Small strain and moderate rotation

Kinematical assumptions leading to the approximate theory of small strain accompanied by moderate rotations are discussed with reference to a three-dimensional continuous body. In particular, the relationship with Korn's inequality is examined. It is found that for bounded bodies the coincidence of small strain and moderate rotation on subsets of non-zero volume measure is not possible. Two explicit examples are presented to illustrate this point.     

A theory of shells with small strain accompanied by moderate rotation

This paper is concerned with a constrained theory of shells in the presence of small strain accompanied by moderate rotation. The constrained theory accounts for the effect of transverse normal strain and includes, of course, the special case (corresponding to the Kirchhoff-Love theory of shells) in which the effect of transverse normal strain is absent. After precise estimates for (local) moderate rotation and relative displacement gradients in terms of infinitesimal strain have been effected, a complete theory is formulated with the use of linear constitutive equations. The nature of the complete theory is further examined when initially the shell-like body is a plate; and it is shown that our kinematical formulae (strain-displacement relations), as well as the relevant differential equations of the theory in the absence of the effect of transverse normal strain, systematically reduce to those used in the von Kármán plate equations. Also, in the light of the present results, an assessment of kinematical aspects of previously developed theories of shells undergoing small strain and moderate rotation is indicated.     

Small attachable interferometric strain gages

Laser-based interferometry from two tiny reflective indentations can be used to measure in-plane strain/displacement over a very short gage length (on the order of 100 μm). If the specimen material is not reflective, then some other means of generating the interference patterns must be found. This paper describes two kinds of attachable gages: plated acetate replicas of indentations and reflective foils that are indented after application. In either case, the gage is applied with the techniques used for foil-resistance gages and the gage itself is very small. The manufacturing procedures are described. The results of experiments comparing the strain to that measured with foil-resistance gages are presented. Finally, the small interferometric gage is used to measure strain on one of the metal strips in a foil-resistance gage.     

THE MOIR GEOMETRY OF PLANE FINITE STRAIN AND ROTATION

It is justified in this paper that the foundation of mathematical theory (12) of finite deformation by the method of co-moving coordinate is identical to Moiré method in experimental mechanics. Hence, the important practical value of this theory is further ascertained.     

Shear measurement using strain gages under large deformation and rotation

The measurement of shear strain under finite deformation and large rotation by using electrical-resistance metallic foil strain gages is studied both analytically and experimentally. Equations for calculating shear strain and axial and circumferential stretches are derived based on the kinematics of general tension-torsion deformation mode. These equations are applied to analyzing pure torsion experimental data. Comparison is made between results obtained with strain gages and a rotary transducer. It is shown that, in case of large rotation, one simple equation can be used to calculate the shear strain up to 30 percent with adequate accuracy.     

Small and large strain rheology of wheat gluten

 The rheological properties of wheat gluten were studied under both small and large deformation and compared with those of the parent flours. The limiting strain of linear viscoelastic behaviour of gluten doughs, 3 × 10⁻², was an order of magnitude larger than that of the flour doughs, 10⁻³. The role of starch in the lower limiting strain of flour doughs was indicated by the exponential decrease in the limiting strain of gluten-starch mixtures with greater quantities of starch. Large strain measurements showed gluten doughs possessed greater shear and elongational viscosities than flour doughs and these differences were greatest at lower shear and elongation rates (0.01 and 0.1 s⁻¹). The larger viscosities of flour and gluten doughs at the low strain rates help to stabilise and prevent the collapse of gas bubbles during bread fermentation and baking. Increasing starch levels in gluten-starch mixtures, at either constant or optimal water levels, lowered the elongational viscosity. Dynamic measurements were, however, more sensitive to the level of water added to the gluten-starch mixtures. The storage modulus decreased with increasing starch levels when constant water levels were used to prepare the mixtures, but when optimal water levels were used the storage modulus increased. Gluten and starch are major contributors to the large and small strain rheological properties of flour doughs; however, gluten-starch mixtures were unable to duplicate exactly the rheological properties of flour doughs, indicating that other flour components such as pentosans, lipids and water soluble proteins also influence dough rheology. Received: 20 March 2001 Accepted: 11 July 2001     

On a moderate rotation theory of laminated anisotropic shells—Part 1. Theory

A moderate rotation theory of laminated anisotropic shells, proposed by Schmidt and Reddy [J. appl. Mech. 55, 611–617.1988], is developed and its application is presented. All aspects of the derivations are explicitly developed and specific forms of the equations are derived in this part. The finite-element formulation and its applications are presented in Part 2 of the paper.     

On a moderate rotation theory of laminated anisotropic shells—Part 2. Finite-element analysis

The finite element model of the moderate rotation theory (MRT) is developed and its application to composite plates and shells is presented. Comparison of results obtained by the moderate rotation theory with the von Kármán non-linear theory and continuum 2D theory is made.     

Admitted region of the joint invariants of the strain and rotation rate tensors

The admitted region of five joint irreducible invariants of the strain and rotation rate tensors calculated as the traces of the products of these tensors is determined.     

On the vanishing of the additive measures of strain and rotation for finite deformations

Explicit formulae for the finite strain and rotation measures are given, in the cases when either one of the infinitesimal tensors of strain and rotation vanishes. Conversely, when the finite strain or rotation measure vanishes, explicit formulae for the infinitesimal tensors of strain and rotation are also obtained.     

The general stress strain relation of soils involving the rotation of principal stress axes

1.IntroductionThestudyofsoils'constitutiverelationismostlylimitedinsuchStressstatethattherotationofprincipalstressaxesisabletobeignored.Soonlythevalueofprincipalstressneedtobeconsideredandthedirectionofprincipal'stressisregardedtobeunchangeable.Onthiscondition,theprincipalaxesof'stressincrement,strainincrementjstressandstrainarethesame.Therelevantexperimentsandengineeringsshowthattherotationofprincipalstressaxeswillgeneratesignificantplasticdeformationandthenoncoaxalityofstressandstrain.First…     

Bifurcations of heteroclinic loop accompanied by pitchfork bifurcation

In this paper, using the local coordinate moving frame approach, we investigate bifurcations of generic heteroclinic loop with a hyperbolic equilibrium and a nonhyperbolic equilibrium which undergoes a pitchfork bifurcation. Under some generic hypotheses, the existence of homoclinic loop, heteroclinic loop, periodic orbit and three or four heteroclinic orbits is obtained. In addition, the non-coexistence conditions for homoclinic loop and periodic orbit are also given. Note that the results achieved here can be extended to higher dimensional systems.     

Nozzle thrust increase by flow rotation

Until recently, in constructing optimum supersonic axisymmetric nozzles, gas motions without rotation about the axis have been considered. This question has been studied rather completely for equilibrium gas flows in [1–6]. Avoidance of flow rotation is a limitation which may reduce the nozzle thrust, other conditions being equal. It is easy to show that for zero nozzle length or for a length that permits obtaining uniform flow at the exist that maximum thrust is provided by uniform flow parallel to the nozzle axis. If the length limitation does not make it possible to do this, then the use of freedom in the gas rotation may increase the nozzle thrust. Using a very simple example it is shown that this possibility is realized.     

Some results for approximate strain and rotation tensor formulations in geometrically non-linear Reissner-Mindlin plate theory

Finite element deflection and stress results are presented for four flat plate configurations and are computed using kinematically approximate (rotation tensor, strain tensor or both) non-linear Reissner-Mindlin plate models. The finite element model is based on a mixed variational principle and has both displacement and force field variables. High order interpolation of the field variables is possible through p-type discretization. Results for some of the higher order approximate models are given for what appears to be the first time. It is found that for the class of example problems examined, exact strain tensor but approximate rotation tensor theories can significantly improve the solution over approximate strain tensor models such as the von Kármán and moderate rotation models when moderate deflections/rotations are present. However, for each of the problems examined (with the exception of a postbuckling problem) the von Kármán and moderate rotation model results compared favorably with the higher order models for deflection magnitudes which could be reasonably expected in typical aeroelastic configurations.     

含主应力轴旋转的土体平面应变问题弹塑性数值模拟

在含主应力轴旋转的土体本构关系研究的基础上,通过含主应力轴旋转的土体平面应变问题的弹塑性数值模拟结果分析,总结主应力轴旋转对土体应力分布与应形影响的规律,得出需要考虑主应力轴旋转的条件及影响的相对大小。     

Self-similar magnetogasdynamic flows accompanied by detonation and combustion waves

Magnetogasdynamic (MGD) flows with detonation waves and combustion fronts have attracted more and more attention in recent years. Intensive heat supply assures such a significant increase in the temperature and pressure behind the heat liberation fronts that the gaseous combustion products become conductive so that the flow map in the electric and magnetic fields can vary substantially as compared with ordinary gasdynamics. In the case of finite gas conductivity, when the magnetic Reynolds numbers R_m are low, the asymptotic laws of detonation wave propagation which either go over into the Chapman-Jouguet (CJ) mode (in a number of cases at a finite distance from the initiation source) or remain overcompressed, have been studied [1]. Stationary flow modes behind detonation waves have been investigated in [2] and the problem of the detonation wave originating at the closed end of the tube emerging in the stationary mode in crossed homogeneous magnetic and electric fields has been examined. Results are presented in this paper of an investigation of one-dimensional self-similar flows caused by piston motion in a hot gas mixture in which a detonation wave or combustion front is propagated. The motion is realized in external electric and magnetic fields which exert a substantial effect on the flow of the conductive combustion products. Domains of application of the governing parameters in which the various flow modes are realized are found by using a qualitative and numerical analysis. The results obtained are used to solve problems about the hypersonic gas flow around a thin wedge in an axial magnetic field.