The reflection method in elasticity and bending of plates

Chicurel, R.; Suppiger, Edward W.

doi:10.1007/bf01595148

Cited by 14 publications

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“…Numerical solutions of the geometrical problem with the aid of layers of edge dislocations and of the mixed problem with the aid of layers of forces on the parts of the boundary with statical boundary conditions and layers of edge dislocations on the parts with geometrical boundary conditions are given in [9,10] (see also [11]). Chicurel, Suppiger [12] and Oliveira [13] apply single forces and layers of forces respectively on curves spatially separated from the boundary. In [14] (see also [15]) the advantages and disadvantages of such an approach are investigated.…”

Section: General Remarksmentioning

confidence: 99%

Systematic compilation of integral equations of the Rizzo type and of Kupradze's functional equations for boundary value problems of plane elastostatics

Heise

1980

J Elasticity

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With the aid of the singularity method (indirect method) 16 integral equations of the Rizzo type and the corresponding functional equations of the Kupradze type for the geometrical, the statical and the mixed boundary value problem of plane elastostatics are established. Up to now only a few of them and not even in all cases the best ones have been used for the numerical treatment of technical problems. The equations have the same kernels as those compiled in [16], however, they differ fundamentally from those by the fact that the boundary values are subjected to an integral transformation before being prescribed as the "right hand sides". Usually such equations are established with the aid of Green's theorem (direct method). By virtue of the systematic deduction of the equations using layers of edge dislocations, edge dislocation dipoles, forces and force dipoles and prescribing the boundary displacements and their derivatives and the boundary tractions and their integrals all equations can be inserted in a uniform and closed scheme of classification. The integral equations of the Rizzo type are represented as special cases of functional equations of the Kupradze type. Because of the different structures of the kernels not all equations are suited for numerical calculations in the same way. To be able to choose the most suitable formulation for every individual problem the conditions of the equations are investigated and compared with those of integral equations of other important types. Since all functions occurring in the equations can be interpreted mechanically in an elementary manner it is possible to understand and apply these equations without special mathematical knowledge. Chapter 1.2 contains an extensive survey of the paper in hand. ZUSAMMENFASSUNGMit Hilfe der Singularit~itenmethode (indirekten Methode) werden 16 Integralgleichungen vom RizzoTyp und 16 Kupradzesche Funktionalgleichungen fiir das geometrische, das statische und das gemischte Randwertproblem der ebenen Elastostatik aufgestellt. Von den Gleichungen wurden bisher nur wenige und nicht einmal in allen F~illen die besten zur numerischen Behandlung technischer Aufgaben benutzt. Die Gleichungen besitzen zwar dieselben Kerne wie die in [16] angegebenen, unterscheiden sich aber yon jenen grundlegend dadurch, dab die Randwerte einer Integraltransformation unterzogen werden, bevor man sie auf der "rechten Seite" vorschreibt, l)blicherweise werden solche Gleichungen mit Hilfe des Greenschen Satzes aufgestellt (direkte Methode). Dank der systematischen Herleitung der Gleichungen unter Verwendung yon Belegungen yon Versetzungen, Versetzungsdipolen, Kriiften und Kriiftedipolen bei Vorgabe der Randverschiebungen und ihrer Ableitungen sowie der Randspannungen und ihrer Integrale lassen sich alle Gleichungen in ein einheitliches und abgeschlossenes Klassifikationsschema einordnen. Die Integralgleichungen vom Rizzo-Typ werden darin als Spezialf~ille yon Kupradzeschen Funktionalgleichungen dargestellt. Wegen ihrer unterschiedlichen Struktur eignen sich ni...

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Section: General Remarksmentioning

confidence: 99%

Systematic compilation of integral equations of the Rizzo type and of Kupradze's functional equations for boundary value problems of plane elastostatics

Heise

1980

J Elasticity

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Condition number of matrices derived from two classes of integral equations

Christiansen

Meister²

1981

Math Methods in App Sciences

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We investigate some integral equations, i. a. the so‐called Kupradze functional equations, where the two variables of the kernel belong to two different point sets. An extensive survey of the literature shows the various applications of these equations. By a discretization of the integral equations they are replaced by systems of linear algebraic equations. The condition number of the corresponding matrices is investigated, analytically and numerically. It is thereby quantitatively found in which way the condition of the matrices deteriorates when the two point sets are moved away from each other.

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Converged stress solutions in thin plates by the extended field method

Donaldson

Chander

Negm

1980

Numerical Meth Engineering

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SUMMARYThis paper presents numerical results calculated by the extended field method for the problem of the forced harmonic vibration of two plates-one rectangular and one triangular. The numerical results demonstrate that the extended field method, which is a deflection-based series solution method, is capable of producing converged stress solutions suitable for being bases of comparison for other approximate methods of analysis.

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The reflection method in elasticity and bending of plates

Cited by 14 publications

References 0 publications

Systematic compilation of integral equations of the Rizzo type and of Kupradze's functional equations for boundary value problems of plane elastostatics

Systematic compilation of integral equations of the Rizzo type and of Kupradze's functional equations for boundary value problems of plane elastostatics

Condition number of matrices derived from two classes of integral equations

Converged stress solutions in thin plates by the extended field method

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