Engineering analysis of tension structures: theory and practice

Wakefield, David

doi:10.1016/s0141-0296(98)00023-6

Cited by 93 publications

(39 citation statements)

References 3 publications

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“…31, the iterative numerical processes are required to obtain the equilibrium state. And the resulting equilibrium state of the equation usually leads to a geodesic surface which usually can be obtained by using iterative nonlinear numerical method [10][11][12][13][14][15]. As mentioned previously, the force density formulation of Eq.…”

Section: Nonlinear Shape Finding Analysis: Geodesic Shape Findingmentioning

confidence: 99%

“…The final shape may result in the geodesic surface that has been obtained by using DR geodesic shape finding analyses [10,11]. The geodesic string element of Barnes [10] and Wakefield [11] and the force density mode of Eq. (33) have conceptually and theoretically identical meanings in the nonlinear shape finding process.…”

Section: Shape Finding Analysis Of a Saddle-type Surfacementioning

confidence: 99%

“…The analysis process is therefore relatively simple compared with the nonlinear process of methods, such as the Newton-Raphson (NR) method [5][6][7][8][9] or the Dynamic Relaxation (DR) method [10][11][12][13][14][15] for minimum surface analysis. Therefore, it can easily be used in practical projects as a repeated shape finding process with respect to various types of configurations and can be incorporated into specific purpose analysis software such as EASY membrane(Technet), FORTEN 4000, RhinoMembrane [16,17].…”

Section: Introductionmentioning

confidence: 99%

“…The main drawback of the FDM is that the final distribution of stress is difficult to control. Therefore, once a form has been found, a vector or matrix method must be used to analyze its response under a load [10,11,15]. method preserves the linearity of original FDM, and overcomes the difficulties of irregular triangular finite element meshes.…”

Section: Introductionmentioning

confidence: 99%

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Advanced Shape Finding Algorithm of Force Density Method Based on Fem

Lee¹,

Han²

2011

Volume 7 Number 4

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This paper proposes a modified formulation of the force density method by adopting finite element method procedures and replacing each edge of a 3-node or 4-node membrane element with a linear line element. The membrane element model, not the cable-net model, is used for simultaneous shape finding and load analysis. The derived force density matrix has a banded, symmetric nature to ensure its effectiveness in an iterative procedure. By using the nonlinear shape finding option, a number of nonlinear shape finding problems can be solved for each force density mode controlling the shape of the surface. Therefore, it is needs not to use the nonlinear numerical method such as NR or DR method. Therefore, the present research may improve the effectiveness and applicability of the FDM in linear and nonlinear shape finding problems. The following numerical examples will verify the various excellent numerical abilities of the proposed FDM.

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Section: Nonlinear Shape Finding Analysis: Geodesic Shape Findingmentioning

confidence: 99%

Section: Shape Finding Analysis Of a Saddle-type Surfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Advanced Shape Finding Algorithm of Force Density Method Based on Fem

Lee¹,

Han²

2011

Volume 7 Number 4

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“…In the UK, the preferred form-finding method is dynamic relaxation 24 . It is viewed as extremely efficient, robust and accurate.…”

Section: Closing Remarksmentioning

confidence: 99%

Computational form-finding methods for fabric structures

Lewis¹

2008

Proceedings of the Institution of Civil Engineers - Engineering

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Form-finding is a process that determines the surface configuration of a fabric structure under pre-stress. This process can be carried out using a variety of numerical methods, of which the most common are: (i) transient stiffness, (ii) force density, and (iii) dynamic relaxation. This paper describes the three methods, discusses their advantages and limitations, and provides insights into their applicability as numerical tools for the design of fabric structures. Further, it describes various approaches to surface discretisation, and discusses consequences of using 'mesh control' and elastic effects in the design of form-found surfaces. A brief discussion of the general recommendations given in the European Design Guide for tensile surfaces structures concludes the paper. EACM-D-08-00023 W. J. Lewis, Computational form-finding…3

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Stress-adapted numerical form finding of pre-stressed surfaces by the updated reference strategy

Wüchner

Bletzinger

2005

Int. J. Numer. Meth. Engng

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SUMMARYIn this paper we present the updated reference strategy for numerical form finding of pre-stressed membranes, which is based on standard finite element discretization. The singularities of the inverse problem are regularized by a homotopy mapping. A projection scheme is proposed where anisotropic pre-stress is defined with respect to an additional reference plane, which reflects the initially developable surface of membrane strips in the production process. Physically problematic combinations of edge geometry and surface stress are solved by a self-adaptive stress correction scheme. The algorithm is based on a local criterion derived from differential geometry. Several examples illustrate the success of each idea and implementation.

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Engineering analysis of tension structures: theory and practice

Cited by 93 publications

References 3 publications

Advanced Shape Finding Algorithm of Force Density Method Based on Fem

Advanced Shape Finding Algorithm of Force Density Method Based on Fem

Computational form-finding methods for fabric structures

Stress-adapted numerical form finding of pre-stressed surfaces by the updated reference strategy

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