Some counterstressed dual-cable structures (German), D Jawerth, Proceedings of the IASS Colloquium on hanging roofs, continuous metallic shell roofs and superficial lattice roofs, Paris, 1962.
The suspension structure in the article, the Jawerth system, is made up of two suspension cables which are stressed against each other using a zigzag of struts. The upper cable forms a concave link polygon and the lower cable a convex one. The erection of various buildings with this system is presented.
Steel cable creates novel structural space systems, L Zetlin, AISC Engineering Journal, First Quarter, 1964.
This paper presents means and design methods to achieve structural systems for suspension roofs which do not exhibit the phenomenon of aerodynamic instability. It does not deal with, nor attempt to determine, the behavior of a suspension roof during flutter. For practical purposes, if factors contributing to self-exciting vibrations are eliminated from a structural system to begin with, investigation of, and design for, flutter becomes irrelevant. The structural system presented in this paper consists of cables interconnected in such a manner that there is always flow of energy from a cable which tends to flutter to other cables which are at a lower energy level.
The design and testing of a cable beam structure for prefabrication, H Buchholdt, B McMillan, V Gill, Proceedings of the IABSE Ninth Congress, Amsterdam, 1972.
This paper contains the description and testing of a cable beam structure which has been developed for prefabrication and low cost. The experimental results nave been compared with the results from two different non-linear theories indicating for which cases the two different theories are applicable.
Stress strain relation for coated fabrics, R Testa, L Yu, Journal of engineering mechanics, Volume 113, Number 11, ASCE 1987.
A constitutive relation is formulated for coated fabrics that exhibit both elastic and inelastic, but time-independent, responses. The nonlinear orthotropic response is represented by an elastic portion related to yarn stretch and coating shear, and an inelastic part related to crimp interchange. A method is proposed to compute the path-dependent inelastic strain and the elastic strain for any loading once material parameters are evaluated from uniaxial tests in the principal directions of elasticity.
Equivalence of a hanging cable net to an orthotropic membrane, G Yamada, Y Kobayashi, S Nakae, Journal of Sound and Vibration, Volume 145, Issue 1, 1991.
In this short note, the equivalence of hanging cable nets to orthotropic membranes is discussed. Cable nets are approximated by the lumped masses at intersections of the cables, and by substituting the kinetic and strain energies of the net system into Lagrange’s equation, the equations of motion of the system are derived. In this case, the intersections of the cables are assumed to be connected by the frictionless pin-joints and the sides of the cable nets to be supported without bending.
On the feasibility of using large scale photogrammetry to accurately determine in-service strain distribution across three-dimensional textile roofs, L Grundig, E Moncrieff, H Schewe, Euromech 334, Textile composites and textile structures, Lyon, 1995.
This paper presents the results obtained from a proof of concept simulation study into the feasibility of using a photogrammetric measurement system to accurately determine in-service strain distribution across full scale three dimensional textile roofs. The simulation has been carried out using synthetic images generated by photo-realistic raytracing software. Such a strategy allows for the incorporation of poor lighting and other potentially degrading effects. Particular attention has been addressed to the expected effects on measurement precision of image resolution; target shape, size, number and contrast; and operator access.
Numerical simulation of the flow over sails in real sailing conditions, T Charvet, F Hauville, S Huberson, Journal of Wind Engineering and Industrial Aerodynamics, Volume 63, Issues 1-3, 1996.
We present recent results concerning the numerical simulation of flow around ship sails. The main purpose of our work has been to derive a numerical model which includes real effects to the utmost. The basic numerical model is made of a lifting surface code for the sail and a vortex method for its wake. This description of the flow is supplemented by considering the fluid structure interaction problem, the sea surface influence on the flow, the effect of non-homogeneous incoming flow (vertical wind gradient and gusts), the ship hull motion, and sail interactions.
Application of a non-convex model of fabric deformations to sail cut analysis, O Maitre, S Huberson, J Cursi, Journal of Wind Engineering and Industrial Aerodynamics, Volume 63, Issues 1-3, 1996.
In this paper, we present a computer model based on an elastic string network representation for sail deformation. The equilibrium equation for this model is written in the form of a minimization problem. The latter is non-convex because of the unilateral-stress behavior of strings. The method of deconvexification has to be used in order to obtain an equivalent problem which is easier to solve. The resulting model is applied to sail cut design problems: bi- and tri-radial cut plans are compared, as well as variations of the elasticity modulus in warp and weft directions. The results are found to be very similar to what is usually observed on actual sail boats.
Finite element analysis of nonlinear orthotropic hyperelastic membranes, S Kyriacou, C Schwab, J Humphrey, Computational Mechanics, Volume 18, Issue 4, 1996.
A finite element method is presented for geometrically and materially nonlinear orthotropic hyperelastic membranes. The constitutive relations are formulated in terms of the invariants of the 2D right Cauchy-Green strain tensor and the resulting system of nonlinear equations solved using a Newton-Raphson approach. Example problems are solved for isotropic and orthotropic membranes, and the effect of various parameters investigated.
Geodesic and semi-geodesic line algorithms for cutting pattern generation of architectural textile structures, L Grundig, L Ekert, E Moncrieff, Proceedings of asia-pacific conference on shell and spatial structures, IASS, Beijing, China, 1996.
The general field of stressed membrane surface structures is first introduced. The design processes typically involved in the design of such membranes, namely Form-finding, Statical Load Analysis and Cutting Pattern Generation, are next described. Specific consideration of Geodesic Line Generation and the requirements for a practical solution strategy are then given. A novel procedure for addressing the complex problem of generating Semi-Geodesic lines is next presented. All the line generation tools implemented in the widespread lightweight structure design system, Easy, including Geodesic and Semi-Geodesic are then described. Finally, these tools are demonstrated using a typical example surface. Due to the general importance of good quality seam line generation, the strategy described is applicable for all cutting pattern generation systems.
A three-dimensional fe nonlinear analysis of membranes, B Wu, X Du, H Tan, Computers & Structures, Volume 59, Number 4, 1996.
This paper presents a three-dimensional finite element method for computing stress and deformation of membrane structures. A conjugate pair of strain and stress tensors, the Green strain tensor and the Second Piola-Kirchhoff stress tensor are adopted to give the constitutive equation of Mooney material. By means of exploiting the plane stress condition of membrane, the hydrostatic pressure is directly expressed as functions of strains. Complex membrane structures, like those initially in box shape with abrupt changes in geometry, can also be analyzed by the proposed method.
Formulation of a curved quadrilateral element for surface definition, P Gosling, W Lewis, Computers & Structures, Volume 61, Number 5, 1996.
Based on a finite element discretisation, the numerical form-finding of geometrically non-linear surfaces spanning arbitrary boundaries and subjected to an initial prestress is presented. A 24 dof quadrilateral finite element is formulated to represent a general curved elastic (or inelastic) geometrically non-linear surface. The proposed isoparametric element is C0 continuous, of constant thickness, and assumes a plane-stress criterion. A rigorous derivation of the expressions describing the strains within a curved surface is offered, while the element equations are written with special consideration of the effects of large strains and large displacements. Assuming small incremental displacements, expressions are derived to explicitly include the adequate representation of rigid body rotations in the element geometric stiffness matrix.
Form-finding of prestressed membranes using a curved quadrilateral finite element for surface definition, P Gosling, W Lewis, Computers & Structures, Volume 61, Number 5, 1996.
Form-finding of minimal surface membranes is investigated in this paper. A curved quadrilateral finite element is used to provide a numerical representation of a thin surface (structural membrane) established between fixed or flexible boundaries. Pre-stress is introduced to generate the form. Application of the matrix based finite element method to the vector based dynamic relaxation algorithm is presented. When analysing minimal surfaces, the assumption of large strains is shown to lead to a stress deviation at equilibrium. Various techniques are proposed to improve the numerical stability of the solution algorithm. The resulting final numerical model adequately represents both large displacements and large summative strains. Comparisons between numerical and experimental solutions to several minimal surfaces demonstrate the accuracy of the proposed formulation.
Dynamic analysis of tension structures, B Tabarrok, Z Qin, Computers & Structures, Volume 62, Number 3, 1997.
The equations of motion for curved membranes are determined via Hamilton’s principle and subsequently solved by the finite element method. Initially linearized equations are determined by considering small amplitude oscillations about the position of static equilibrium: Later, more accurate equations are determined by taking account of geometrical nonlinearities in the displacement-strain relationships.
The form-finding of structures possessing a constant surface stress, PhD Thesis, T Lewis, Department of Engineering, University of Warwick, England, 1997.
A method for the generation of structures of a constant surface stress is presented; the prime application being the form-finding of light-weight tension structures. However, rigid forms generated from the principle are also discussed. The numerical approach adopted for the solution to the geometrically non-linear problem of form-finding is that of the Dynamic Relaxation method, incorporating kinetic damping. The numerical solutions produced describe surfaces of a minimum surface area and a zero mean curvature.
Formulation of constitutive equations for fabric membranes based on the concept of fabric lattice model, S Kato, T Yoshino, H Minami, Proceedings of the fifth international conference on computational plasticity, Barcelona, Spain, 1997.
The present paper discusses on a new formulation for continuum constitutive equations of fabric membranes based on a fabric lattice model. The equations consider the material nonlinearities of yarns and coatings and include crimp interchange between warp and weft yarns. The equations are formulated in an incremental form which can be directly applied to FEM. The validity of the constitutive equations is discussed by comparing with those obtained from testing.
Analysis of membrane structures based on fabric lattice model considering viscous characteristics, S Kato, H Minami, T Yoshino, T Namita, Proceedings of the IASS international symposium on shell & spatial structures, Singapore, 1997.
The present paper aims at proposing an analysis method for stress-deformation of tensioned membrane structures based on fabric lattice model including the viscous characteristics. In this study the fabric lattice model previously proposed by the first author for the static case is extended to include the effects of the material viscosity into the time dependent constitutive equations.
Large displacement analysis for ideally flexible sails, O Maitre, J Cursi, S Huberson, European Journal of Mechanics - A/Solids, Volume 17, Number 4, 1998.
We consider the equilibrium of a sail under aerodynamic field of external forces. The sail is considered to be an ideally flexible structure, having the behavior of a network of stress unilateral strings: all the internal efforts are traction efforts. This model leads to a Non Convex Optimization Problem and a complete theory can be established, leading to relevant results of uniqueness for the field of stresses, even if configurations of equilibrium are not unique.
Form finding and optimization of membranes and minimal surfaces, K Bletzinger, Lecture notes, Technical university of Denmark, Lyngby, 1998.
Membrane structures are very attractive alternatives to span large distances. They are very light, elegant, and effective. The material is optimally used since the structures are subjected only to membrane tension stresses. The art of form finding means to find the optimal deflected and finally visual shape due to a given stress distribution acting on the deformed structure. The problem is very closely related to the determination of minimal surfaces.
Experimental and analytical study on visco-elasto-plastic characteristics of ptfe-coated glass fiber fabric under cyclic loadings, S Kato, H Minami, S Segawa, T Yoshino, Proceedings of the lightweight structures in architecture, enginnering and construction IASS/IEAust/LSAA international congress, Sydney, Australia, 1998.
The paper discusses the validity of the constitutive equations, previously proposed by the present authors, for the visco-elasto-plastic behaviors of fabric membranes by comparing the simulated behaviors with the experimental results recently performed also by the present authors. The constitutive equations are formulated based on Fabric Lattice Model where important material elements in the fabric material are replaced into intrinsic bar elements with time dependent behaviors as well as material non-linearities for which material constants are assumed to be as much compatible with measured results in experiments. The experiments are performed under two conditions; one is the relaxation test under a constant bi-axial strains with initial bi-axial tensions and the other one is the cyclic test under re-tension by five times after each relaxation in each re-tensioning process. The experimental results are compared with the simulated behaviors and the comparison shows a fair agreement.
The surface stress density method as a form-finding tool for tensile membranes, B Maurin, R Motro, Engineering Structures, Volume 20, Number 8, 1998.
Form-finding for membrane tension structures is a delicate operation, which must ensure both the absence of compressive areas and interactive control of the forms generated. Until now, methods have generally been based on large displacements and strain analysis that provide non-linear formulations; resolution and computation are, therefore, too complex and cumbersome. This paper describes a new method of form-finding which reflects a wish to provide architects with a simple, effective and reliable investigations suited to their needs. The surface stress density method uses surface triangular elements with an isotropic stress tensor and leads to an interactive procedure, which converges, on configurations that satisfy the laws of static equilibrium.
A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations, J Bonet, A Burton, Computer methods in applied mechanics and engineering, Volume 162, Number 1, 1998.
This paper presents a simple isotropic hyperelastic constitutive equation that can be used to model fiber oriented elastic materials in the fully nonlinear range. The hyperelastic strain energy function that defines this material is given in terms of three new material parameters and equations relating these material parameters to the Poisson ratio and the Young modules of the material along the fiber direction and on the orthogonal plane are derived. Expressions for the second Piola-Kirchhoff tensor, the Cauchy stress tensor and the Lagrangean and Eulerian elasticity tensors are also obtained. Static and dynamic applications of this material are used to illustrate its performance.
A new approach to geometric nonlinearity of cable structures, A Kwan, Computers & Structures, Volume 67, Number 4, 1998.
The basic structural principles surrounding nonlinear behavior of cable networks are explained through the example of a two-link structure. The nonlinear static response to load for this structure is then derived explicitly using the proposed simple approach. The proposed approach is then tested on three three-dimensional cable networks and the results compared with those obtained by three other techniques, namely geometric stiffness matrix, dynamic relaxation and general minimum energy.
Finite element analysis of dynamic response of wrinkling membranes, S Kang, S Im, Computer Methods in Applied Mechanics and Engineering, Volume 173, Issues 1-2, 1999.
A new iterative scheme for finite element analysis of wrinkling membranes, originally devised for static analysis, is extended for analyzing dynamic response of wrinkling membranes. The scheme is found to be successfully implemented with an explicit total Lagrangian finite element code based upon the central difference method. The finite element implementation of the scheme is straightforward, and only minor modifications are needed for existing membrane finite element codes. The validity of the scheme is demonstrated via a numerical simulation of an inflating automotive airbag, made of orthotropic membranes, under impulse pressure loading.
Form finding and analysis of tension structures by dynamic relaxation, M Barnes, International Journal of Space Structures, Volume 14, Number 2, 1999.
The paper describes numerical procedures, based on the method of dynamic relaxation with kinetic damping, for the form finding, analysis and fabrication patterning of wide-span cable nets and grid shells, uniform or variably prestressed fabric membranes and battened membrane roofs. The historical development of the method is briefly reviewed and a full description is then given which accounts for cable or strut elements, membrane elements and spline beam elements. All of these elements are implemented in their natural stiffness form allowing for gross geometrical and material non-linearities, with automatic controls to ensure stablility and convergence of the method.
Woven fabric composite material model with material nonlinearity for nonlinear finite element simulation, A Tabiei, Y Jiang, International Journal of Solids and Structures, Volume 36, Issue 18, 1999.
The objective of the current investigation is to develop a simple, yet generalized, model which considers the two-dimensional extent of woven fabric, and to have an interface with nonlinear finite element codes. A micromechanical composite material model for woven fabric with nonlinear stress-strain relations is developed and implemented in ABAQUS for nonlinear finite element structural analysis. Within the model a representative volume cell is assumed. Using the iso-stress and iso-strain assumptions the constitutive equations are averaged along the thickness direction. The cell is then divided into many subcells and an averaging is performed again by assuming uniform stress distribution in each subcell to obtain the effective stress-strain relations of the subcell. The stresses and strains within the subcells are combined to yield the effective stresses and strains in the representative cell. Then this information is passed to the finite element code at each material point of the shell element.
Formulation of constitutive equations for fabric membranes based on the concept of fabric lattice model, S Kato, T Yoshino, H Minami, Engineering Structures, Volume 21, Number 8, 1999.
The present paper proposes and discusses a new formulation of continuum constitutive equations for fabric membranes for architecture. The formulation is based on a fabric lattice model where the structure of the fabric membranes is replaced into an equivalent structure composed of truss bars representing yarns and coated materials. The equations consider the material nonlinearities of yarns and coatings and include crimp interchange between warps and wefts. Since the equations are formulated in an incremental form in terms of in-plane strains, the formulations can be directly applied to FEM analysis of the fabric membranes. The validity of the proposed constitutive equations is discussed by comparing the simulated results with those obtained by testing the materials under uni-axial, bi-axial and shear loadings.
Generation of surfaces via equilibrium of forces, Y Zhang, B Tabarrok, Computers & Structures, Volume 70, Number 6, 1999.
This paper deals with the generation of minimal surfaces subject to a prescribed volume constraint and surfaces with a given mean curvature. The generation of a surface with a desired curvature is related to finding the equilibrium state of the surface under a uniform state of tension and under a prescribed pressure. Assuming an initial configuration, the surface is discretized into nodes and elements, and its final equilibrating configuration is found in a stepwise manner. In each step, the nodal forces are calculated and the surface is allowed to undergo displacements proportional to the nodal forces. Thus, the equilibrium state of the surface is obtained iteratively. The generation of a minimal surface subject to a prescribed volume constraint is also considered and analyzed by a generalization of the method outlined. Numerical examples are given to illustrate the described approach.
Tensioned fabric shape-finding, A Caner, R Hsu, Journal of Structural Engineering, Volume 125, Number 9, ASCE 1999.
Tensioned glass fiber-reinforced fabric has been used in roofs and canopies for various permanent structures such as stadiums and airport terminals all around the world. At its final state of geometry, the fabric shall be all in tension in its natural stable shape. The natural shape of the fabric can be generated by refining a 2D computer model to determine the 3D state using a geometric nonlinear analysis program for the personal computer. This paper presents an actual design case using a general purpose structural analysis program to reduce the complexity involved in finding the true natural shape of the tensioned fabric roofs.
Numerical analyses of cable roof structures, Licentiate Thesis, G Tibert, Department of Structural Engineering, Royal Institute of Technology, Sweden, 1999.
An extensive literature survey, concerned with both practical and theoretical aspects of cable roofs, is presented. The simple force density method is presented in detail and applied to a number of different types of cable roof structures. The method worked well for structures composed of only cables, but not for structures with compression members. Three analytical finite cable elements are presented. Two elements are mathematically exact and can accurately model both taut and slack cables using only one element per cable. A static analysis of the Scandinavium Arena in Gothenburg has been performed.
Numerical determination of mechanical elastic constants of textile composites, X Peng, J Cao, 15th Annual technical conference of the american society for composites, Texas, 2000.
This paper presents a novel procedure for predicting the effective nonlinear elastic moduli of textile composites through a combined approach of the homogenization method and the finite element method. The homogenization method is used first to obtain the effective elastic moduli of the fiber yarn based on the properties of the constituent phases. A unit cell is then built to enclose the characteristic periodic pattern in the composites. Various numerical tests such as uni-axial tension and trellising test are performed by 3D finite element analysis on the unit cell. Characteristic behaviors of force versus displacement are obtained. Meanwhile, trial mechanical elastic constants are imposed on a four-node shell element with the same size as the unit cell to match the force-displacement curves. The effective nonlinear mechanical stiffness tensor is thus obtained numerically as functions of elemental strains. The procedure is exemplified on a plain weave glass composite and is validated by comparing with 30-degree bias trellising and bi-axial tensile test results.
Nonlinear finite element for plain woven fabrics, O Kuwazuru, N Yoshikawa, 20th International congress of theoretical and applied mechanics, Chicago, 2000.
A new planar finite element is formulated to analyze the nonlinear behaviour of plain woven fabrics. The difficulty for the finite element formulation of the fabrics is on the handling of the nonlinearity caused by the discontinuity between threads. We introduce a strain-displacement relationship in lieu of the conventional one based on the continuum mechanics, since the discontinuity between threads violates the hypothesis of the continuum too much. Assuming that the friction among threads and the flexural rigidity of threads are negligibly small, we categorize the deformation of fabric into three types, that is, skewing, straightening and extension of threads. Each deformation is characterized by the new strain-displacement relationship with newly defined crimp parameter. The finite element is formulated on the principle of virtual work and solved by the Newton-Raphson method, since the obtained strain-displacement relationship gives rise to a kind of geometrical nonlinearity.
New numerical model of composite fabric behaviour, J Billoet, A Cherouat, Advanced composites letters, Volume 9, Number 3, 2000.
The present study concerns the modelling of the behaviour of pre-impregnated woven fabric during the forming process. The mechanical approach is based on a mesostructural model. It allows us to take into account the mechanical properties of fibres and resin and the various dominating mode of deformation of woven fabrics during the forming process. Shear and tensile tests of composite fabric specimens are proposed and compared with the experimental results in order to demonstrate the efficiency of our approach. Different numerical simulations and experiments of shaping process have been carried out in order to validate the proposed computational formulation. The various forming parameters examined have included the initial shape of fabric, fibre orientations and viscosity of resin.
Developability conditions for prestress optimization of a curved surface, M Ohsaki, J Fujiwara, Architectural Information Systems Laboratory, Report Number 00-05, Kyoto university, 2000.
Developability conditions are presented for prestressed curved surfaces to be reduced to plane sheets by relaxing the stresses. Those conditions are applied to an optimization problem for minimizing the deviation of stresses from the target values. Formulations based on the displacements defined by the local and global coordinates of finite elements are presented, and it is shown that the umbers of constraints by those formulations are same if triangular elements are used. Performances of those formulations are compared in the numerical examples, and the local formulation is shown to leads to more accurate estimation of stresses that are actually generated by connecting and stretching the plane sheets.
Finite element analysis of air supported membrane structures, J Bonet, R Wood, J Mahaney, P Heywood, Computer methods in applied mechanics and engineering, Volume 190, Number 5-7, 2000.
This paper deals with the finite element analysis of closed membrane structures that contain an enclosed fluid such as air. The change in the fluid pressure resulting from the application of external forces is evaluated and taken into account in the formulation of the equilibrium equations. The membrane formulation presented avoids the need for local co-ordinate axes by using the isoparametric finite element plane as a material reference configuration. The membrane material is modelled using standard large strain hyperelastic constitutive equations. The volume of fluid is obtained by integrating over the membrane surface and Boyle's law is used to determine the changes in air pressure that result from changes in volume. Full linearization of the internal pressure forces and the resulting additional term in the tangent operator are derived.
Finite element modelling of orthotropic material behaviour in pneumatic membranes, S Reese, T Raible, P Wriggers, International Journal of Solids and Structures, Volume 38, Issue 52, December 2001.
In this paper, we develop a model to describe the hyperelastic material behaviour of pneumatic membranes reinforced with roven-woven fibres. A generalized stored energy function is developed via a series of loading tests on a representative sample of this composite material. The exponents in the effective law are chosen so as to fulfil basic restrictions, discussed in the body of the paper, as well as to match certain experimental values. Numerical examples demonstrate the application of the approach to inflated rubber matrix materials, as well as laminated shells.
Form finding of membrane structures by the updated reference method with minimum mesh distortion, J Bonet, J Mahaney, International Journal of Solids and Structures, Volume 38, Issues 32-33, 2001.
This paper presents a new technique for the solution of the well-known form finding problem in membrane structures. The technique proposed is based on the updated reference configuration method proposed by Bletzinger in which an area functional is minimized within the context of a finite element discretisation. In this paper an additional functional term is introduced with the aim of minimizing the mesh distortion during the form finding process. This new term provides in-plane stiffness which prevents the emergence of mechanisms without the need for ad hoc changes of the tangent matrix.
Review of form-finding methods for tensegrity structures, G Tibert, S Pellegrino, Accepted by International Journal of Space Structures, 2001.
Seven form-finding methods for tensegrity structures are reviewed and classified. The three kinematical methods include an analytical approach, a non-linear optimisation, and a pseudo-dynamic iteration. The four statical methods include an analytical method, the formulation of linear equations of equilibrium in terms of force densities, an energy minimisation, and a search for the equilibrium configurations of the struts of the structure connected by cables whose lengths are to be determined, using a reduced set of equilibrium equations. It is concluded that the kinematical methods are best suited to obtaining only configuration details of structures that are already essentially known, the force density method is best suited to searching for new configurations, but affords no control over the lengths of the elements of the structure. The reduced coordinates method offers a greater control on elements lengths, but requires more extensive symbolic manipulations.
A bendable finite element for the analysis of flexible cable structures, P Gosling, E Korban, Finite elements in analysis and design, Volume 38, 2001.
An element formulation is developed for an analysis of cable structures where load reversal (tension to compression) may be significant. Strain energy associated with the deformation of an individual element is defined to include both membrane and bending components. Through the assumption of large strains and prestress, geometric non-linearity is introduced. Isoparametric absolute and relative interpolation schemes are combined to describe a C0 eight-degrees-of-freedom cable element applicable to three-dimensional space subsequent to transformation. Coupled with the Newton-Rapson scheme, solutions to numerical examples validate and demonstrate the capabilities of the proposed methodology.
New concept of pseudo-continuum model for plain-weave fabrics, O Kuwazuru, N Yoshikawa, Advancing affordable materials technology, pages 564-573, Proceedings of the 33rd SAMPE international technical conference, Seattle, 2001.
A new concept of pseudo-continuum model is proposed to analyze the complicated nonlinear behaviour of plain-weave fabrics. Subjected to an extension in an arbitrary direction, plain-weave fabric undergoes three kinds of thread deformation, that is, skewing, straightening and extension. On the assumption of no friction and no flexural rigidity with respect to the threads, a pseudo-continuum model is constituted by a new strain-displacement relationship which translates the three kinds of deformation to two kinds of strain, that is, axial extension and transverse compression of warp and weft. The finite element is formulated by means of the principle of virtual work in the total Lagrangian form. The mechanical nonlinearity and anisotropy of the plain-weave fabrics caused by geometrical nonlinearity of threads are elucidated through numerical examples concerning the uniaxial tensile tests.
FE analysis of large deformations of membranes with wrinkling, M Stanuszek, Finite Elements in Analysis and Design, article in press, accepted 12 November 2001.
The numerical analysis of large deformations of flexible membrane structures is considered in this paper. Taking advantage of the natural approach applied to the tension systems, complex membrane structures of arbitrary shape with wrinkling allowed are analyzed. In the study, the Finite Element Method with triangular membrane elements is used. The geometrical nonlinearity as a result of large displacements, shape dependent loads (internal pressure) and unilateral static boundary conditions add considerable complexity to the analysis of such objects. In the case of wrinkling a new concept of taking wrinkles into account based on the cable analogy is proposed.
Cutting pattern design of membrane structures considering viscoelasticity of material, J Fujiwara, M Ohsaki, K Uetani, Proceedings of the IASS Symposium on Theory, design and realization of shell and spatial structures, Nagoya, Japan, 2001.
A method is presented for determination of cutting patterns of membrane structures considering viscoelasticity of material. A constitutive law is proposed to represent viscoelastic behavior of material in the range around the target stress level. By using the proposed constitutive law, relaxation behavior of a membrane structure is estimated without time-history analysis. The effectiveness of the proposed method is discussed in the example.
Non-linear dynamic analysis of cable-suspended structures subjected to wind actions, M Lazzari, A Saetta, R Vitaliani, Computers & Structures, Volume 79, Issue 9, 2001.
The numerical analysis of the response of wind-loaded flexible structures is presented. Initially the modeling and simulation of wind velocity are studied, by considering stationary, multivariate stochastic process, according to its prescribed cross-spectral density matrix. In the second part of the paper, geometrically non-linear structures subjected to wind loads are investigated, by means of a finite element approach. One test example is presented to show the reliability of the numerical procedure to solve geometrically non-linear problem in dynamic field. Finally, the study of a real structure characterized by an initial pre-tension layer subject to wind action is carried out.
Numerical and experimental aeroelastic analysis of sails, D Coiro, F Nicolosi, F Scherillo, U Maisto, High Performance Yacht Design Conference, Auckland, 2002.
A computer code has been developed to perform the viscous aerodynamic analysis of a multi-sail system including mast effect. The code is based on 3D vortex lattice method coupled to 2D boundary layer solution along streamlines. Three nodes iso-parametric triangular elements have been chosen for the finite element method. To validate the structural computer code an experimental test has been set up and a simple machinery has been built allowing shape measurements of a rectangular membrane under constant pressure load.
Cable nets for bat habitat preservation, J Kretzmann, New Mexico Abandoned Mine Land Bureau, Santa Fe, New Mexico, 2002.
Cable-supported structures have been used in architectural and engineering practice for long spans, such as suspension bridges, and to cover large areas with a minimum of support columns, such as sports arenas and aviaries. Similarly, in bat habitat preservation in underground mines and caves, use of cable nets is particularly well adapted to large span, usually vertical, openings. Nets also provide a solution at smaller vertical openings where equipment access is constrained because of steep slopes or other barriers. A critical design and construction requirement for cable nets is the necessity for solid anchorage, generally into competent rock around the opening.
A finite-element model for the analysis of wrinkled membrane structures, R Ziegler, W Wagner, K Bletzinger, Universitat Karlsruhe, Institut fur Baustatik, 2002.
The problem of wrinkling in membrane structures has been a field of research since the publication of the tension field theory for plane structures. Significant progress in wrinkling analysis of arbitrarily shaped membranes has been made with the development of numerical methods. In the paper we present the enhancements of a standard finite element membrane formulation which allow to depict the wrinkles within the plane of the structure. A mathematical-numerical method is derived, which describes a valid stress state by minimizing the differences in the stress density function while observing the wrinkling conditions. A consistent linearization of the proposed algorithms ensures quadratic convergence behavior.
A new technique for optimum cutting pattern generation of membrane structures, J Kim, J Lee, Engineering Structures, Volume 24, Number 6, 2002.
In general, the cutting pattern for membrane structures is determined by dividing the complicated curved 3-D surface into several 2-D plane strips by using the geodesic line method or flattening technique. In this paper, a new analytical method for determining an optimum cutting pattern considering material properties is presented. The optimization method proposed can diminish the deviations occurring from numerical errors as well as from material properties.
Formfinder - concept for a software-tool to assist architects in the preliminary design of form-active structures, PhD Thesis, R Roithmayr, Vienna University of Technology, Austria, 2003.
The text describes the concept for the realisation of a software-tool entitled Formfinder. The tool is intended to assist architects in the preliminary design of form-active systems. Form-active structure systems are structure systems of flexible, non-rigid matter, in which the redirection of forces is effected through particular form design and characteristic form stabilization. The designer outlines the desired design just as he or she would use a pen and a sheet of paper. The software visualizes the behaviour of a form-active system and guides the designer to a possible next step. A model-based recognition algorithm analyses the sketch and compares analogies with information stored in a data base.
Equilibrium conditions of a tensegrity structure, D Williamson, R Skelton, J Han, International Journal of Solids and Structures, Volume 40, Issue 23, 2003.
This paper characterizes the necessary and suffcient conditions for tensegrity equilibria. Static models of tensegrity structures are reduced to linear algebra problems, after first characterizing the problem in a vector space where direction cosines are not needed. This is possible by describing the components of all member vectors. While our approach enlarges (by a factor of 3) the vector space required to describe the problem, the advantage of enlarging the vector space makes the mathematical structure of the problem amenable to linear algebra treatment. Using the linear algebraic techniques, many variables are eliminated from the final existence equations.
The making of a tensegrity tower, H Klimke, S Stephan, MERO GmbH, 2003.
A tensegrity tower was conceived for the fair in Rostock (Germany). The modules of the tower consist of three compression members of about 10 m length and nine cables, six horizontal cables and three diagonal cables. The key problem of tensegrity structures with respect to the production is the big movement of each module due to prestressing of the cables. All deflections have to be anticipated in the design of the components to eventually meet the desired geometry of the tower.
Finite element analysis of membrane structures, R Taylor, University of California at Berkeley, 2003.
This report summarizes the formulation for a large displacement formulation of a membrance composed of three-node triangular elements. A formulation in terms of the deformation gradient is first constructed in terms of nodal variables. In particular, the use of the right Cauchy-Green deformation tensor is shown to lead to a particulary simple representation in terms of nodal quantities. This may then be used to construct general models for use in static and transient analyses.
Approximate solution for a nearly flat square membrane subject to a uniform force per unit area, V Arcaro, A Palisoc, Proceedings of the IASS international symposium on shell & spatial structures, Taiwan, 2003.
This text presents an approximate solution for a nearly flat square membrane subject to a uniform transverse force per unit area. The total potential energy of the membrane is minimized with respect to the parameters of an assumed function for its displacements. This text corrects an error in the expression presented in the book Theory of Plates and Shells by Timoshenko and Woinowsky-Krieger (1959) and also in the book Tension Structures by Leonard (1988), extending the analytical solution for any value of the Poisson ratio. Comparing the analytic solution with the solution from ANSYS shows reasonable agreement.
Stability and mechanism order of isotropic prestressed surfaces, B Maurin, R Motro, International Journal of Solids and Structures, Volume 41, Issues 9-10, 2004.
The surface stress density method has been proposed as an effective form-finding tool for the design of fabric membranes. It enables tensile shapes to be determined by considering the isotropic prestress tensors in the membrane. The first objective of this paper is to demonstrate that the forms calculated in accordance with this mechanical property are stable. The second is to calculate their mechanism order. The approach is based on an energy criterion, pointed out by writing out the potential strain energy of the system and by using Lejeune-Dirichlet's theorem.
A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function, M Itskov, N Aksel, International Journal of Solids and Structures, Volume 41, Issue 14, 2004.
In the present paper we propose a set of orthotropic and transversely isotropic strain energy functions that (a) are polyconvex, (b) are proved to be coercive and (c) satisfy a priori the condition of the stress-free natural state. These conditions ensure the existence of the global minimizer of the total elastic energy and for this reason are very important in the context of a boundary value problem. The proposed hyperelastic model is represented by a power series with an arbitrary number of terms and corresponding material constants.
Deformation analysis of inflated cylindrical membrane of composite with rubber matrix reinforced by cords, B Marvalova, T Nam, XXI International Congress of Theoretical and Applied Mechanics, 2004.
We present the orthotropic hyperelastic material model for numerical simulation of the loading of the cylindrical membrane. The coefficients of strain energy function of the hyperelastic orthotropic material are fitted to the experimental results by the nonlinear least squares method. The components of the deformation gradient are determined from measured displacements of the grid points drawn on the cylindrical surface of the spring. The stress tensor is calculated from the membrane theory.
Optimization of class-2 tensegrity towers, M Masic, R Skelton, SPIE 11th Annual International Symposium on Smart Structures and Materials, 2004.
This paper concerns the optimal mass-to-stiffness ratio design of class-2 tensegrity towers. For different loading scenarios, the procedure seeks the topology and geometry of the structure that yields an optimal design satisfying common constraints. The domain of feasible tensegrity geometries is defined by imposing tensegrity equilibrium conditions on both unloaded and loaded structure. Remaining constraints include strength constraints for all elements of the structure and buckling constraints for bars. The symmetry of the design is imposed by restricting the domain of geometric variables and element parameters. The static response of the structure is computed by using a nonlinear large displacement model. The problem is cast in the form of a nonlinear program. The infuence of material parameters on the optimal shape of the structure is investigated.
An integrated analysis of membrane structures with flexible supporting frames, J Li, S Chan, Finite Elements in Analysis and Design, Volume 40, Issues 5-6, 2004.
Conventional analysis and design for tensioned membrane structures are separated by two assemblages, fixing the support positions and determining the equilibrium shape of the cable-membrane at first and checking the adequacy of the steel structure against support reactions. Under this methodology, the interaction between the cable-membrane and the steel structure is neglected. An integrated nonlinear finite element (FE) analysis, including cable element, membrane element and beam element in the FE library, is proposed in this paper for analysis of tensioned membranes supported by steel structures. The interaction between the support structure and the cable-membrane is examined through numerical study of a saddle shade pavilion structure.
Numerical solution of hyperelastic membranes by energy minimization, R Bouzidi, A Van, Computers & Structures, Volume 82, Issues 23-26, 2004.
A numerical approach is presented for solving problems of finitely deformed membrane structures made of compressible hyperelastic material and subjected to external pressure loadings. Instead of following the usual finite element procedure that requires computing the material tangent stiffness and the geometric stiffness, here we solve the membrane structures by directly minimizing the total potential energy, which proves to be an attractive alternative for inflatable structures.
Finite element formulation for modeling sliding cable elements, B Zhou, M Accorsi, J Leonard, Computers & Structures, Volume 82, Issues 2-3, 2004.
Sliding cable elements are developed to solve the general problem of constraining a string of cable elements to continuously pass through a prescribed moving node. These elements can be used for a wide variety of applications and in the current work are used to model various features in parachute systems. The principle of virtual work and total Lagrange formulation are used to derive the element internal force vector, tangent stiffness matrix, and time-dependent mass matrix and body forces. The element equations are implemented in a geometrically nonlinear, transient implicit finite element program.
Development of a wrinkling algorithm for orthotropic membrane materials, T Raible, K Tegeler, S Lohnert, P Wriggers, Computer Methods in Applied Mechanics and Engineering, Volume 194, Issues 21-24, 2005.
A commonly known problem while investigating membrane structures is the well wrinkling phenomena. In this work, we present and compare robust algorithms to predict wrinkled regions within complex membrane structures. Special focus is set on the application to isotropic and orthotropic membrane material formulations. As reference the solution of a 3-dshear test calculation is used. Special focus is set on the local and global characteristics of wrinkling.
Description and comparison of existing methods for static membrane structure formfinding, MSc Thesis, D Cooper, University of Stuttgart, Germany, 2005.
Different mechanically oriented methods and algorithms developed in the past to determine the form of membrane structures will be presented to give a state of the art. Two methods will be picked out and they will be discussed in more detail and illustrated with numerical examples. The results will then be analyzed to compare these methods.
Numerical form-finding of tensegrity structures, G Estrada, H Bungartz, C. Mohrdieck, International Journal of Solids and Structures, 43, 2006.
A novel and versatile numerical form-finding procedure that requires only a minimal knowledge of the structure is presented. Both equilibrium geometry and force densities are iteratively calculated. A condition of a maximal rank of the force density matrix and minimal member length, were included in the form-finding procedure to guide the search of a state of self-stress with minimal elastic potential energy. It is indeed able to calculate novel configurations, with no assumptions on cable lengths or cable-to-strut ratios. Moreover, the proposed approach compares favorably with all the leading techniques in the field.
Finite element analysis of prestressed structural membranes, A Gil, J Bonet, Finite Elements in Analysis and Design, 42, 2006.
A very powerful approach by means of the Nonlinear Continuum Mechanics theory is introduced for the analysis of prestressed membrane structures. Membranes and cables in taut, wrinkled or slack state are considered adequately in the numerical procedure. A finite element approximation along with a Newton-Raphson numerical scheme provide a very elegant and accurate way to solve the structural problem. To reveal the flexibility and robustness of the procedure, a complete assemblage of fabric textile, reinforcing cables and rigid members will be analyzed from its initial design stage to its final loaded configurations.
Eight-node quadrilateral double-curved surface element for membrane analysis, D Hegyi, I Sajtos, G Geiszter, K Hincz, Computers & Structures, Volume 84, Issues 31-32, 2006.
The dynamic relaxation method is applied to membrane analysis using an eight-node quadrilateral element. The element uses second order shape functions to approximate the geometry of the structure. The element is based on the element of Gosling and Lewis. They used a finite element approach. In this paper exact tensorial calculation is used to determine the exact deformation between the deformation-free state and the actual state.
Ranse investigations of downwind sails and integration into sailing yacht design processes, K Graf, H Renzsch, 2nd High Performance Yacht Design Conference, Auckland, 2006.
A fluid structure interaction method has been developed to calculate the viscous turbulent flow around flexible trimmable downwind sails. The structural part of the method is based on a Finite Element presentation of the sail modelled as a membrane. Minimization of the total potential energy function using a quasi Newton type method is carried out to calculate the displacement of the sail under aerodynamic loads. The flow around the deformed sail is calculated solving the Reynolds Averaged Navier Stokes Equation using a Finite Volume approach.
Wrinkled membranes I: experiments, Y Wong, S Pellegrino, Journal of Mechanics of Materials and Structures, Volume 1, Issue 1, 2006.
This paper presents a detailed experimental study of the evolution and shape of reversible corrugations, or wrinkles, in initially flat, linear-elastic and isotropic thin foils subject to in-plane loads. Two sets of experiments were carried out, on a rectangular membrane under simple shear and on a square membrane subjected to two pairs of equal and opposite diagonal forces at the corners.
Wrinkled membranes II: analytical models, Y Wong, S Pellegrino, Journal of Mechanics of Materials and Structures, Volume 1, Issue 1, 2006.
We present a general analytical model for determining the location and pattern of wrinkles in thin membranes and for making preliminary estimates of their wavelength and amplitude. A rectangular membrane under simple shear and a square membrane subject to corner loads are analysed.
Wrinkled membranes III: numerical simulations, Y Wong, S Pellegrino, Journal of Mechanics of Materials and Structures, Volume 1, Issue 1, 2006.
This is the third and final part of a study of wrinkles in thin membrane structures. High-fidelity, geometrically nonlinear finite element models of membrane structures, based on thin-shell elements, are used to simulate the onset and growth of wrinkles. The simulations are carried out with the ABAQUS finite element package.
Evaluation of membrane structure designs using boundary web cables for uniform tensioning, H Sakamoto, K Parka, Y Miyazaki, Acta Astronautica, 60, 2007.
The present paper begins with a brief review of existing designs of membranes surrounded by catenary cables and shear compliant borders. The paper then introduces weblike cables that surround the membrane, and analyzes the consequent reduction in mass and volume. In addition, a series of quasi-static finite element analyses demonstrates the attenuation of wrinkles by the web cables when support points are perturbed. The paper concludes that the proposed design preserves a biaxially prestressed membrane even in disturbed conditions, with a minimal suspension-cable mass and volume.
Advanced material model for coated fabrics used in tensioned fabric structures, J Pargana, D Lloyd-Smith, B Izzuddin, Engineering Structures, 29, 2007.
An accurate and reliable material model for plain weave coated fabrics used in the construction of Tensioned Fabric Structures is developed in this paper. The paper begins with an account of the material response of these fabrics, furnishing an understanding of the key elements that a successful material model should encompass. The paper also contains a review of existing models, which has highlighted the need for an accurate, reliable and fully calibrated material model. The proposed material model consists of a series of nonlinear elastic elements, frictional elements and rigid links to model the yarns, and an isotropic plate to model the coating.
Modelling and optimization of sails, M Spalatelu-Lazar, F Lene, N Turbe, Computers & Structures, article in press, 2007.
The aim of this paper is to improve the quality and the performances of sails by using non-linear modeling, numerical experimentation and optimization methods. The sail is represented by a triangular structure made of composite materials (unidirectional or woven composite) well modeled by an orthotropic membrane behavior. Under the wind pressure, the sail is submitted to large displacements and small strains. Initial pre-tension load which ensures that the surface is reasonably free of wrinkles is required. The numerical solution is carried out by means of a modified Newton-Raphson method. The mathematical problem of optimization relates to the displacement in the transverse direction of the sail. The parameter of design is the fiber orientation. The optimization method uses the Nelder-Mead algorithm, efficient to solve non-linear problems.