Lectures on Cauchy’s Problem in Linear Partial Differential Equations. By J. Hadamard. Pp. viii+316. 15s.net. 1923. (Per Oxford University Press.)

In this paper some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m or = 1 Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations A mixed boundary value problem from the theory of elasticity is considered as an example Particularly for integral equations where the kernel contains, in addition to the dominant term (t,x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results

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On the solution of integral equations with strong ly singular kernels

An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment

Dynamic Modeling and Vibration Characteristics Analysis of Submerged Stiffened Combined Shells

Prof. David E. Allan Prof. Robert E. Lutz II Melbourne, Australia Los Angeles, California James R. Atwood Paul McCarthy Washington, D.C. Chicago, Illinois Prof. Richard M. Buxbaum Ewell E. Murphy, Jr. Berkeley, California Houston, Texas Georges R. Delaume Richard C. Pugh Washington, D.C. New York, New York Sir Joseph Gold William Dill Rogers Washington, D.C. Washington, D.C. John L. Gornall, Jr. Dean Jeswald W. Salacuse Atlanta, Georgia Medford, Massachusetts Dr. Christine Gray Prof. Kenneth R. Simmonds Oxford, England London, England Prof. Robert E. Hudec Prof. Willem C. Vis Minneapolis, Minnesota New York, New York Stanley B. Lubman San Francisco, California

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Board of Editorial Advisors

This paper describes the method of determining the normal modes of vibrations and natural frequencies of elastic shells of revolution with an arbitrary meridian, partially filled with a fluid. The modes of vibration of the shells with fluids are determined as a linear combination of the natural modes of vibration in vacuum. The solution of the problem of hydroelastic vibrations has been obtained using the methods of the boundary element (BEM) and the finite element (FEM). Numerical investigations of vibrations of hemi-spherical shells conveying fluid have been conducted and analyzed. Illustrative examples are provided to demonstrate the accuracy and efficiency of the developed numerical procedure.

Free vibrations of shells of revolution filled with a fluid

An approximate solution of hypersingular integral equations

Accuracy optimal methods for evaluating hypersingular integrals

A method to evaluate the fundamental solutions of thick sandwich plates by the use of the Fourier transform technique is developed. The fundamental solution is presented in the Fourier integral form and the calculation of this solution is discussed in detail. A special care is taken for representation and calculation of the hypersingular integrals entering in this presentation.

Fundamental solutions for thick sandwich plates

A study is made of the bending analysis of isotropic, linear elastic sandwich plates with arbitrary shape and boundary conditions. The problem is examined by means of the indirect boundary element method (IBEM) in the context of the small-deflection, first-order shear deformation theory. The behavior of the plate is governed by a system of the differential equations expressed in terms of the potential and stream functions. The resulting boundary integral equations are formulated. The numerical solutions of these equations follow the routine procedure of the BEM. The numerical results obtained demonstrate the efficiency and accuracy of the proposed technique.

E.S. Ventsel

Papers

Free vibrations of shells of revolution filled with a fluid

An approximate solution of hypersingular integral equations

Accuracy optimal methods for evaluating hypersingular integrals

Fundamental solutions for thick sandwich plates

A boundary element method applied to sandwich plates of arbitrary plan form