Parallel computation schemes for dynamic relaxation

Topping, B. H. V.; Khan, Asad I.

doi:10.1108/02644409410799407

Cited by 45 publications

(20 citation statements)

References 5 publications

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“…The method was independently proposed by Day [20] and Otter [21] for the analysis of prestressed concrete pressure vessels, although (as noted by Topping [22]) its con-90 cept was already known by Rayleigh. The method has been extensively used for a wide range of structural problems with both geometric and material non-linearities as for instance, the form finding and load analysis of tension structures [23] where it provides more reliable results in terms of solution convergence if compared to the well known iterative matrix schemes with Newton-Raphson method [24].…”

Section: The Dynamic Relaxation Methodsmentioning

confidence: 99%

“…The method has been extensively used for a wide range of structural problems with both geometric and material non-linearities as for instance, the form finding and load analysis of tension structures [23] where it provides more reliable results in terms of solution convergence if compared to the well known iterative matrix schemes with Newton-Raphson method [24]. More-95 over, the DR does not require assembling/manipulation of a global stiffness matrix, hence it is relatively easy to implement and is highly suitable for parallel computing [22].…”

Section: The Dynamic Relaxation Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Form finding and structural analysis of actively bent timber grid shells

D’Amico

Kermani

Zhang

2014

Engineering Structures

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Grid shells are efficient structural systems covering large open spaces with relatively small amount of materials. Also, post forming techniques allow realization of geometrically complex (free-form) shapes by means of standard connection systems.However, due to complexity of the analysis-design process, they are rarely utilized in construction design. In this paper, a 'facilitating' numerical framework is introduced in which, for a given continuous reference shape, a geometrically similar discrete model is found by implementation of a six degree of freedom formulation of the Dynamic Relaxation method, to handle members bending and torsional stiffness. A grid cutting pattern algorithm is introduced, as well as methods to numerically simulate the double-layer construction technique and a novel (singlenode) cylindrical joint model. The methods are extensively tested and validated on a range of structures, from 'simple' single-rod cases to more complex, actively bent, grid shell frameworks.

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Section: The Dynamic Relaxation Methodsmentioning

confidence: 99%

Section: The Dynamic Relaxation Methodsmentioning

confidence: 99%

Form finding and structural analysis of actively bent timber grid shells

D’Amico

Kermani

Zhang

2014

Engineering Structures

View full text Add to dashboard Cite

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“…In contrast with viscous damping, which assumes that connection between the nodes has a viscous force component, kinetic damping is artificial damping with no real effect. Employed successfully by many authors, kinetic damping has been found to be stable and rapidly convergent when dealing with large displacements (Barnes, 1999;Papadrakakis, 1981;Topping and Khan, 1994). When kinetic damping is employed, the viscous damping coefficients in Eq.…”

Section: Fictitious Masses and Kinetic Dampingmentioning

confidence: 97%

Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm

Ali

Rhode-Barbarigos

Smith

2011

International Journal of Solids and Structures

162

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a b s t r a c tTensegrities are spatial, reticulated and lightweight structures that are increasingly investigated as structural solutions for active and deployable structures. Tensegrity systems are composed only of axially loaded elements and this provides opportunities for actuation and deployment through changing element lengths. In cable-based actuation strategies, the deficiency of having to control too many cable elements can be overcome by connecting several cables. However, clustering active cables significantly changes the mechanics of classical tensegrity structures. Challenges emerge for structural analysis, control and actuation. In this paper, a modified dynamic relaxation (DR) algorithm is presented for static analysis and form-finding. The method is extended to accommodate clustered tensegrity structures. The applicability of the modified DR to this type of structure is demonstrated. Furthermore, the performance of the proposed method is compared with that of a transient stiffness method. Results obtained from two numerical examples show that the values predicted by the DR method are in a good agreement with those generated by the transient stiffness method. Finally it is shown that the DR method scales up to larger structures more efficiently.

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“…An iterative process has traditionally been applied to solve these equations of motion for the form-finding of cable-net and membrane structures (Williams 2001;Topping and Iványi, 2008;Adriaenssens et al, 2012;Richardson et al, 2013) with discussions on the effects of the given parameters on convergence also available (Barnes, 1977;Topping and Khan, 1994) and so further elaboration is not needed here. However, a simple example is presented below, implementing the method on the free-form surface show in Fig.20.…”

Section: Grid Relaxationsmentioning

confidence: 99%

Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions

Jun

Shepherd

et al. 2019

J. Comput. Civ. Eng.

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Free-form grid structures have been widely used in various public buildings, and many are bounded by complex curves including internal voids. Modern computational design software enables the rapid creation and exploration of such complex surface geometries for architectural design, but the resulting shapes lack an obvious way for engineers to create a discrete structural grid to support the surface that manifest the architect's intent. This paper presents an efficient design approach for the synthesis of free-form grid structures based on "guide line" and "surface flattening" methods, which consider complex features and internal boundaries. The method employs a fast and straightforward approach, which achieves fluent lines with bars of balanced length. The parametric domain of a complete NURBS (Non-Uniform Rational B-Spline) surface is firstly divided into a number of patches, and a discrete free-form surface formed by mapping dividing points onto the surface. The free-form surface was then flattened based on the principle of equal area. Accordingly, the flattened rectangular lattices are then fit to the 2D surface, with grids formed by applying a guide-line method. Subsequently, the intersections of the guide-lines and the complex boundary are obtained, and the guide-lines divided equally between boundaries to produce grids connected at the dividing points. Finally, the 2D grids are mapped back onto the 3D surface and a spring-mass relaxation method is employed to further improve the smoothness of the resulting grids. The paper concludes bypresenting realistic examples to demonstrate the practical effectiveness of the proposed method.

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Parallel computation schemes for dynamic relaxation

Cited by 45 publications

References 5 publications

Form finding and structural analysis of actively bent timber grid shells

Form finding and structural analysis of actively bent timber grid shells

Analysis of clustered tensegrity structures using a modified dynamic relaxation algorithm

Computational Grid Generation for the Design of Free-Form Shells with Complex Boundary Conditions

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