Non‐linear structural analysis by dynamic relaxation

Brew, J. S.; Brotton, D. M.

doi:10.1002/nme.1620030403

Cited by 80 publications

(42 citation statements)

References 10 publications

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“…The following is the summary of results given in Reference [5]. For a multidimensional, linear system, the stability of the iterative scheme depends on the values of t; K and M deÿned earlier, and in particular on 1 , the largest eigenvalue of the matrix M −1 K. For stability [5]:…”

Section: Stability Of the Iterative Solutionmentioning

confidence: 99%

Computational form‐finding of tension membrane structures—Non‐finite element approaches: Part 1. Use of cubic splines in finding minimal surface membranes

Brew

Lewis

2002

Numerical Meth Engineering

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SUMMARYThis paper, presented in three parts, discusses a computational methodology for form-ÿnding of tension membrane structures (TMS), or fabric structures, used as rooÿng forms. The term 'form-ÿnding' describes a process of ÿnding the shape of a TMS under its initial tension. Such a shape is neither known a priori, nor can it be described by a simple mathematical function. The work is motivated by the need to provide an e cient numerical tool, which will allow a better integration of the design=analysis=manufacture of TMS. A particular category of structural forms is considered, known as minimal surface membranes (such as can be reproduced by soap ÿlms). The numerical method adopted throughout is dynamic relaxation (DR) with kinetic damping.Part 1 describes a new form-ÿnding approach, based on the Laplace-Young equation and cubic spline ÿtting to give a full, piecewise, analytical description of a minimal surface. The advantages arising from the approach, particularly with regard to manufacture of cutting patterns for a membrane, are highlighted.Part 2 describes an alternative and novel form-ÿnding approach, based on a constant tension ÿeld and faceted (triangular mesh) representation of the minimal surface. It presents techniques for controlling mesh distortion and discusses e ects of mesh control on the accuracy and computational e ciency of the solution, as well as on the subsequent stages in design.Part 3 gives a comparison of the performance of the initial method (Part 1) and the faceted approximations (Part 2). Functional relations, which encapsulate the numerical e ciency of each method, are presented.

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Section: Stability Of the Iterative Solutionmentioning

confidence: 99%

Computational form‐finding of tension membrane structures—Non‐finite element approaches: Part 1. Use of cubic splines in finding minimal surface membranes

Brew

Lewis

2002

Numerical Meth Engineering

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“…Dynamic relaxation is employed to investigate the actuation requirements (number of active elements) for folding and unfolding as well as the structural response of the module throughout shape transformations. Dynamic relaxation is an explicit numerical form-finding and analysis method of tensile structures (Day, 1965;Adriaenssens 2008;Ali et al, 2011;Richardson et al, 2013;Siu et al, 2013;Segal et al, 2015;) that avoids stiffness-matrix calculations (Brew and Brotton 1971) exploring the fact that the static solution for a structure subject to loading is the steady state of a step-force damped vibration. In this study, the spline-element formulation by Adriaenssens and Barnes (2001) is employed in the dynamic relaxation scheme to study elastic deformations due to bending.…”

Section: A Structurally Integrated Adaptive Tensegrity Structurementioning

confidence: 99%

Dialectic Form Finding of Structurally Integrated Adaptive Structures

Rhode-Barbarigos¹,

Charpentier²,

Adriaenssens³

et al. 2015

American Journal of Engineering and Applied Sciences

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Structural engineering, prompted by advances in mechanics and computing as well as design principles such as sustainability and resilience, is evolving towards adaptive structures. Adaptive structures are structures that use active components to change shape and properties in response to their environment and/or to their users' desires. Form-found structures, such as tensegrity and shell structures, can be designed to accommodate such changes within their structural behavior. Dialectic form finding is an extension of the traditional form-finding process integrating performance-related constraints and criteria in the search of a geometry in static equilibrium. Two examples of dialectic form-found structurally integrated adaptive structures are presented. The first example is a shape-shifting tensegrity-inspired structure, while the second example is a shapeshifting shell structure. Both systems are designed to explore elastic deformations for shape changes reducing actuation requirements and highlighting the potential of the proposed method.

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“…Besides the damping factor it includes the parameter c which determines the rate of the loading process. In order to find its appropriate value, the load time history p(t) is substituted into equation (3). After multiplication by pTM -, equation (3) can be solved for p'y(t) providing at the end of the interval:…”

Section: Jrt(t)mh(t) + 6yt(t)[ -Ml(t) + Ch(t)]lb = 0 (13)mentioning

confidence: 99%

“…Both viscous and kinematic damping may be used. 3 Within the framework of vector iteration methods, DR is often referred to as a three-term recursive formula. Valuable relations of DR to three other iterative methods have been e~tablished.~ Several authors have proposed automatic procedures for the evaluation of the iteration Algorithmic simplicity and small computer storage requirements are distinct merits of the method.…”

Section: Introductionmentioning

confidence: 99%

Optimum load time history for non‐linear analysis using dynamic relaxation

Rericha¹

1986

Numerical Meth Engineering

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SUMMARYA modification of the dynamic relaxation method is proposed which facilitates static analysis of non-linear problems. Continuous loading in time is adopted instead of the ordinary step function of time. Inertia and damping forces arising during the loading process are kept at a minimum using an optimum load time history. This results from the stationary condition of an appropriate functional. The equation of motion is included as a subsidiary condition. Continuous load-deflection curves can be obtained. An incremental solution is avoided. Application of the method is extremely simple. Existing programs based on explicit time integration schemes can be easily adapted for it. Sample solutions are presented.

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Non‐linear structural analysis by dynamic relaxation

Cited by 80 publications

References 10 publications

Computational form‐finding of tension membrane structures—Non‐finite element approaches: Part 1. Use of cubic splines in finding minimal surface membranes

Computational form‐finding of tension membrane structures—Non‐finite element approaches: Part 1. Use of cubic splines in finding minimal surface membranes

Dialectic Form Finding of Structurally Integrated Adaptive Structures

Optimum load time history for non‐linear analysis using dynamic relaxation

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