Numerical study of dynamic relaxation with kinetic damping applied to inflatable fabric structures with extensions for 3D solid element and non-linear behavior

Rodríguez, Juan Luis Rodríguez; Rio, Gérard; Cadou, Jean-Marc; Troufflard, Julien

doi:10.1016/j.tws.2011.07.011

Cited by 29 publications

(18 citation statements)

References 16 publications

(30 reference statements)

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“…Dynamic relaxation has been used successfully to solve a wide variety of equilibrium problems in tension structures such as membranes and cables (Silling 1988(Silling , 1989Shugar 1990;Haseganu and Steigmann 1994;Epstein and Forcinito 2001;Taylor and Steigmann 2009;Rezaiee-pajand et al 2011;Rodriguez et al 2011). Here, we briefly summarize the dynamic relaxation method implemented by Taylor et al (2014) for the simulation of equilibrium deformations in thin sheets.…”

Section: Dynamic Relaxation Methodsmentioning

confidence: 99%

A comparative analysis of numerical approaches to the mechanics of elastic sheets

Taylor

Davidovitch

Qiu

et al. 2015

Journal of the Mechanics and Physics of Solids

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Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of wrinkles in these problems have important implications in design and is an area of increasing interest in the fields of physics and engineering. In this work, several numerical approaches previously proposed to model equilibrium deformations in thin elastic sheets are compared. These include standard finite element-based static post-buckling approaches as well as a recently proposed method based on dynamic relaxation, which are applied to the problem of an annular sheet with opposed tractions where wrinkling is a key feature. Numerical solutions are compared to analytic predictions, enabling a quantitative evaluation of the predictive power of the various methods. Results indicate that static finite element approaches are highly sensitive to initial imperfections, relying on a priori knowledge of the equilibrium wrinkling pattern to generate optimal results. In contrast, dynamic relaxation is much less sensitive to initial imperfections and can generate solutions for a wide variety of loading conditions without requiring knowledge of the equilibrium solution beforehand.

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Section: Dynamic Relaxation Methodsmentioning

confidence: 99%

A comparative analysis of numerical approaches to the mechanics of elastic sheets

Taylor

Davidovitch

Qiu

et al. 2015

Journal of the Mechanics and Physics of Solids

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“…in [1], [2] and [3]) is suitable for actions with very short duration, such as explosions or the impacts of vehicles against obstacles, i.e. actions generally studied via transient dynamic analysis.…”

Section: Comparison Of the Used Numerical Methodsmentioning

confidence: 99%

Explicit and implicit method in nonlinear seismic analysis

et al. 2017

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Abstract. The paper deals with suitability of use of the explicit and implicit method in heavily nonlinear seismic analysis. Considering typical time of duration of earthquakes from several seconds to approximately twenty seconds, it would seem that use of the implicit method is definitely more suitable. The shape of accelerograms, however, requires quite short time steps. For the explicit method, on the other hand, very short time steps are required in order to obtain a stable solution. Both methods must be compared with respect to a heavily nonlinear response, typical for seismicity. Conclusions of the paper are made on the basis of detailed numerical study and may be very useful for practice. Numerical methods of direct integration of equation of motionIn the following text let us introduce the numerical methods used in the study. A system of motion equations of a discrete model of a structure subjected to a dynamic load can be written ( )

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“…The Explicit form of the Finite Element Method is based on a reformulation of the problem of static equilibrium to an artificial problem of dynamics with damping. Damping can be considered both explicitly with damping coefficients, and implicitly [13], [14].…”

Section: Explicit Form Of the Finite Element Methodsmentioning

confidence: 99%

Parallel Computation on Multicore Processors Using Explicit Form of the Finite Element Method and C++ Standard Libraries

Rek

Němec

2016

Strojnícky Casopis – Journal of Mechanical Engineering

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In this paper, the form of modifications of the existing sequential code written in C or C++ programming language for the calculation of various kind of structures using the explicit form of the Finite Element Method (Dynamic Relaxation Method, Explicit Dynamics) in the NEXX system is introduced. The NEXX system is the core of engineering software NEXIS, Scia Engineer, RFEM and RENEX. It has the possibilities of multithreaded running, which can now be supported at the level of native C++ programming language using standard libraries. Thanks to the high degree of abstraction that a contemporary C++ programming language provides, a respective library created in this way can be very generalized for other purposes of usage of parallelism in computational mechanics.

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Numerical study of dynamic relaxation with kinetic damping applied to inflatable fabric structures with extensions for 3D solid element and non-linear behavior

Cited by 29 publications

References 16 publications

A comparative analysis of numerical approaches to the mechanics of elastic sheets

A comparative analysis of numerical approaches to the mechanics of elastic sheets

Explicit and implicit method in nonlinear seismic analysis

Parallel Computation on Multicore Processors Using Explicit Form of the Finite Element Method and C++ Standard Libraries

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