The natural force density method for the shape finding of taut structures

Pauletti, Ruy Marcelo de Oliveira; Pimenta, Paulo de Mattos

doi:10.1016/j.cma.2008.05.017

Cited by 64 publications

(33 citation statements)

References 16 publications

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“…This approach is known as the generalized FDM formulation based on FEM described in literatures [8,9,[16][17][18][19].…”

Section: Fdm Formulation Based On Femmentioning

confidence: 99%

“…The various formulation of force density modes are proposed and explained in papers [18,19] and commercial software (Forten 4000, Easy, Rhinomembrane [16,17]) by their unique methodologies. The relationship between force density and equilibrium equation of system may be linear and nonlinear with respect to the element length.…”

Section: Linear and Nonlinear Shape Finding Analysis According To Thementioning

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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“…This approach is known as the generalized FDM formulation based on FEM described in literatures [8,9,[16][17][18][19].…”

Section: Fdm Formulation Based On Femmentioning

confidence: 99%

Section: Linear and Nonlinear Shape Finding Analysis According To Thementioning

confidence: 99%

Advanced Shape Finding Algorithm of Force Density Method Based on Fem

Lee¹,

Han²

2011

Volume 7 Number 4

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“…The designer must therefore obtain the initial equilibrium configuration, taking into account how the system is assembled in practice and the geometric constraints imposed. Although little attention has been paid in the literature to the shape-finding of the catenary system, it is a well-known and challenging problem in the design of other cable structures, such as light large-area roofs or cable-supported bridges [21][22][23][24][25][26]. As pointed out in [27,28], the initial configuration of the catenary can strongly influence the results of the dynamic simulation.…”

Section: Introductionmentioning

confidence: 99%

“…A review of shape-finding methods can be found in [21]. The non-linear displacement method [22,23] and the force density method [24][25][26] are the two most commonly used formulations. The method proposed in this work can be considered a variation of the non-linear dis-placement method, and even though it is a general method, we applied it to finding the initial configuration of a railway catenary.…”

Section: Introductionmentioning

confidence: 99%

A 3D absolute nodal coordinate finite element model to compute the initial configuration of a railway catenary

Tur¹,

Garcia²,

Baeza³

et al. 2014

Engineering Structures

105

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ElsevierTur Valiente, M.; García, E.; Baeza González, LM.; Fuenmayor Fernández, FJ. (2014) AbstractIn this paper we propose a method of finding the initial equilibrium configuration of cable structures discretized by finite elements applied to the shape-finding of the railway overhead system. Absolute nodal coordinate formulation finite elements, which take into account axial and bending deformation, are used for the contact and messenger wires. The other parts of the overhead system are discretized with non-linear bars or equivalent springs. The proposed method considers the constraints introduced during the assembly of the catenary, such as the position of droppers, cable tension, height of the contact wire, etc. The main result of the shape-finding problem is the computation of the length of droppers. A comparison of the results obtained for reference catenaries in the bibliography is also included.

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“…It is represented by the force density method derived from special discretization and linearization techniques (Schek, 1974). Although this method enables fast determination of equilibrium surfaces, it should be pointed out that additional iterative procedures are inevitable when it is used to model minimal surface forms (Maurin and Motro, 1998;Pauletti and Pimenta, 2008), and thus some of its attractiveness is lost. Unlike the preceding two methods, in the dynamic equilibrium methods (e.g., dynamic relaxation method (DRM)), a steady equilibrium shape for an initially unbalanced structure is achieved by simulating a damped vibration process over time .…”

Section: Introductionmentioning

confidence: 99%

An efficient numerical shape analysis for light weight membrane structures

Yang

Shen

Luo

2014

J. Zheijang Univ.-Sci.

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Abstract:The determination of initial equilibrium shapes is a common problem in research work and engineering applications related to membrane structures. Using a general structural analysis framework of the finite particle method (FPM), this paper presents the first application of the FPM and a recently-developed membrane model to the shape analysis of light weight membranes. The FPM is rooted in vector mechanics and physical viewpoints. It discretizes the analyzed domain into a group of particles linked by elements, and the motion of the free particles is directly described by Newton's second law while the constrained ones follow the prescribed paths. An efficient physical modeling procedure of handling geometric nonlinearity has been developed to evaluate the particle interaction forces. To achieve the equilibrium shape as fast as possible, an integral-form, explicit time integration scheme has been proposed for solving the equation of motion. The equilibrium shape can be obtained naturally without nonlinear iterative correction and global stiffness matrix integration. Two classical curved surfaces of tension membranes produced under the uniform-stress condition are presented to verify the accuracy and efficiency of the proposed method.

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The natural force density method for the shape finding of taut structures

Cited by 64 publications

References 16 publications

Advanced Shape Finding Algorithm of Force Density Method Based on Fem

Advanced Shape Finding Algorithm of Force Density Method Based on Fem

A 3D absolute nodal coordinate finite element model to compute the initial configuration of a railway catenary

An efficient numerical shape analysis for light weight membrane structures

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