Some General Methods
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BANICHUK, Nikolay, BARSUK, Alexander A., JERONEN, J., TUOVINEN, Tero, NEITTAANMAKI, Pekka. Some General Methods. In: Solid Mechanics and its Applications, 2020, nr. 259, pp. 145-177. ISSN 0925-0042. DOI: https://doi.org/10.1007/978-3-030-23803-2_4
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Solid Mechanics and its Applications
Numărul 259 / 2020 / ISSN 0925-0042

Some General Methods

DOI: https://doi.org/10.1007/978-3-030-23803-2_4

Pag. 145-177

Banichuk Nikolay1, Barsuk Alexander A.2, Jeronen J.3, Tuovinen Tero3, Neittaanmaki Pekka3
 
1 Institut pe Probleme Mecanice, Academia de Stiinte a Rusiei,
2 Moldova State University,
3 Department of Mathematical Information Technology, University of Jyvaskyla
 
Disponibil în IBN: 27 martie 2021


Rezumat

In this chapter, we take a brief general look into elastic stability in the setting of classical solid mechanics. We introduce the different types of stability loss, and then look at conditions under which merging of eigenvalues may occur. We consider a problem where applying symmetry arguments allows us to eliminate multiple (merged) eigenvalues, thus reducing the problem to determining a classical simple eigenvalue. We discuss a general technique to look for bifurcations in problems formulated as implicit functionals. Finally, we consider a variational approach to the stability analysis of an axially moving panel (a plate undergoing cylindrical deformation).

Cuvinte-cheie
Classical solid mechanics, Eigen-value, Elastic stability, Functionals, General method, Stability analysis, Stability loss, Variational approaches