On the theory of heat for micromorphic bodies

The paper deals with the problem of heat flow in a micromorphic continua with microtemperatures. The master balance laws of micromorphic continua established by Eringen [Int. J. Eng. Sci. 8 (1970) 819] and the entropy balance postulated by Green and Naghdi [Proc. R. Soc. Lond. A 357 (1977) 253] are used to obtain a new theory of heat for materials with inner structure. The theory permits propagation of heat as thermal waves at finite speed. In the framework of the linear theory a uniqueness result and a solution of Galerkin type are established. The effect of concentrated loads is also studied.     

On complex potentials in the theory of microstretch elastic bodies

The paper is concerned with the plane strain problem in the equilibrium theory of microstretch elastic solids. We show that the complex variable technique of the classical theory of elasticity can be extended to the theory of microstretch elastic bodies. The method is used to study the effect of the stress concentration around a circular hole.     

Variational problem of heating thin bodies

The problem of heating thin bodies optimally, in terms of a composite minimum fuel cost and metal loss by oxidation, is solved analytically. The solution is based on L. S. Pontryagin's maximum principle.Translated from Inzhenerno-Fizieheskii Zhurnal, Vol. 23, No. 3, pp. 545–549, September, 1972.     

Boundary integral equations for thin bodies

A boundary integral equation formulation for thin bodies which uses CBIE (conventional BIE) only is well known to be degenerate. A mixed formulation for a thin rigid scatterer which combines CBIE and HBIE (hypersingular BIE) is motivated by examining the discretized form of the integral equations, and this formulation is shown to be non-degenerate for thin non-rigid inclusion problems. A near-singular integration procedure, useful for singular integrals as well, is presented. Finally, numerical examples for acoustic wave scattering from rigid and soft scatterers are presented.     

On third-order radiation theory for axisymmetric bodies undergoing heave motion of multiple frequencies

Summary As a first step in the development of a nonlinear theory for calculating the response of an axisymmetric system to an irregular sea, the radiation problem for axisymmetric floating or immersed bodies in a periodic heave motion, composed of a number of harmonic components, is considered by means of a third-order potential theory.It is shown that the knowledge of only first- and second-order potential functions is required for the calculation of all forces up to the third order. A boundary integral equation method is proposed for the determination of these potential functions.     

Analysis of the stressed state of bodies with multilayer thin coatings

We develop a procedure for the analysis of the stress-strain state of structural elements with thin multilayer coatings based on the simulation of these coatings by shells with the corresponding geometric and mechanical characteristics. In this approach, the influence of coatings on the mechanical state of the entire body-coating system is described by special generalized boundary conditions. The efficiency of the proposed approach is demonstrated by comparing the results obtained by using the developed approximate procedure with the exact solution of a Lamé test problem of loading of a solid cylinder with n-layer coating. Pidstrygach Institute of Applied Problem in Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lvov, Ukraine. Translated from Problemy Prochnosti, No. 1, pp. 136–150, January–February 2000.     

Heating of “thin” bodies in liquid media

Heating of thin (Bi0.25) bodies in liquid media is examined, taking into account crystallization and fusion at the body-medium interface.     

On the contact of two heated bodies

The axially symmetric Hertz thermoelastic contact problem is solved under the assumption that the contact heat resistance is inversely proportional to pressure. We consider heat flows directed both inside the body whose coefficient of thermal distortion is smaller and in the opposite direction.Warsaw University, Warsaw, Poland. Franko L'viv State University, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 5, pp. 32–39, September – October, 1995.     

An applied electro-magneto-elastic thin plate theory

The physical variational principle (PVP) in a static magneto-elastic field without source current is discussed first, and then, the PVP in a general electromagnetic field is derived. It is especially useful in the plate vibration problem. Using the PVP and the pseudo total stress principle, the electro-magneto-elastic thin plate bending theory in first order and a Mindlin-type plate bending theory for a moderate thickness plate are easily obtained. This method significantly simplifies the derivation of the governing equations of the thin and moderate plates with nonlinear electromagnetic behavior. The Maxwell stress is naturally included in the governing equation. Using the governing equation of a thin plate, the analyses of the stability and vibration of a plate in an external homogeneous magnetic field are discussed.     

The general theory of thin elastic shells

Variationsl methods can consistently be used to derive the equations of shell theory, by introducing a finite number of internal constraints. A systematic derivation of particular nonlinear and linear theories becomes then possible. Variational methods serve also to prove the existence and in some cases the uniqueness of the solution. They provide also with error estimates.     

Analytical integral algorithm in the BEM for orthotropic potential problems of thin bodies

There exist nearly singular integrals for boundary layer effect problem and thin body effect problem in the boundary element method (BEM). A new completely analytical integral algorithm is proposed and applied to evaluate the nearly singular integrals in the BEM for two-dimensional orthotropic potential problems of thin bodies. The completely analytical integral formulas are derived with integration by parts for the linear boundary interpolation. The present algorithm applies these analytical formulas to deal with the nearly singular integrals. The unknown potentials and fluxes at boundary nodes are firstly calculated accurately and then the physical quantities at the interior points are computed. Two benchmark numerical examples on heat conduction demonstrate that the present algorithm can handle thin structures with the thickness-to-length ratio down to 1.E−08. This indicates that the BEM is especially accurate and efficient for numerical analysis of thin body problems.     

On the tearing of thin sheets

We perform an experimental study to investigate the propagation of one or two cracks in a thin elastic sheet of a brittle material torn in an out-of-plane shear mode. We observe that a single crack always follows a straight path, whereas two cracks propagating simultaneously follow curved paths and merge, forming a tongue-like shape. The present experimental setup allows the understanding of how the energy introduced at a large scale is focused at the crack tip. We find that the geometry of the sheet is determined by the direction of a large scale force, applied to the crack tip, which is perpendicular to cracked surfaces. While the material is deformed at large scales under mode III loading, the geometry of system in the vicinity of the crack tip adapts such that the material is locally broken under a pure mode I loading.     

Application of energy density theory on finite cracked bodies

Abstract

A new concept of the energy release rate of a finite cracked body is proposed. Considering the global view of the strain energy density field, the new fracture parameter presented here is different from the conventional energy release rate that only depends on the stress field around the crack tip but neglects the influences induced by the boundary conditions on the far field. Based on the hypothesis of the energy density theory, fracture initiation and termination, respectively can be predicted by the local and global relative minima of the strain energy density function. The new energy release rate is then defined as the integration of the strain energy density along the fracture trajectory from the initiation point to the destination point. The results show that the difference between the new and the conventional energy release rate becomes more pronounced if the material has a large core region (or the material is more ductile) and if the height‐width ratio of a finite cracked plate is comparatively small.     

Description of the strength of porous bodies on the basis of percolation theory

A method is proposed for estimating the strength of porous materials in destructive rupture on the basis of the percolation theory of regularly packed spheres. The results of calculation by this method are in good agreement with experimental data in the whole porosity range of the material.