Summary
The matrix of fundamental solutions of time-independent equations of motion for linear elasticity with couple-stresses is employed to construct a vector potential of volume distribution. APoisson formula is obtained by applying the basic operator to the potential. The formula agrees with that ofKupradze for classical elastokinetics.
Zusammenfassung
Die Matrix der Grundlösungen der zeitunabhängigen Bewegungsgleichungen der linearen Elastizität mit Momentenspannungen wird angewendet um ein Vektorpotential der Volumsverteilung zu konstruieren. Durch Anwendung des Grundoperators auf das Potential wird einePoissonsche Formel erhalten. Diese Formel stimmt mit der Formel vonKupradse für die klassische Elastokinetik überein.
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References
Doyle, J. M.: Singular solutions in elasticity. Acta Mech.4 (1967).
Kellog, O. D.: Foundations of Potential Theory. New York: Frederick Ungar, 1929.
Kupradze, V. D.: Dynamical problems in elasticity. Progress in solid mechanics Vol. III. Amsterdam: North Holland, 1963.
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Chowdhury, K.L. On the poisson formula of elasticity. Acta Mechanica 10, 27–35 (1970). https://doi.org/10.1007/BF01176654
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DOI: https://doi.org/10.1007/BF01176654