Showing papers on "Torsion (mechanics) published in 1979"
274 citations
TL;DR: In this article, an alternative form of the hyperbolic sine relationship is developed for use as a constitutive equation at elevated temperatures, and an optimization technique may be applied to results from torsion tests to determine the constants in this equation and that this method must be more accurate than those presented previously.
Abstract: An alternative form of the hyperbolic sine relationship is developed for use as a constitutive equation at elevated temperatures. It is shown how an optimization technique may be applied to results from torsion tests to determine the constants in this equation and that this method must be more accurate than those presented previously. Experimental results for two aluminium alloys indicate that the activation energy during hot torsion testing is the same as the activation energy for bulk self-diffusion. It is shown that thermal changes occurring during testing affect results significantly.
210 citations
185 citations
01 Aug 1979
TL;DR: In this paper, a model consisting of a series of N+ 1 identical rigid rods connected at their ends by torsion springs and undergoing rotational brownian motion about their fixed symmetry axes is proposed as a model for the torsions dynamics of DNA.
Abstract: A model consisting of a series of N+ 1 identical rigid rods connected at their ends by torsion springs and undergoing rotational brownian motion about their fixed symmetry axes is proposed as a model for the torsion dynamics of DNA. The fluorescence anisotropy bfbnund flunrophores is expressed in terms of angular correlation functions, the subsequent calculation of which is virtually identical to that recently presented for the dynamic structure factor of tIse RouseuZimm model. Tin complete time course of the fluorescence anisotropy is divided into four zones, (i) initial exponential decay zone, (ii) iotermediate zone, (iii) longest internal mude zone, and (iv) uniform mode zone. Simple approximate expressions for the lluoresccnee anisotropy are derived for the initial exponential decay zone and for the intermediate zone. The mag- nitude of end-effects, due to enhanced amplitudes of motion near the chain ends, in the intermediate zone is investigated botls numerically and analytically, and the domain of validity of the approximate expression pertinent to that zone is de- termined to be 100-fold smaller than previously supposed. The fluorescence anisotropy decay data of Wahl, Paoletti and Le Pecq for ethidium bound to DNA is interpreted in terms of this nsodel. Although relaxations in zones (iii) and (iv) can be ruled out, it is possible to obtain equally good fits to the decay dala either in zone (i) witls parameters pertinent to a rod-length of 86 base-pairs or in zone (ii) with parameters pertinent to a rod-length of I base pair. However, other data, in- cluding the steady-state polarization anisotropy in concentrated sucrose solution, definitely favor the zone (i) fit with a rod-length of 86 base-pairs, thus providing evidence for isolated torsion joints, or inhomogeneities in the torsional rigidity, nf that particular calf-thymus DNA. A comparison of twisting energies compused from the present optimum torsion con- stants with the measured free-energies of supercoil formation is also given.
140 citations
TL;DR: In this article, a stiffness matrix is derived for straight cable elements subjected to tension and torsion, and the equations of equilibrium are then linearized in a consistent manner to give a liner stiffness matrix.
Abstract: A new element stiffness matrix is derived for straight cable elements subjected to tension and torsion The cross-section of a cable, which may consist of many different structural components, is treated in the following as a single composite element The derivation is quite general; consequently, the results can be used for a broad category of cable configurations Individual helical armourning wires, for instance, may have unique geometric and material properties In addition, no limit is placed on the number of wire layers Furthermore, compressibility of the central core element can also be considered The equations of equilibrium are first derived to include ‘internal’ geometric non-linearties produced by large deformations (axial elongation and rotatioin) of a straight cable element These equations are then linearized in a consistent manner to give a liner stiffness matrix Linear elasticity is assumed throughout Excellent agreement with experimental results for two different cables validates the correctness of the analysis
136 citations
108 citations
TL;DR: In this paper, it was shown that the curvature can be expressed in terms of the torsion and its covariant derivatives, which is the fundamental geometric object in supergravity.
Abstract: The first Bianchi identities are used to show, that in extended supergravity the curvature can be expressed in terms of the torsion and its covariant derivatives. The second Bianchi identities are shown to hold on account of the first ones. Thus all expressions containing the curvature may be written in terms of the torsion, which is the fundamental geometric object in supergravity.
97 citations
TL;DR: In this article, an extension of the Batho-Bredt analysis is presented for a cylindrical tube of arbitrary cross-section with an arbitrary circumferential distribution of fiber composite plies.
Abstract: In Part 1 expressions are derived for the coupled torsional, extensional and flexural stiffnesses of a fibre composite tube, such as a helicopter blade, which is subjected to torsion, longitudinal tension, chordwise and flapping bending moments and shear. The theory is an extension of Batho-Bredt engineering analysis and is valid for a cylindrical tube of arbitrary cross-section with an arbitrary circumferential distribution of fibre composite plies. Particular attention is paid to the coupling effects in which an asymmetric fibre lay-up results in a twisting of the tube under bending and/or tension. Consideration is also given to the influence on the stiffness characteristics of an initial twist in the tube. In Part 2 the analysis of Part 1 is developed numerically for tubes representative of GFRP blades. Static and dynamic aspects are considered which pave the way for aeroelastic tailoring studies of such blades.
85 citations
TL;DR: In this paper, the authors show that Sines'criterion does not conform strictly with experimental results and they correct Sines's criterion so that fatigue failure occurs when the octahedral shearing stress amplitude attains a material constant value, which decreases not only in proportion to the normal mean stress, but also in proportional to the octanhedral normal stress amplitude.
Abstract: Criteria of fatigue strength of a round bar subjected to combined static and repeated bending and torsion have already been published by Findley and Sines together with empirical formulas by Gough. However, it is only Sines’criterion, by which the fatigue limit under combined bending and torsion is calculated, when completely reversed and pulsating fatigue limits and mean stresses are known. The authors show that Sines’criterion does not conform strictly with experimental results and they correct Sines’criterion so that fatigue failure occurs when the octahedral shearing stress amplitude attains a material constant value which decreases not only in proportion to the octahedral normal mean stress, but also in proportion to the octahedral normal stress amplitude. Applying the authors’criterion to combined repeated bending and torsion, plus coexistent static bending and torsion, a design formula was derived. The formula was compared with experimental results of Gough.
58 citations
TL;DR: In this article, a theory of gravity which allows for propagating torsion was developed, and a plausible procedure for quantizing the torsions and metric fields was presented, and the motion of spinning test particles in combined metric and torsionic background fields was discussed.
Abstract: A theory of gravity is developed which allows for propagating torsion. The theory predicts the existence of torsion in a vacuum and torsion waves emitted by sources with varying spin. The motion of spinning test particles in combined metric and torsion background fields is discussed. A plausible procedure for quantizing the torsion and metric fields is presented.
54 citations
TL;DR: In this paper, a generalized theory of free torsional vibration for a wide class of suspension bridges with double lateral systems is developed, taking into account warping of the bridge deck cross section and the effect of torsial rigidity of the towers.
Abstract: A generalized theory of free torsional vibration for a wide class of suspension bridges with double lateral systems is developed, taking into account warping of the bridge deck cross section and the effect of torsional rigidity of the towers. The analysis is based on a linearized theory and on the use of the digital computer. A finite element approach is used to determine vibrational properties in torsion. Simplifying assumptions are made, and Hamilton's principle is used to derive the matrix equations of motion. The method is illustrated by numerical examples. The objective of the study is to clarify the torsional behavior of suspension bridges and to develop a method of determining a sufficient number of natural frequencies and mode shapes to enable an accurate practical analysis.
TL;DR: In this paper, a modified form of the BKZ elastic fluid is used to describe the normal stress and shear stress responses of PMMA in two-step torsion strain histories.
Abstract: A modified form of the BKZ elastic fluid is presented. The specific form chosen is used to describe the normal stress and shear stress responses of PMMA in two‐step torsion strain histories. Our results show that the modified form of the BKZ theory does not account for mechanical aging effects in PMMA. However, the response of mechanically conditioned PMMA to the strain histories tested is described by the modified theory. An interesting result is that the normal stress response to a two‐step strain history in which the second step strain is half the first step is predicted to be independent of the duration of the first step and identical to the response to a single‐step history at the strain level of the second step. This response is observed experimentally.
Book•
18 Jun 1979TL;DR: In this article, the authors present a model of the Jacobian matrix with a constant number of tensors and a linear tensor representation of the elasticity of the tensors.
Abstract: 1. Kinematics of Continuous Media.- 1.1. Material and Spatial Coordinates.- 1.2. Neighborhood Transformations.- 1.3 Composition of Changes of Configuration.- 1.4 Measure of the State of Local Deformation. Green's and Jaumann's Strain.- 1.5 Rigid-Body Rotations of a Neighborhood.- 1.6 The Kinematical Decomposition of the Jacobian Matrix.- 1.7 Geometric Interpretation of Infinitesimal Strains.- 1.8 The Eulerian Viewpoint in Kinematics. Almansi's Strain.- 1.9 Eulerian Measures of Rates of Deformation and Rotation.- 1.10 Temporal, Variation of the Polar Decomposition of the Jacobian Matrix.- 2. Statics and Virtual Work.- 2.1. The Concept of Stress. True Stress.- 2.2. The Piola Stresses.- 2.3. Translational Equilibrium Equations.- 2.4. Rotational Equilibrium Equations.- 2.5. Statics and Virtual Work.- 2.6. Commutativity of the Operators ? and Di.- 2.7 Virtual Work in a Continuous Medium.- 2.8. Statics and Virtual Power for True Stresses.- 2.9. Statics and Virtual Work in Infinitesimal Changes of Configuration.- 3. Conservation of Energy.- 3.1. Constitutive Equations for Piola's Stresses.- 3.2. The Kirchhoff-Trefftz Stresses.- 3.3 The Constitutive Equations of Geometrically Linear Elasticity.- 4. Cartesian Tensors.- 4.1. Bases and Change of Basis.- 4.2 Tensors.- 4.3 Some Special Tensors.- 4.4 The Vector Product.- 4.5. Structure of Symmetric Cartesian Tensors of Order Two. Principal Axes.- 4.6. Fundamental Invariants and the Deviator.- 4.7. Structure of Skew-Symmetric Cartesian Tensors of the Second Order.- 4.8. Matrix Representation of Tensor Operations.- 5. The Equations of Linear Elasticity.- 5.1. Compatibility of Strains in a Simply Connected Region.- 5.2. Compatibility of Strains in a Multiply Connected Region.- 5.3. Principal Elongations and Fundamental Invariants of Strain.- 5.4. Principal Stresses and Fundamental Invariants of the Stress State.- 5.5. Octahedral Stresses and Strains.- 5.6. Mohr's Circles.- 5.7. Statics and Virtual Work.- 5.8. Taylor's Development of the Strain Energy.- 5.9. Infinitesimal Stability.- 5.10. Hadamard's Condition for Infinitesimal Stability.- 5.11. Isotropy and Anisotropy.- 5.12. Criteria for Elastic Limits.- 5.13. Navier's Equations.- 5.14. The Beltrami-Michell Equations.- 6. Extension, Bending, and Torsion of Prismatic Beams.- 6.1. Green's and Stokes' Formulas.- 6.2. The Centroid.- 6.3. Moments of Inertia.- 6.4. The Semi-Inverse Method of Saint-Venant.- 6.5. Resultants of Stresses on a Cross Section.- 6.6. Calculation of the Transverse Displacements.- 6.7. Equations Governing the Shear Stresses.- 6.8. Calculation of the Longitudinal Displacement.- 6.9. Separation of Solutions.- 6.10. Pure Torsion.- 6.11. The Center of Torsion for a Fully Constrained Section.- 6.12. Bending without Torsion.- 6.13. The Stiffness Relation for the Twist.- 6.14. Total Energy as a Function of the Deformations of the Fibers.- 6.15. Total Energy as a Function of Generalized Forces.- 6.16. The Generalized Constitutive Equations for Bending and Torsion of Beams.- 6.17. One-Dimensional Formulation of Bending and Torsion of Beams.- 6.18. Applications.- A. Stress function for torsion of the elliptic bar.- B. Stress functions for torsion of the circular bar.- C. Stress functions with poles.- D. Torsion of a triangular bar.- E. Torsion of a rectangular bar.- F. Bending of a circular bar.- G. Bending of a circular tube.- H. Bending of a rectangular bar.- 7. Plane Stress and Plane Strain.- 7.1. Lemmas for the Integration of Partial Differential Equations in Complex Form.- 7.2. The Structure of a Biharmonic Function.- 7.3. Structure of the Solution of the Problems of Plane Strain.- 7.4.Structure of the Solution of the Problem of Plane Stress.- 7.5. Generalized Plane Stress.- 7.6. Airy's Stress Function.- 7.7. Complex Representation of Airy's Function.- 7.8. Polar Coordinates.- 7.9. Applications in Cartesian Coordinates.- A. The state of hydrostatic stress.- B. Uniform gradient of areal dilation.- C. Pure uniform shear.- D. Linear variation of a normal stress.- E. Simple extension.- F. Pure bending.- G. Shear lag.- H. Bending by shear forces.- I. Saint-Venant's bending of a rectangular beam with flanges.- J. Transverse loading of a beam with flanges.- 7.10. Applications in Polar Coordinates.- A. Circular aperture with traction-free circumference in a plate in plane stress.- B. Volterra's dislocation of the circular ring.- C. Bending of beams with constant curvature.- D. The annular ring loaded by shear tractions.- E. The thick tube under pressure.- F. Concentric cylindrical tubes and rings.- G. Force concentrated at the origin in an infinite plate.- 8. Bending of Plates.- 8.1. Basic Hypotheses.- 8.2. Application of the Canonical Variational Principle.- 8.3. The Two-Dimensional Canonical Principle.- 8.4. Further Connections Between the Two- and Three-Dimensional Theories.- 8.5. Other Types of Approximations.- 8.6. Kirchhoff's Hypothesis.- 8.7. Boundary Conditions in Kirchhoff's Theory.- 8.8. Kirchhoff's Variational Principle.- 8.9. Structure of the Solution of the Equations of Plates of Moderate Thickness.- 8.10. The Edge Effect.- 8.11. Torsion of a Plate.- 8.12. Saint-Venant's Bending of a Plate.- 8.13. Particular Solutions for Transverse Load.- 8.14. Solutions in Polar Coordinates.- 8.15. Axisymmetric Bending.
TL;DR: In this article, the buckling of cylindrical shells under the simultaneous action of torsion, external pressure, and axial compression was investigated, taking into account the exact form of the boundary conditions and nonlinear prebuckling deformations.
Abstract: This study consisted of a theoretical and experimental investigation of the buckling of circular cylindrical shells under the simultaneous action of torsion, external pressure, and axial compression. Laminated anisotropic behavior was considered, as was the effect of small axisymmetric shape imperfections. The theoretical analysis took into account the exact form of the boundary conditions and nonlinear prebuckling deformations. Interactive stability surfaces were computed for a variety of laminate configurations together with approximate formulas for buckling under these three loading conditions. Comparisons with experimental data obtained from buckling tests on glass/epoxy cylinders were also made.
TL;DR: In this paper, an isoparametric finite element formulation for the torsion and the flexure due to end shears for the beam cross-sections of arbitrary shape is presented.
Abstract: This paper presents an isoparametric finite element formulation for the torsion and the flexure due to end shears for the beam cross-sections of arbitrary shape. Isoparametric line elements are developed using this formulation for the beam cross-sections consisting of very thin wall open or close multicells. Isoparametric transition elements are also developed for the beam cross-sections consisting of both thin wall sections and solid like sections. Numerical examples are presented to demonstrate the accuracy and the applications of such elements.
TL;DR: In this paper, the distortions within beams and rods undergoing large displacements and rotations are derived from three-dimensional elasticity by an asymptotic procedure, based on the premise that strains vary more gradually along the rod than in transverse directions, taking full account of the shape of the cross section, the traction conditions on the lateral boundary and any material anisotropy.
TL;DR: In this paper, two limiting forms of fiber geometry are considered: no migration, and complete fibre equivalence as a direct consequence of migration, respectively, the fiber-stress distribution is analyzed, and the component of yarn torque due to these stresses is derived.
Abstract: The torque generated during yarn-twisting is considered to have three components, due, respectively, to fibre torsion, fibre-bending, and the internal fibre tensile and compressive stresses within the yarn. An analysis of the yarn torque generated by fibre torsion will be given in a later paper, and the component due to fibre-bending has been evaluated by other authors. It is proposed that the nature of the fibre tensile-stress distribution within a yarn is likely to be the most influential factor governing the magnitude of yarn torque. The distribution of stress, as a function of the fibre position in the yarn, depends largely on the facility with which fibres can migrate throughout the yarn cross-section. In this paper, two limiting forms of fibre geometry are considered: no migration, and complete fibre equivalence as a direct consequence of migration. For each case, the fibre-stress distribution is analysed, and the component of yarn torque due to these stresses is derived.
TL;DR: In this paper, the authors used minimum potential and complementary energy for the establishment of upper and lower bounds for the influence coefficients of cantilever beams in terms of influence coefficients, based on previous work for the problem of end-loaded cantilevers with loading conditions prescribed by displacements rather than stresses, for the purpose of defining shear center location.
TL;DR: For a large class of Lagrangian-based torsion theories, it was shown in this article that a macroscopic gyroscope is insensitive to the Torsion field.
Abstract: We demonstrate that for a large class of Lagrangian-based torsion theories a macroscopic gyroscope is insensitive to the torsion field: there can be no coupling of the torsion to the gyroscope's angular momentum of rotation. To detect torsion a polarized system with a net elementary particle spin is needed. These conclusions are evident from the conservation laws, which form the basis for deriving the equations of motion.
TL;DR: In this article, the generalized displacement field functions are represented by the exact solutions of the coupled homogeneous differential equations governing the static behavior, which also permits the evaluation of exact work-equivalent nodal forces due to external loadings.
Abstract: Exact solutions to the linear static behavior including warping torsion of thin-walled spatial curved beam structures are obtained by the displacement formulation through the use of minimum potential energy. The generalized displacement field functions are represented by the exact solutions of the coupled homogeneous differential equations governing the static behavior, which also permits the evaluation of exact work-equivalent nodal forces due to external loadings. The obtained total torsional moment is separated through an analytical procedure into St. Venant and warping torque. Several examples are presented and comparisons made.
TL;DR: In this paper, it was shown that a high static torsion step produces particles, and that the spin contact interaction of the Einstein-Cartan-Sciama-Kibble theory of gravitation provides a new mechanism for matter creation as compared with Einsteinian relativity.
Abstract: With the help of the formalism of [3] (hereafter referred to as Paper I) we show that a high static torsion step produces particles. We thereby verify earlier expectations that the spin contact interaction of the Einstein-Cartan-Sciama-Kibble theory of gravitation provides a new mechanism for matter creation as compared with Einsteinian relativity.
TL;DR: Based on the familiar skew bending model, methods of analyses are presented in this article for predicting the strength of plain and reinforced concrete beams that are subjected to torsion and contain a small transverse opening.
Abstract: Based on the familiar skew bending model, methods of analyses are presented in this paper for predicting the strength of plain and reinforced concrete beams that are subjected to torsion and contain a small transverse opening. Test results of 22 beams—three of them having reinforcement around the opening are also presented. The predictions of the theory are compared with these results as well as those reported in the literature. They show good agreement. Also, a suitable form of reinforcement around the opening is proposed to eliminate the weakness due to an opening.
TL;DR: In this paper, the absence of torsion in conventional gravity could in fact be dynamical, and a gravitational Meissner effect might produce instanton-like vortices of nonzero torsions concentrated at four-dimensional points.
Abstract: We suggest that the absence of torsion in conventional gravity could in fact be dynamical. A gravitational Meissner effect might produce instanton-like vortices of nonzero torsion concentrated at four-dimensional points; such torsion vortices would be the gravitational analogs of magnetic flux vortices in a type II superconductor. Ordinary torsion-free spacetime would correspond to the field-free superconducting region of a superconductor; a dense phase of “torsion foam” with vanishing metric but well-defined affine connection might be the analog of a normal conductor.
TL;DR: In this paper, the Yang-Mills field strength was modified and a generalisation of the usual minimal coupling procedure was proposed to allow a simple but non-trivial type of dynamic torsion to couple to all gauge fields in a consistent manner.
Patent•
26 Dec 1979TL;DR: A torsional damper integral with a torsion bar is described in this article, where the damper is not directly connected to any support structure and the torque applied by the torsions to the dampers on one side of the mid length is equilibrated by torque exerted by the torques on the opposite side of its mid length.
Abstract: A torsional damper integral with a torsion bar wherein the damper is not directly connected to any support structure. Torque applied by the torsion bar to the damper on one side of the damper's mid length is equilibrated by torque exerted by the torsion bar to the damper on the opposite side of its mid length. In this manner, a part of the torsion load is transmitted to the energy dissipating damper.
TL;DR: In this paper, the influence of the torsional strain on the magnetic properties of twisted amorphous ribbons has been analyzed in two ways: the magnetoelastic anisotropy induced by torsion and the inverse Widemann effect.
Abstract: Measurements of magnetisation, Matteucci effect, and inverse Widemann effect have been performed on Fe40Ni40P14B6 amorphous ribbons under torsion. Influence of the torsional strain on the magnetic properties of the sample is analysed in two ways. Information about the distribution of the easy directions of magnetisation has been obtained from remanence measurements of magnetisation. Matteucci effect and inverse Widemann effect. The dynamic evolution of magnetisation has beeen deduced from coercive force determination in DC longitudinal and transverse of 'circular' fields, as well as from frequency response in AC fields. The magnetic behaviour of twisted amorphous ribbons seems to be caused by the inhomogeneous arrangements of magnetoelastic anisotropy induced by torsion when the latter is high enough to overcome the initial anisotropy distribution present in the sample. Possibilities of technological applications of the observed properties are also discussed.
TL;DR: In this paper, the v-G material property curve (where v is the crack velocity and G the crack extension force) was established from the experimental apparent crack velocity, the average crack-extension force, and the observed crack profile.
Abstract: The v-G material property curve (where v is the crack velocity and G the crack-extension force) was established from the experimental apparent crack velocity, the average crack-extension force, and the observed crack profile. (FS)
TL;DR: In this paper, the authors derived growth stress distributions in trees using the hypothesis that longitudinal and circumferential growth strains are continuously induced at the periphery of the growing stem and used a plane strain combined with pure torsion model to compute the internal stresses and strains due to forces and moments caused by new growth increment.
Abstract: Growth stress distributions in trees are derived using the hypothesis that longitudinal and circumferential growth strains are continuously induced at the periphery of the growing stem. A plane strain combined with pure torsion model is used to compute the internal stresses and strains due to forces and moments caused by the new growth increment. The twisting angle of the pure torsion model is caused by the shear stresses set up in the growth increment as the growth strains are induced along the grain axis and the coupling of axial and torsional effects due to the elastic constants for the inclined grain material. Detailed stress distributions are derived for a range of constant grain angle cases. The extreme sensitivity of the torsional shear distribution to small grain angles is noteworthy.
TL;DR: In this paper, the importance of determining the temperature at varying strains and strain rates during the twisting of a torsion specimen is emphasized and it is argued that previous analyses are inadequate.
Abstract: The importance of determining the specimen temperature at varying strains and strain rates during the twisting of a torsion specimen is emphasized and it is argued that previous analyses are inadequate. A three-dimensional finite-diflerence model is developed and a method of obtaining an ‘average’ temperature rise is presented. It is shown that significant temperature profiles are set up during torsion testing and that axial conduction cannot be assumed to be zero. The assumption of a laminar boundary layer is acceptable. Results are presented for two aluminium alloys.