Existence and uniqueness theorems for cusped prismatic shells in the <i>N</i>th hierarchical model

This paper deals with a class of linearly elastic material bodies of a special shape, namely the cuspidate prismatic shell-like bodies introduced by I. Vekua, studied in the framework of Vekua's 0-order approximation theory. It is shown per exempla that when such bodies are subject to concentrated boundary loads, concentrated internal contact interactions may arise. This fact helps to motivate the quest for a generalization of the standard theory, which covers only diffuse internal contact interactions.

show abstract

“…4); surveys of investigations into elastic cuspidate prismatic shells are found in [1,5,7]. Beginning from Sect.…”

Section: Fig 4 a Cuspidate Platementioning

confidence: 99%

“…With the help of Fig. 1a, 1 consider the two-dimensional version of Flamant's problem, where the applied load f = f e 1 ( f > 0) gives rise to the equilibrium stress field S F (ρ, ϑ) = − 2 π f ρ −1 cos ϑ e(ϑ) ⊗ e(ϑ), (ρ, ϑ) ∈ (0, +∞) × [−π, +π].…”

Section: S(x)n(x) = L(x)mentioning

confidence: 99%

Concentrated contact interactions in cuspidate prismatic shell-like bodies

et al. 2010

Self Cite

View full text Add to dashboard Cite

show abstract

“…Evidently, if 0 ≤ κ < 1, a profile (a normal cross-section of the prismatic shell at the cusped edge) has a smooth boundary, while if κ ≥ 1, the profile is not smooth, namely, ends with an angle φ ∈ [0, π[ at cusped edge. Cusped prismatic shells of the form (71) are investigated at most (see [3], [14], [15], [19] and the references given there). When ω is a half-plane x 2 ≥ 0, the Flamant, Cerutti, and Carothers type problems are solved in explicit forms, which in the particular case κ = 0 coincide with the classical Flamant, Cerutti, and Carothers formulas for the plate of a constant thickness [20]- [23].…”

Section: Analysis Of the Constructed Modelsmentioning

confidence: 99%

Vekua type hierarchical models for prismatic shells with mixed conditions on face surfaces

Jaiani

2016

Composite Structures

View full text Add to dashboard Cite

I.Vekua constructed hierarchical models for elastic prismatic shells, in particular, plates of variable thickness, when on the face surfaces either stresses or displacements are known. In the present paper other hierarchical models for cusped, in general, elastic isotropic and anisotropic prismatic shells are constructed and analyzed, namely, when on the face surfaces (i) a normal to the projection of the prismatic shell component of a stress vector and parallel to the projection of the prismatic shell components of a displacement vector, (ii) a normal to the projection of the prismatic shell component of the displacement vector and parallel to the projection of the prismatic shell components of the stress vector are prescribed. We construct also hierarchical models, when other mixed conditions are given on face surfaces. In the zero approximations of the models under consideration peculiarities (depending on sharpening geometry of the cusped edge) of correct setting boundary conditions at edges are investigated. In concrete cases some boundary value problems are solved in an explicit form. As an example of application of the constructed Vekua-type models to composite structures, as example, an unidirectional lamina with fibers parallel to x 2 -axis under shear strain is considered. Tension-compression is treated as well.

show abstract

“…in [16][17][18]. In [16] the well-posedness of BVPs for elastic cusped plates (i.e. symmetric prismatic shells) in the N-th approximation N !…”

Section: Introductionmentioning

confidence: 99%

Harmonic vibration of prismatic shells in zero approximation of Vekua's hierarchical models

Chinchaladze

Gilbert

2013

Applicable Analysis

View full text Add to dashboard Cite

In this article elastic cusped symmetric prismatic shells (i.e., plates of variable thickness with cusped edges) in the zero approximation of I.Vekua's hierarchical models is considered. The well-posedness of the boundary value problems (BVPs) under the reasonable boundary conditions at the cusped edge and given displacements at the non-cusped edge is studied in the case of harmonic vibration. The approach works also for non-symmetric prismatic shells word for word. The classical and weak setting of the BVPs in the case of the zero approximation of hierarchical models is considered. Appropriate weighted functional spaces are introduced. Uniqueness and existence results for the variational problem are proved. The structure of the constructed weighted space is described and its connection with weighted Sobolev spaces is established. Moreover, some sufficient conditions for a linear functional arising in the right-hand side of the variational equation to be bounded are given.

show abstract

Existence and uniqueness theorems for cusped prismatic shells in the Nth hierarchical model

Cited by 15 publications

References 23 publications

Concentrated contact interactions in cuspidate prismatic shell-like bodies

Concentrated contact interactions in cuspidate prismatic shell-like bodies

Vekua type hierarchical models for prismatic shells with mixed conditions on face surfaces

Harmonic vibration of prismatic shells in zero approximation of Vekua's hierarchical models

Contact Info

Product

Resources

About