In-plane Torsion Research Articles

Wrinkling on stretched circular membrane under in-plane torsion:: bifurcation analyses and experiments

Wrinkling on a stretched circular membrane under in-plane torsion is a typical and classical problem in the study of wrinkling on membrane structures. This paper presents the experiment and bifurcation analysis concerning this problem. Both isotropic polyester film and orthotropic PVC coated textile are considered. The nonlinear finite element method is used in the analysis. In the experiment, a method to measure stresses in the wrinkled membranes is proposed, and stresses are measured. The stress distributions and the shape of wrinkles observed in the experiments agreed well with those obtained by the analyses. The results of experiments and analyses also show that the tension field is formed in the wrinkled membranes.

Decohesive carrying capacity of a disk under tension and in-plane torsion

An elastic–perfectly plastic circular disk, with rigid circular inclusion of the radius a, subjected to simultaneous uniform radial tension and in-plane torsion is considered. External radius of the disk is assumed to be infinitely large, just to simplify the boundary conditions. Limit load-carrying capacity of such a disk cannot be reached, it is preceded by decohesive carrying capacity (DCC), defined by infinitely large radial strains ε r. They attain their upper bound for r= a; then the shearing strains γ r θ at r= a increase infinitely as well. In contradistinction to the limit carrying capacity, the decohesive carrying capacity depends essentially on Poisson's ratio v. Interaction curves corresponding to DCC are shown in the plane of external loadings. A comparison with the condition of discontinuous bifurcation under uniform stresses and strains is given, and full agreement is found, though in the case under consideration the state of stress is evidently non-uniform. Diagrams of stress and strain distribution at the moment of decohesion are also presented.

Six-dimensional calculation of intermolecular states in molecule-large molecule complexes by filter diagonalization: Benzene–H2O

We present an approach toward the dynamically exact calculation of intermolecular states in molecule-large molecule complexes. The approach employs an intermolecular Hamiltonian specifically formulated with the case of molecule-large molecule complexes in mind. In addition, it makes use of filter diagonalization techniques to diagonalize that Hamiltonian. The approach is applied to the calculation of J=0 intermolecular states below about 110 cm−1 in the benzene–H2O complex. The results of the calculation are interpreted in terms of five internal rotation states, a doubly degenerate bending mode and a singly degenerate stretching mode, the latter two modes involving the relative translation of the monomer moieties in the complex. The internal rotation states are discussed in the context of the two-dimensional, free internal rotation/water in-plane torsion model of Pribble et al. [J. Chem. Phys. 103, 531 (1995)]. It is shown that that model is largely successful in identifying the important features of the low-energy benzene–H2O states that involve rotation and/or libration of water. It is also shown, though, that multimode couplings can have major effects on the detailed nature of the intermolecular level structure of the species.

An assumed enhanced displacement gradient ring-element for finite deformation axisymmetric and torsional problems

When analyzing axisymmetric solids under torsion the possible reduction of the problem by one dimension, say the independence of the displacement- and rotation-field of the cylindrical (angle) co-ordinate Θ, should always be exploited. Whereas in the geometrically linear range the purely torsional problem, described by the rotational angle χ only, is always decoupled from the purely axisymmetric problem, described by the radial and axial displacements u and v only, this is not the case in finite deformation torsional problems. Thus, the finite deformation axisymmetric finite element with five enhanced gradient parameters can easily be extended to a finite deformation axisymmetric and torsional finite element with seven enhanced gradient parameters. Numerical results of two classical benchmarks, the in-plane torsion test and the necking of a circular bar, are presented. © 1998 John Wiley & Sons, Ltd.

An assumed enhanced displacement gradient ring‐element for finite deformation axisymmetric and torsional problems

When analyzing axisymmetric solids under torsion the possible reduction of the problem by one dimension, say the independence of the displacement- and rotation-field of the cylindrical (angle) co-ordinate Θ, should always be exploited. Whereas in the geometrically linear range the purely torsional problem, described by the rotational angle χ only, is always decoupled from the purely axisymmetric problem, described by the radial and axial displacements u and v only, this is not the case in finite deformation torsional problems. Thus, the finite deformation axisymmetric finite element with five enhanced gradient parameters can easily be extended to a finite deformation axisymmetric and torsional finite element with seven enhanced gradient parameters. Numerical results of two classical benchmarks, the in-plane torsion test and the necking of a circular bar, are presented. © 1998 John Wiley & Sons, Ltd.

面内捩りを受ける円形張力膜のしわ : 有限要素法による分岐解析と実験の比較

In this paper finite element analyses of wrinkling on membranes are carried out, and the results are compared with the results of our experiments. An illustrative example is stretched circular membrane under inplane torsion, which is a classical problem in the study of wrinkling. Wrinkling is considered as a bifurcation phenomenon. It is analyzed by using four-node membrane finite elements considering geometrical nonlineality. Both isotropic and orthotropic membranes are treated. Membranes are assumed to be elastic. Formulation of the element, a method of introducing initial stresses and a method of bifurcation analysis are shown. First computations for several kinds of shear modulus are carried out and shapes of wrinkles and stress fields are compared. Second computations corresponding to the experiments are carried out. Principal stresses in wrinkling fields and shapes of wrinkles obtained by the analyses and the experiments show good agreement. However, details of the shapes are a little different, since in the analyses the fineness of a finite element mesh is not sufficient.

面内捩りを受ける円形張力膜のしわ : ポリエステルフィルムとC種膜の実験

The problem of circular stretched membranes under inplane torsion is a typical example in studying wrinkling on membrane structures. In this paper experiments of the example are carried out. A feature of the experiment is that both isotropic polyester films and orthotropic coated fabrics are treated, since membranes used in spatial architectures are usually orthotropic. Few studies on wrinkling on orthotropic membranes can be found. Another feature of the experiment is that stresses in the wrinkled membranes are measured. For that purpose, first a method for measuring stresses in thin membranes is presented. Second stresses in the wrinkled circular membranes are measured by using the method, and finally principal stresses are obtained. The results show that (1)there are no compressive stresses in the wrinkled membranes, (2)directions of tensile principal stresses almost coincide with directions of wrinkles, and (3)in the coated fabrics, these two kinds of directions almost coincide with directions of fabrics. Photos of wrinkles on various kinds of membranes are also shown.

回転対称膜構造に発生するしわの有限要素法による解析

An important characteristic of membranes is that they cannot support compressive stresses since they have almost zero bending rigidity. Therefore, when compressive stresses exist in a membrane structure, wrinkling occurs. In this paper, four examples of wrinkling on membrane structures of revolution are analyzed as a bifurcation buckling problem by using conical frustum finite elements considering geometrical nonlinearity. Post-wrinkling behavior is examined by following bifurcation paths. Illustrative examples are l)a hemispherical shell under meridional tension, 2)a spherical shell under external pressure, 3)an inflated membrane of ellipsoid and 4)a circular membrane under inplane torsion. In the circular membrane, results obtained by using quadrilateral elements and Mikulas's theoretical solution are also shown in order to discuss their applicability to the analysis of wrinkling.

A Self-Sensing Piezolaminated Actuator Model for Shells Using a First Order Shear Deformation Theory

A composite piezolaminated shallow thin shell theory has been developed in which the individual laminae are capable of electromechanical transduction. Utilizing a first order shear deformation approximation and assuming that an electrical field may be applied only across the thickness of a given lamina, the resulting shell theory shows that piezolaminae are capable of exciting and sensing bending, torsion, inplane shearing, and inplane stretching. Piezolaminae are shown to be incapable of exciting and sensing transverse shear unless a three-dimensional electrical field is applied. Inplane shearing and torsion transduction only becomes possible when the dominant rolling axis of a given piezolamina is skewed such as not to coincide with a principal geometric axis. Constitutive relationships are derived which describe how each piezolamina may function simultaneously as both a sensor and an actuator. Two-dimensional piezoelectric field functions are introduced which describe how nonuniformly distributed electromechanical transduction will affect the nature of the applied excitation and acquired measurement. The equations of motion are also given for a shell in which transverse shear deformation is neglected according to Love's first approximation.