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In this paper, we describe the structure analysis by the finite element method of the gas-inflatable membrane structure with initial shape before pressure loading, on the assumption of the structure analysis of the gas-inflatable membrane reflector. The initial shape is assumed to be a paraboloid of revolution or similar shape. In the finite element formulation, to consider the influence of the initial shape, the strain based on the extensional strain is introduced. The experiment is also conducted to compare with the numerical calculation result. The agreement of the experiment result and the numerical result shows that our finite element formulation is appropriate.

The elastic constants are approximately determined using a multi-step linear approximation method for more accurate material nonlinear analysis of coated fabric membrane structures. The approximate determination is performed within each quadrilateral or triangular surface defined on the surfaces of the biaxial elongation property formed with the data of stress-strain curves measured by biaxial extension testings. Two types of 40 × 40 cm square flat membrane model of a PTFE coated plain-weave glass fiber fabric are analyzed applying finite element method adapting a 20-steps linear approximation method. One of the models is an inplane deformation model subjected to biaxial extension under the condition of stress ratio of 1:1. The stress-strain response in the central region of the membrane is analyzed. And the other model is a membrane deformed by the application of air pressure. The relation between the central deflection and the pressure is analyzed. The results of analysis showed excellent coincidences with experimental results.

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.

The property of the added air mass of a plane membrane suspended between supports and vibrating in x‐y plane with a half‐sine fundamental mode is obtained again by analysis with a normal method which differs from that presented in the last proceedings. The method used in this paper is that based on a source distribution modeling approach (the last method was that based on a vortex distribution modeling approach). The calculated result of a, the ratio of the added air mass to the mass of the membrane itself, is 0.94/(m/(r)), where m is the mass per unit area of the membrane, r the density of the air flow and l the length of the membrane. This result is roughly equal to that obtained from the method in the last paper.

[6](1,4)Naphthalenophane (1a), [6](1,4)anthracenophane (2a), and their peri-substituted derivatives 1b, 1c, and 2b were synthesized from 8-bromo[6]paracyclophane (4) by a benzoannelation method. The 1H NMR spectral properties of 1b, 1c, and 2b as well as the X-ray crystallographic structure analysis of 1b indicate that their bridged aromatic rings are more distorted than those of the corresponding parent systems, 1a and 2a. Thermally reversible photochemical isomerization of 1b and 2b took place readily, giving the corresponding Dewar valence isomers, 10b and 11b.

Follows a presentation at a symposium in 1993 where the authors presented an experimental investigation on a fluttering membrane for use in a wind‐tunnel. Analyses the fluttering of an object by a theoretical method. Compares the experimental results with those of the theoretical and discusses their effectiveness. States that the present analysis is effective for approximate investigations.

[6](1,4)Naphthalenophane (1a), [6](1,4)anthracenophane (2a), and their peri-substituted derivatives 1b, 1c, and 2b were synthesized from 8-bromo[6]paracyclophane (4) by a benzoannelation method. The 1H NMR spectral properties of 1b, 1c, and 2b as well as the X-ray crystallographic structure analysis of 1b indicate that their bridged aromatic rings are more distorted than those of the corresponding parent systems, 1a and 2a. Thermally reversible photochemical isomerization of 1b and 2b took place readily, giving the corresponding Dewar valence isomers, 10b and 11b.

Coated plain-weave fabrics are used as a membrane material of membrane structures including architectural membrane structures such as clear span air-supported membrane structure, flexible containers and airships. Uni/biaxial extension properties of coated fabrics are vary important for the design of membrane structures. In the present paper, the authors first presented SEM photographs of the surface and cut section to understand the structure of this material. Then unidirectional tensile tests were done up to failure. The stress-strain curves showed nonlineality and anisotropy. Some discussion was done on these properties. Poisson's ratio showed extreme nonlinearity at the stress region up to 20% of the failure stress which is the design stress. Specimens used here were a PTFE-coated grass fiber fabric and a PVC-coated polyester fabric which are widely used in the field of architectural membrane structure.

The crack-tear-strength properties of coated plain-weave fabrics, specimen A (PTFE-coated glass fiber fabric) and specimen C (PVC-coated polyester fiber fabric), were investigated by uni/bi-axial tensile testing using the specimens which had the breadth of 20-40cm and the initial crack length of 2a=0.5-5.0cm at the center. The crack-tear-strength, Tp, to 2a=1cm, where Tp was defined as the maximum tensile stress measured during the crack propagation, decreased abruptly to less than 50% of the uniaxial tensile breaking stress. Tp in the warp of specimen A with 2a=0.5-5.0cm on the biaxial stress condition was lower than that on the uniaxial stress condition, but it was opposite for specimen C. The coating materials did not affect the value of Tp. Further more, it was discussed that either the authors' or Racah's equation could be used as the mathematical expression of 2a-Tp curve measured.

The membrane materials are generally in various states of biaxial deformation in membrane structures, and also have visco-elasticity in addition to the peculiar nonlinearity. The biaxial extension curves, therefore, should be measured under the experimental conditions of iterative extension and various tensile speeds. In this paper, the authors selected PTFE coated plain-weave glass fiber and PVC coated plain-weave polyester fiber fabrics as the specimens, and measured the uni/biaxial extension curves up to the design stress (assumed to be 20% of the uniaxial breaking stress) under the experimental conditions of iterative extension and two different tensile speeds. The nonlinearity, the slope, and the iteration time up to convergence of the extension curves were studied. The dependences of these factors on tensile speed were also discussed. The main result of discussions was that the slope of extension curves depended upon tensile speed.

The biaxial stress-strain curves of PTFE-coated glass fiber (specimen A) and PVC-coated polyester fiber (specimen B) plain-weave fabrics were measured by maintaining the ratio of warp stress/fill stress at 1/1, 2/1 and 1/2. The extension curves, especially that of specimen A, showed peculiar high nonlinearity which was evident in the fill extension curves consisting of the parts of very small slope in the lower stress region and of steep slope in the stress region later. For the precise and practical structural analysis of membrane structure, the author presented a method of multi-step-linear approximation to the extension curves measured on many stress ratio conditions corresponding to a variety of biaxial deformation states in the real structure. The least square method was applied, and the error, which results from the approximation of elastic constants in the constitutive equation for each secant line through the extension curve, was made to be minimum in this method. By applying the method, the three-step-linear approximation was conducted on the specimens and the errors were evaluated. According to the result of the approximation, the accuracy was good for the practical application but was not so sufficient about the fill extension curve of specimen A. However, it can be generally said that the present method can be applied for the elastic structural analysis of membrane structures.

Tensile strength of specimens of coated fabric which had a crack, a bias crack and a circular defect respectively was measured using a uniaxial and using a biaxial tensile tester. Then, uniaxial and biaxial tensile strength figures were compared, and strengths for the three types of defect condition were compared. Further, uniaxial strengths of four types of coated fabric material specimens with cracks were measured, and the anisotropy of tensile strength along warp and filling was investigated. And, relations between crack opening ratio under deformation and stress were measured on the specimen.

Methods for analysing coated plain-weave fabric which has properties of nonlinear elasticity have not yet been satisfactorily developed. In this paper, a method which is promising for use in engineering applications like the strength analysis of membrane structures is presented. The finite element method using a rectangular element consisting of plain-weave fabric and coating material which is assumed to be an isotropic elastic plate of plane stress is applied to the method. Verification of the method is made by using uniaxial stress-strain responses. A square piece of coated plain-weave fabric with a square hole in it is analyzed as an example of application of the present method.

Method for deformation analysis of coated plain- weave fabrics which have nonlinear mechanical properties has been reported on this journal [1]. Following this, in this paper, biaxial tensile tester developed by the authors and the crucial specimen for the tester are introduced.And convergence properties of solution given by application of the method on the crucial specimen model of calculation are studied concerning to the coarseness of subdivision of finite ele ment and to the number of steps of iterative calculation.Finally, the methods are verified comparing biaxial stress-strain curves given by the calculation and the measurement.As a result, it is concluded that the method can be progressed toward the application to deformation analysis of membrane structures.

Practical procedure for evaluation of strength of coated fabrics with crack requires a formula which bears on expression of an inherent property of the materials in phenomenon of the crack extension.