A novel torsion/bending element for dynamic relaxation modeling

Barnes, Michael R.; Adriaenssens, Sigrid; Krupka, Meghan T.

doi:10.1016/j.compstruc.2012.12.027

Cited by 42 publications

(41 citation statements)

References 12 publications

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“…Dynamic relaxation has been employed for the static analysis of truss structures [18,19], cable structures [20][21][22], tensegrity structures [23,24], prestressed net structures and membranes [25][26][27], reciprocal frames [28], spline structures [29] as well as for dynamic analyzes [30,31]. In this paper, dynamic relaxation is employed for the cross-sectional analysis of inflatable membrane dams.…”

Section: Dynamic Relaxation: the Basic Schemementioning

confidence: 99%

Form finding and analysis of inflatable dams using dynamic relaxation

Streeter

Rhode-Barbarigos

Adriaenssens

2015

Applied Mathematics and Computation

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Section: Dynamic Relaxation: the Basic Schemementioning

confidence: 99%

Form finding and analysis of inflatable dams using dynamic relaxation

Streeter

Rhode-Barbarigos

Adriaenssens

2015

Applied Mathematics and Computation

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“…in case of circular cross-section). Also, for naturally curved rods with isotropic cross-section, torsional stiffness can be taken into account by considering translational DoF only [32].…”

Section: Discrete Formulation: 3 4 or 6 Degrees Of Freedom?mentioning

confidence: 99%

“…This will make possible to reduce the number of existing contributions to only few, as those most relevant to our need. In particular: a set of 'main' references throughout the paper is represented by the works of Adriaenssens and Barnes on stressed spline structures [30,31,32].…”

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confidence: 99%

A finite-difference formulation of elastic rod for the design of actively bent structures

D’Amico

Zhang

Kermani

2016

Engineering Structures

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A discrete formulation of elastic rod has been tailored for the particular design task of geometric modelling, form finding and analysis of actively bent structural systems. The rod element is fully described by using vector based quantities, hence making it easy to implement and be suitable for explicit resolution methods such as the Dynamic Relaxation (DR). From this point of view, the model under consideration aims to provide a natural enhancement, of existing DR schemes of elastic rods, primarily formulated for analysis/design of stressed spline structures with isotropic cross-section, whilst, the proposed formulation allows for the general case of initially straight rods with anisotropic cross-section and torsional stiffness effects, to be taken into consideration. In order to avoid numerical conditioning problems, the method adopts a reduced Degrees of Freedom approach, however, the design limitations usually involved with such an approach, are 'removed' by adopting the Bishop theory of framed curves, hence making it possible to reduce to only three (translations) the Degrees of Freedom to be explicitly computed by numerical integration of the corresponding acceleration terms.

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“…More recently, new DR developments have been proposed in the works of Wood and Han and Lee . To allow for the form‐finding and analysis of a wider range of force‐modeled systems, more recent element formulations have included alternative membrane and pneumatic elements, non‐regular tensegrity modules , reciprocal frame links , pulley elements with friction , and beam and torsion elements .…”

Section: Introduction Context and Research Questionmentioning

confidence: 99%

The geodesic dynamic relaxation method for problems of equilibrium with equality constraint conditions

Miki

Adriaenssens

Igarashi

et al. 2014

Numerical Meth Engineering

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SUMMARYThis paper presents an extension to the existing dynamic relaxation method to include equality constraint conditions in the process. The existing dynamic relaxation method is presented as a general, gradient‐based, minimization technique. This representation allows for the introduction of the projected gradient, discrete parallel transportation and pull back operators that enable the formulation of the geodesic dynamic relaxation method, a method that accounts for equality constraint conditions. The characteristics of both the existing and geodesic dynamic relaxation methods are discussed in terms of the system's conservation of energy, damping (viscous, kinetic, and drift), and geometry generation. Particular attention is drawn to the introduction of a novel damping approach named drift damping. This technique is essentially a combination of viscous and kinetic damping. It allows for a smooth and fast convergence rate in both the existing and geodesic dynamic relaxation processes. The case study was performed on the form‐finding of an iconic, ridge‐and‐valley, pre‐stressed membrane system, which is supported by masts. The study shows the potential of the proposed method to account for specified (total) length requirements. The geodesic dynamic relaxation technique is widely applicable to the form‐finding of force‐modeled systems (including mechanically and pressurized pre‐stressed membranes) where equality constraint control is desired. Copyright © 2014 John Wiley & Sons, Ltd.

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A novel torsion/bending element for dynamic relaxation modeling

Cited by 42 publications

References 12 publications

Form finding and analysis of inflatable dams using dynamic relaxation

Form finding and analysis of inflatable dams using dynamic relaxation

A finite-difference formulation of elastic rod for the design of actively bent structures

The geodesic dynamic relaxation method for problems of equilibrium with equality constraint conditions

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