Complex potential formalisms for bending of inhomogeneous monoclinic plates including transverse shear deformation

This paper develops complex potential formalisms for the solution of the bending problem of inhomogenoeus anisotropic plates, on the basis of the most commonly used refined plate theories. Being an initial step in that direction, it works out such formalisms only in connection with the bending problem of shear deformable homogeneous plates as well as plates having a special type of inhomogeneity along their thickness direction. The adopted type of inhomogeneity is however still general enough to include certain classes of plates made of functionally graded material as well as the classes of cross- and angle-ply symmetric laminates as particular cases. The basic formalism, similar to that developed by Stroh in plane strain elasticity, is detailed in relation with the equilibrium equations of a generalized plate theory that accounts for the effects of transverse shear deformation and includes conventional, refined theories as particular cases. Some interesting specializations, related to the most important of those conventional plate theories, are then presented and discussed separately. Hence, the outlined formalisms provide, for the first time in analytical form, the general solution of the partial differential equations associated with the most commonly used refined, elastic plate theories.     

Elastic anomalies in strontium titanate

The anomalies of the second and third-order elastic constants have been considered for the phase transition of strontium titanate within the framework of Landau’s theory. All the anomalies of the second-order elastic constants have been obtained in a single formula using Kronecker delta functions and relations among them have been established. The real parts ofC*₁₁ andC*₄₄ decrease steeply across the transition temperature and thereafter flatly tend to their asymptotic values in the low temperature phase agreeing qualitatively with experimental observations. We have also derived expressions for the third-order elastic anomalies and discussed the temperature variation of the real part ofC*₁₁₁. We have derived expressions for the attenuation of the longitudinal and transverse waves along certain simple symmetry directions and have shown that there is nearly good agreement with experimental observations.     

A full-field approach for the elastic characterization of anisotropic materials

In the paper a procedure is described whereby the characterization of isotropic and anisotropic laminae is carried out by full-field measurement of the surface rotations under proper flexural loads. The analytic formulation does not necessarily imply a numerical calibration and the elastic constants are determined by integrating the whole experimental data on the surface of the specimen. Measurements were carried out by phase-stepped speckle interferometry using a shearometer based on Michelson design. The experimental instrumentation, including the loading device, and the procedures for the manipulation of experimental data are detailedly described; experimental results obtained on a steel specimen and a composite laminate are also reported.     

Dynamics of coupled systems

A survey in the form of a review of the author’s research results in the area of dynamics of coupled rotations and coupled systems is presented. The theorem on the existence of a trigger of the coupled singularities and the separatrix in the form of the number eight is presented with a few examples of coupled rotations of the simple systems with debalances. Also, a survey of models and dynamics of coupled systems composed of a number of deformable bodies (plates, beams or belts) with different properties of materials and discrete layer properties is presented and mathematically described. The constitutive stress–strain relations for materials of the coupled sandwich structure elements are presented for different properties: elastic, viscoelastic and creeping. The characteristic modes of the coupled system vibrations are obtained and analyzed for different kinds of materials and structure composition. The visualization of the characteristic numbers and modes and eigenamplitude forms are presented. Structural analysis of sandwich structure vibrations is done.     

Focussed surface acoustic waves on an anisotropic crystal, studied by optical probing

Efficient focussing of surface acoustic waves has been achieved using a properly shaped gold film deposit on the −22.3° rotated Y-cut surface of quartz. The acoustic wave field was studied with laser probing techniques. A more than threefold increase in intensity and a tenfold decrease in beam width was observed at the focal point. The focussing action was obtained with the elastic wave equivalent of the Fresnel phase-reversal zone plate of optics. The multiple foci of this device allowed a simultaneous generation of acoustic waves in nearly all directions on the surface. Consequently, the surface wave velocity anisotropy could be determined completely. The experimental results are in very good agreement with the calculated velocity anisotropy. Electromagnetic diffraction theory is adopted to the two dimensional anisotropic system to analyse the performance of the focussing device.     

Elastic constants of sodium chlorate from 77 K to 350 K

The elastic constantsC ₁₁,C ₁₂ andC ₄₄ of sodium chlorate single crystal have been evaluated using 10 MHz ultrasonic pulse echo superposition technique. The values areC ₁₁=4.90,C ₁₂=1.39,C ₄₄=1.17 (× 10¹⁰ N/m ²) at 298 K and 6.15, 2.16, 1.32 (×10¹⁰ N/m ²) at 77 K. The data agree well with the values measured earlier up to 223 K. Brief mention is also made of the low temperature bonding problems in these soft crystals.     

On the efficacy of pseudo-coordinates—Part 2: moving boundary constraints

In this paper an argument is presented in favor of utilizing felicitous or natural coordinates in the model formulation of complex hybrid parameter multiple body mechanical systems (HPMBS). Specifically for this paper, HPMBS that consist of continuua that are subjected to spatially and temporally varying non-holonomic boundary conditions. This is the second paper of a two part series of papers that is presented to clarify the novelty and usefulness of a recently developed Gibbs-Appell type projection based HPMBS modeling tool. The purpose of the paper is to show that with the novel use of pseudo-coordinates and speeds (as defined by the author) it is completely natural to provide minimal configuration space dimensionality yet still retain rigorous analytical formulation tractability.Presented in this work, as a demonstrative arguing point, is the development of the hybrid parameter motion equations for a rolling flexible-disk material cutting device. This device consists of a circular flexible continuum (the cutter) along with the requisite mounting rigid hub and handle. This non-holonomically constrained device is modeled executing spatial motion constrained to the plane via moving constraints applied to the boundary of the planar continuum. Also included in this work are numerical results bolstering the claims made herein. These numerical results demonstrate that the methodology elucidated provides low-order models suitable for modeling complicated devices. These low-order models are in contrast to the current modeling trend of ever-increasing degrees of freedom.     

Electron-sodium elastic scattering in the presence of strong non-resonant laser field

The elastic differential cross-section forē-Na scattering in the presence of non-resonant laser field is studied for the exchange ofℓ=0, 1, 2 photons. The undressed contribution is evaluated within the framework of the eikonal Born series approximation and the effect of exchange is taken into account via the Ochkur approximation. The sodium atom has been treated in the frozen core approximation with special attention to the effect of the dressing of the target by the laser field. The ‘dressing’ of the target leads to quite an increase in the cross-section over the ‘undressed’ value near the forward direction for the exchange of one or two photons.     

An Extended Beam Theory for Smart Materials Applications Part II: Static Formation Problems

In this paper we further develop the theory of the extended Timoshenko beam model, as first introduced in Part I [5] of this work, with particular emphasis on applications of the model in formation theory [11], [12]. We begin with formal development of the equilibrium equations of static formation theory in the context of the extended Timoshenko model, giving a rigorous discussion of existence, uniqueness, and regularity of weak solutions with appropriate assumptions on the coefficients. We continue to obtain the fundamental duality relationship in the context of weak solutions and indicate its usefulness in investigations of approximate formability. Optimal formation problems and corresponding necessary conditions for optimality are discussed. We conclude with a discussion of a particular problem of joint optimization of controls and actuator densities in the context of a prismatic extended Timoshenko beam and we present the results of some computational studies. Accepted 14 November 1996