Summary
The present paper exhibits a variational principle in which variation and differentation with respect to time are not permutable. The formulation is equally valid for systmes with finite and infinite number of degrees of freedom. The merit and efficiency of the method is demonstrated by means of several examples. The numerical aspects of the variational principle are also studied. Special attention is paid to the linear and nonlinear heat conduction problem. Heat conduction with cylindrical symmetry and temperature dependent material properties is discussed in details.
Zusammenfassung
In dieser Arbeit wird ein Variationsprinzip angegeben, bei dem Variation und Ableitung nach der Zeit nicht vertauschbar sind. Die Formulierung gilt für Systeme mit endlich vielen Freiheitsgraden wie auch für solche mit unendlich vielen. Vorzüge der Methode werden an Hand einiger Beispiele demonstriert. Untersucht werden auch numerische Aspekte des Variationsprinzips. Besondere Betonung liegt dabei auf lineare wie nichtlineare Wärmeleitungsprobleme. Die Wärmeleitung zylindersymmetrischer Probleme und temperaturabhängiger Materialeigenschaften sind im Detail erörtert.
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Dedicated to the memory of Prof. Dr.Rastko Stojanovic, teacher and friend.
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Vujanovic, B. On one variational principle for irreversible phenomena. Acta Mechanica 19, 259–275 (1974). https://doi.org/10.1007/BF01176491
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DOI: https://doi.org/10.1007/BF01176491