Elastoplastic deformation of shells of revolution under nonaxisymmetric loading (review)

On linearization of the stiffness characteristics of flexible beams made of physically nonlinear materials

“…This follows from the standard hypotheses for beams, plates, and shells with large deflections [1,2,4,8,10].…”

“…The progressively severe operating conditions of associated structures require the use of not only rigid, but also flexible members whose deflections are commensurable with their thickness [1,2]. An important point here is that two complicating factors should be taken into account: geometrical nonlinearity due to large deflections [1, 2] and physical nonlinearity due to inelasticity [4,10].…”

“…The progressively severe operating conditions of associated structures require the use of not only rigid, but also flexible members whose deflections are commensurable with their thickness [1,2]. An important point here is that two complicating factors should be taken into account: geometrical nonlinearity due to large deflections [1, 2] and physical nonlinearity due to inelasticity [4,10].A great many works [1-4, 8, 10] addressed the behavior of thin-walled structural members taking into account either one factor or the other. However, the mutual influence of geometrical and physical nonlinearities has not been studied adequately [3,10].…”

“…Thin-walled structural members are widely used in modern engineering [1][2][3][4]. The progressively severe operating conditions of associated structures require the use of not only rigid, but also flexible members whose deflections are commensurable with their thickness [1,2].…”

Resonant electromechanical vibrations of piezoelectric shells of revolution (review)

“…Monolithic shells made of polarized piezoceramics and having the form of a truncated cone with a hole at the vertex are used as components of ultrasonic focusers, while segmented hollow and solid cylinders underlie powerful acoustic transmitters in sonars. Piezoceramic shells of revolution polarized in different directions of a polar coordinate system were addressed in [47,48,59,60,61,64,65,87,97]; such studies are reviewed in [42,43,62,88,89]. Some studies carried out by Shul'ga and his disciples are concerned with the forced vibrations of a viscoelastic piezoceramic cylinder with azimuthal, radial, or thickness polarization [3, 4, 8, 78-80, 84, 85].…”