Multilayer Bodies Research Articles

Nonaxisymmetric thermal and stressed state of layered bodies of revolution with rectilinearly orthotropic layers

A procedure is described for investigating the temperature fields and stressed states of multilayer bodies of revolution consisting of inelastically deformed, isotropic materials and rectilinearly orthotropic materials, in which one of the principal directions of anisotropy of the thermophysical and mechanical characteristics of the material coincides with the axis of revolution of the body. The procedure combines a semianalytical finite element technique with the method of successive approximations.

Heat conduction in a multilayer composite wedge

A new method for analytically solving a problem of steady-state heat conduction for multilayer composite wedge-shaped bodies is suggested based on a generalization of the integral Mellin transform.

Experimental verification and theoretical simulation of fracture behaviours of composite materials

The paper presents an experimental and analytical study of composite laminates subjected to cyclic loads. Experimental results indicate that transverse crack formation jeopardizes the load carrying capability of the laminates by decreasing the elastic moduli of the material even though the number of transverse cracks seems to saturate at each load amplitude with the number of cycles. Experimental results are compared with theoretical predictions. A microscopic model has been developed to predict the micro-behaviour of the composite through the formation and coalescence of voids related to the stress concentration in the neighbourhood of fibres and to the stress singularity due to an edge macro-crack. In addition, a 3D FE analysis has been developed in order to evaluate the elastic stress fields within a multi-layer body which provides the actual boundary stresses for micro-damage analyses of the considered microelement.

Three-dimensional simulation of electrothermal deicing systems

This paper examines three-dimensional transient heat transfer in a multilayered body that is ice covered. The physical application studied is the process of melting and removal of ice from aircraft components by use of electrothermal heaters. To model the ice-phase change, a predictor-corrector technique is used which assumes a phase for each ice gridpoint. This allows the use of the method-of-Douglas three-dimensio nal alternating direction numerical solver to iteratively converge on the correct phase of each ice node for each time step. Three-dimensional results are presented and the usefulness of the code as a design tool is illustrated. Comparisons between experimental deicer test results and numerical simulations are discussed. Nomenclature Cp = specific heat capacity, Btu/lb-°F H = enthalpy, Btu/lb h = heat transfer coefficient, Btu/h-ft2-°F k = thermal conductivity, Btu/h-ft-°F L = latent heat of fusion of ice, Btu/lb Q = rate of heat generation per unit volume, Btu/h-ft3 Rx — jc-direction Fourier number, dimensionless Ry = y-direction Fourier number, dimensionless Rz = z-direction Fourier number, dimensionless T = temperature, °F

The performance and applications of PZT composite transducer with 3-3 connectivity

The performance of 3-3 connectivity composite piezoelectric transducers is discussed. This type of transducer has been successfully used in ultrasonic imaging (frequency range: 150~600 kHz). Using a simple hardware system, this type of transducer can recognize a very thin aluminum plank (6 mm in thickness) in water, and it can clearly recognize a multilayer body.

Stressed state of multilayer thick-walled longitudinally corrugated cylindrical shells

Isolated papers [I, 5] have been published on the three-dimensional problem of determining the stress-strain state of composite bodies with noncanonical (in particular, transversely or longitudinally corrugated) interfaces. However, this class of three-dimenslonal boundary-value problems is of both scientific and applied interest in view of the necessity, for example, of investigating the stress--strain state and rigidity of multilayer bodies with corrugated surfaces of contact of the layers, formed, in particular , by explosive welding [6]. So far some analytic solutions have been obtained, and numerical calculations have been performed for specific axisymmetric problems of two-layer [4] and three-layer [2] cylindrical shells with transversely corrugated (wavy) interfaces. In the present article we present the solution of a three-dimensional boundary-value problem for a composite longitudinally corrugated cylindrical shell by using a variant of the boundary shape perturbation method [3].

The concept of residual stress in rock

The purpose of this paper is to clarify the concept of residual stress in rock. Residual stress is stress near a point in a body subjected to zero external tractions and to zero temperature gradients, excluding body forces. Thus, residual stresses can develop in rock if there are local phase transformations, inelastic strains, or differences in thermal or elastic properties. In these cases, residual stresses can result from changes in temperature, applied stress or configuration of the body. Analysis of residual stresses at the scale of mineral grains within a polycrystalline aggregate such as rock is virtually intractable. One can, however, obtain important insights into residual stresses within bodies with widely spaced sources of residual stress, such as inclusions, and within bodies comprised of multilayers. The analyses indicate that patterns of residual stress in rock can be expected to be extremely complicated. For example, study of residual stresses in a body containing a circular inclusion indicates that: 1. (1) There is a single state of residual stress within an inclusion but the state within the surrounding medium is variable. Thus, values of residual stress within rocks reported in the literature generally are of minor value because the sizes and shapes of the sources and the positions of the measurements relative to the positions of sources of residual stresses in the bodies have not been determined. 2. (2) Residual stresses within an inclusion can be tensile or compressive, even though the applied stresses were compressive, depending upon the source of residual stress. 3. (3) The magnitudes and orientations of residual stresses in an isolated body of rock containing one or more inclusions depends upon the size and shape of the body. The same general conclusions are derived from an analysis of residual stresses in a simple multilayered body. 4. (4) In addition, however, the anisotropy of a multilayered body tends to cause principal residual stresses to parallel the layers rather than to parallel the applied stresses that were responsible for inducing the residual stresses. Thus, without identifying the sources of residual stresses in a body, one cannot infer the directions of principal tectonic stresses that might have been responsible for the residual stresses. Comparison of the theoretical results with measurements of change of residual stress in blocks of granite, with maximum dimensions of 2.5 m in the field and 0.2 m in the lab oratory, suggests that sources of residual stress are inhomogeneous elements or elements of inelastic deformation within the blocks that are smaller than the blocks themselves, but larger than individual mineral grains. The sources of residual stress are unknown in these granites.

Pinocytotic uptake and intracellular distribution of colloidal thorium dioxide by cultured sensory neurites.

Sensory ganglia from 9-day chick embryos were grown on collagen coated coverslips for36 h in the presence of nerve growth factor, producing a profuse neuritic outgrowth. The cultures were then incubated for varying periods in a colloidal suspension of thorium dioxide, and the pinocytotic uptake of this marker was followed by electron microscopy. Following brief exposures (3 min), most of the labelled organelles consisted of smooth surfaced vesicles and vacuoles; with longer exposures, the bulk of the marker accumulated first in cup-shaped pre-multivesticular bodies and ultimately in multivesicular bodies. The marker was also taken up into coated vesicles, dense-cored and electron lucent tubules,dense-cored vesicles and dense bodies of the multi-layered myelin body configuration. In addition, evidence suggestive of exocytosis was also obtained; views of apparent fusion of labelled multivesicular bodies with the plasmalemma involving extrusion of vesiclesand marker particles into the extracellular space were regularly encountered following long exposures.

Nonsteady heat conduction in a layered medium

The process of nonsteady heat transfer in a plane multilayer body is investigated for boundary conditions of the third kind. The roots of the characteristic equation of the problem are determined by successive approximations.

Contact strain and folding instability of a multilayered body under compression

The contact strain which develops in a host rock during compression-folding of a more “competent” layer is treated mathematically and demonstrated by tests on composite models of rubber sheets and blocks with different rigidities. The contact strain is found to be negligible outside a zone about one initial wavelength wide on either side of the folded sheet. This theoretical conclusion based upon the contact deformation resulting from the initial small-amplitude buckles is also, according to the experimental tests, valid for rather strong buckling. Second-order folding of a thin “competent” layer laying within the contact zone of a thicker buckled “competent” layer is demonstrated by experimental tests. Considerations of the stresses connected with the contact strain and the stress distribution in the buckling “competent” layer itself give a simple expression for the initial stable wavelength which develops in response to compression parallel to the layering. The strain distribution in folded multilayers consisting of a set of thin “competent” sheets evenly spaced in an uniform less “competent” body is considered theoretically. In such multilayers the stable initial wavelength as developed during compression will, according to the theory, increase somewhat with decreasing spacing between the “competent” layers if all other conditions are equal. If the spacing is close enough (the limit depends upon the relative mechanical properties of the two substances) the multilayer will buckle as an unit in the sense that one half-wave covers the whole length of the body. This agrees with compression tests on multilayered rubber blocks. In the last two sections of the paper a theory of viscous buckling of thick layers is developed both for the case of a single layer enclosed in a large uniform body and for the case of a multilayer of alternating “competent” and “incompetent” layers. In this theory shear parallel to layering plays an important part. For a single embedded layer the thick-layer model gives a little smaller wavelength/thickness ratio than the simple but less realistic thin-layer model. For multilayers strain parallel to layering becomes very significant, particularly when the spacing between the competent layers is small, and the thick-layer model differs considerably from the simpler thin-layer model. A theory of buckling of a multilayer withn alternating competent-incompetent layers sandwiched between two very thick uniform bodies is also developed.

Some Problems on Heat Conduction in Stratiform Bodies

Problems on heat conduction in multilayer bodies lead usually to complicated calculations. The present paper gives an idea of specific difficulties arising in the ease of infinite composite solides. General deductions are applied to a special class of questions.

Steady temperature in multilayer bodies

The general solution of fundamental problems of conduction of heat in composite solids is known1)2)3). The mathematical deductions are, of course, of considerable difficulty and solutions in closed form are not readily to be found in literature, despite their great practical importance. We give here closed formulae for steady temperature fields in multilayer bodies whose surface is kept at a constant temperature, or when radiation takes place at the surface into a medium with a prescribed temperature. The author has not found in the literature a closed form of solution like the one obtained in this article. Also the common way of treating all three fundamental cases (slabs, cylinders and spheres) may very likely be regarded as a now one. Industrial significance of the following considerations is evident. The paper is divided into two main parts. First comes the general solution of the basic mathematical problem, the second part applies theoretical results to special cases.

Heat waves in multilayer cylindrical bodies

This paper generalizes the results of an analogy between the propagation of heat waves in stratiform bodies and the transmission of electrical waves through a passive four-pole, as given by Van Gorcum1). It extends the author’s considerations on heat waves in an infinite multilayer flat wall2) to the case of cylindrical bodies.