On Boussinesq’s problem for a cracked halfspace

This paper examines the axisymmetric elastostatic problem that deals with the action of a concentrated normal force on the surface of an isotropic elastic halfspace containing a penny-shaped crack. The mathematical formulation of the elasticity problem should take into consideration the sense of action of the concentrated force. The paper presents the development of Fredholm integral equations of the second-kind that are associated with this category of problem and indicates the numerical technique that is adopted for their solution. The numerical results are presented for the stress intensity factors generated at the penny-shaped crack experiencing either opening or closure.     

Asymptotic behavior and inverse problem in layered scattering media

The main challenge of noninvasive optical biopsy is to obtain an accurate value of the optical coefficients of an encapsulated organ (muscle, brain, etc.). The idea developed by us is that some interesting information could be deduced from the long-time behavior of the reflectance function. This asymptotic behavior is analyzed for layered media in the framework of the diffusion approximation. A new method is derived to obtain accurate values for the optical parameters of the deepest layers. This method is designed to work in a specific long-time regime that is still within the scope of standard time-of-flight experiments but far from being included in the mathematically defined asymptotic region. The limits of this method, linked to the cases where the asymptotic behavior is no longer governed by the deepest layer, are then discussed.     

Radio-wave diagnostics of plane layered dielectrics using the inverse problem

We have developed a method for the radio-wave nondestructive testing of exfoliations in a dielectric layer. The method is based on the multifrequency sounding in 5-mm wavelength range and the solution of the inverse problem with determining the thicknesses of separate layers of a dielectric structure. We have also determined experimentally the precision and resolution of this method.     

Application of hierarchical matrices to boundary element methods for elastodynamics based on Green's functions for a horizontally layered halfspace

This paper presents the application of hierarchical matrices to boundary element methods for elastodynamics based on Green's functions for a horizontally layered halfspace. These Green's functions are computed by means of the direct stiffness method; their application avoids meshing of the free surface and the layer interfaces. The effectiveness of the methodology is demonstrated through numerical examples, indicating that a significant reduction of memory and CPU time can be achieved with respect to the classical boundary element method. This allows increasing the problem size by one order of magnitude. The proposed methodology therefore offers perspectives to study large scale problems involving three-dimensional elastodynamic wave propagation in a layered halfspace, with possible applications in seismology and dynamic soil–structure interaction.     

Some generalized anti-plane strain problems for an inhomogeneous elastic halfspace

This paper develops a generalized formulation of the theory of anti-plane deformations of a linear elastic solid, the Lamé constants of which depend on a single spatial variable. The generalized theory is applied to the study of a generalized screw dislocation, a semi-infinite crack and a finite crack located in a halfspace region where the elastic inhomogeneity is depth dependent. The problems examined in this paper are relevant to the modelling of cracks located in inhomogeneous geological materials and the study of surface defects associated with functionally graded materials.     

The statical Reissner-Sagoci problem for an internally loaded transversely isotropic halfspace

The present paper examines the elastostatic problem related to the axisymmetric rotation of a rigid circular punch which is bonded to the surface of a transversely isotropic elastic halfspace region. The rotation of the punch is induced by a concentrated couple which acts at a finite distance from the punch along the axis of symmetry. The resulting rigid rotation of the punch is evaluated in exact closed form.     

Concerning of a particular inverse problem

A coefficient inverse problem for an elliptic equation with the coefficient in the form of a stationary random field is considered. S. Petersburg State University, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 62, No. 2, pp. 338–341, March–April, 1996.     

Some aspects of the variational principles problem in elasticity

We give a brief survey of the subject, from a personal point of view. An attempt has been made to clarify historical and motivational aspects, in particular with reference to the differences between infinitesimal and finite elasticity, and with reference to implicit or explicit moment equilibrium considerations. The writing of this paper was occasioned by the preparation of an Opening Address for the Second International Conference on Variational Methods in Engineering, 17–19 July 1985, at the University of Southampton, England.     

Some estimates for a buckling problem

Summary On the basis of the exact non-linear equation describing the shape of an elastic column buckled under its own weight, estimates of maximum deflection are obtained. Also, a method to estimate lower bounds to the critical load is presented.

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Einige Abschätzungen für ein Knickproblem

Zusammenfassung Es werden auf der Basis der exakten, nichtlinearen Gleichung, welche die Gestalt einer elastischen, unter dem Eigengewicht knickenden Säule beschreibt, Abschätzungen der maximalen Ausbiegung erhalten. Es wird auch eine Methode zur Abschätzung unterer Schranken der kritischen Last vorgestellt.

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With 1 Figure     

Some matrix aspects of generalized dimensional analysis

Summary Recent group theoretic techniques effective for reducing the number of variables in systems of partial differential equations are invoked to formulate a generalized approach to dimensional analysis. It is then shown that significant conclusions can be elicited upon consideration of adimensional matrix arising via the group formulation. In particular, a generalized form of Sedov's self-similarity criterion is shown to exist within the framework of the approach developed. The presentation is concluded by consideration of three illustrations.This research has been sponsored in part by the Mathematics Research Center, United States Army, The University of Wisconsin, under Contract No. DA-31-124-AR0-D-462. The paper is based upon a presentation made at the Sixteenth Conference of Army Mathematicians, Bethesda, Maryland, May, 1970.     

An inverse geometry problem for the localisation of skin tumours by thermal analysis

In this paper, the dual reciprocity method (DRM) is coupled to a genetic algorithm (GA) in an inverse procedure through which the size and location of a skin tumour may be obtained from temperature measurements at the skin surface. The GA is an evolutionary process which does not require the calculation of sensitivities, search directions or the definition of initial guesses. The DRM in this case requires no internal nodes. It is also shown that the DRM approximation function used is not an important factor for the problem considered here. Results are presented for tumours of different sizes and positions in relation to the skin surface.     

Solution of the internal inverse problem for a bulk anisotropic body

An approach to the problem of modeling temperature fields of bulk anisotropic bodies is developed and realized on the basis of the equivalence principle.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 3, pp. 455–458, March, 1989.     

Nonlinear-eigenvalue problem for heat conduction in a one-dimensional coupled-thermoelastic layered composite

The dynamic treatment of a one-dimensional transient coupled-thermoelastic problem of heat conduction is made for a layered plate which is exposed to a uniform sudden heating or cooling. The basic equations are transformed into a system of matrix equations, and the problem is formulated as a non-linear eigenvalue problem of a polynomial matrix. Numerical computations are made for a plate of the sandwitch structure. The real-valued eigenvalues and the complex-valued eigenvalues are given, corresponding to the thermal and mechanical modes of behaviour of the plate, respectively. The variation of those eigenvalues with the thermoelastic coupling coefficient is examined.     

Numerical solution for an inverse variational problem

Optimization and Engineering - In the present work, firstly, we use a minimax equality to prove the existence of a solution to a certain system of varitional equations providing a numerical...