobian calculation strategy developed in this thesis proved to be the most efficient. Previous research has primarily focused on implementing linear elastic material laws within ANCF, with far less attention given to hyperelastic material laws within ANCF. This thesis partially addresses this gap by demonstrating how the new generalized internal force and Jacobian calculation strategy for linear elastic materials can be extended to the class of hyperelastic materials based on the principal invariants of the right Cauchy-Green deformation tensor. A two-term Mooney-Rivlin material law is compared with a linear material law to provide context for the relative execution performance of this proposed computational strategy.
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653 $a Computational strategies
653 $a Hyperelastic material laws
653 $a Linear elastic
653 $a Multibody dynamics
653 $a Nonlinear flexible bodies
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773 0 $t Dissertations Abstracts International $g 84-06B.
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