scholarly journals Closure to “Discussions of ‘Stability of Thin Elastic Plates Covering an Arbitrary Simply Connected Region and Subject to Any Admissible Boundary Conditions’” (1953, ASME J. Appl. Mech., 20, pp. 591–592)

1953 ◽  
Vol 20 (4) ◽  
pp. 592-593
Author(s):  
G. A. Zizicas
Keyword(s):  
Boundary Conditions ◽  
Connected Region ◽  
Elastic Plates ◽  
Simply Connected Region ◽  
Simply Connected ◽  
Thin Elastic Plates

Stability of Thin Elastic Plates Covering an Arbitrary Simply Connected Region and Subject to any Admissible Boundary Conditions

1953 ◽  
Vol 20 (1) ◽  
pp. 23-29
Author(s):  
G. A. Zizicas
Keyword(s):  
Boundary Conditions ◽  
Direct Method ◽  
Elastic Plates ◽  
Simple Manner ◽  
Particular Solutions ◽  
Isotropic Plates ◽  
Simply Connected Region ◽  
Simply Connected ◽  
A Direct Method ◽  
Thin Elastic Plates

Abstract The Bergman method of solving boundary-value problems by means of particular solutions of the differential equation, which are constructed without reference to the boundary conditions, is applied to the problem of stability of thin elastic plates of an arbitrary simply connected shape and subject to any admissible boundary conditions. A direct method is presented for the construction of particular solutions that is applicable to both anisotropic and isotropic plates. Previous results of M. Z. Krzywoblocki for isotropic plates are obtained in a simple manner.

A Conformal Proof of a Jordan Curve Problem

1969 ◽  
Vol 12 (5) ◽  
pp. 673-674 ◽  
Author(s):  
G. Spoar ◽  
N.D. Lane
Keyword(s):  
Jordan Curve ◽  
Connected Region ◽  
Inversive Plane ◽  
Simply Connected Region ◽  
Simply Connected

The following theorem appears in [1].Let R be a closed simply connected region of the inversive plane bounded by a Jordan curve J, and let J be divided into three closed arcs A1, A2, A3. Then there exists a circle contained in R and having points in common with all three arcs.

scholarly journals Enhanced Single-Degree-of-Freedom Analysis of Thin Elastic Plates Subjected to Blast Loading Using an Energy-Based Approach

2020 ◽  
Vol 2020 ◽  
pp. 1-29
Author(s):  
M. D. Goel ◽  
T. Thimmesh ◽  
P. Shirbhate ◽  
C. Bedon
Keyword(s):  
Boundary Conditions ◽  
Blast Waves ◽  
Degree Of Freedom ◽  
Elastic Plates ◽  
Nonlinear Parameters ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Impulsive Loads ◽  
Technical Interest ◽  
Thin Elastic Plates

Single-degree-of-freedom (SDOF) models are known to represent a valid tool in support of design. Key assumptions of these models, on the other hand, can strongly affect the expected predictions, hence resulting in possible overconservative or misleading estimates for the response of real structural systems under extreme actions. Among others, the description of the input loads can be responsible for major design issues, thus requiring the use of more refined approaches. In this paper, a SDOF model is developed for thin elastic plates under large displacements. Based on the energy approach, careful attention is given for the derivation of the governing linear and nonlinear parameters, under different boundary conditions of technical interest. In doing so, the efforts are dedicated to the description of the incoming blast waves. In place of simplified sinusoidal pressures, the input impulsive loads are described with the support of infinite trigonometric series that are more accurate. The so-developed SDOF model is therefore validated, based on selected literature results, by analyzing the large displacement response of thin elastic plates, under several boundary conditions and real blast pressures. Major advantage for the validation of the proposed SDOF model is obtained from experimental finite element (FE) and finite difference (FD) models of literature, giving evidence of a rather good correlation and confirming the validity of the presented formulation.

$\beta$-transformation, natural extension and invariant measure

2000 ◽  
Vol 20 (5) ◽  
pp. 1271-1285 ◽  
Author(s):  
GAVIN BROWN ◽  
QINGHE YIN
Keyword(s):  
Invariant Measure ◽  
Lebesgue Measure ◽  
Natural Extension ◽  
Connected Region ◽  
Two Dimensional ◽  
Constant Multiple ◽  
Unit Square ◽  
Simply Connected Region ◽  
Simply Connected ◽  
Dimensional Lebesgue Measure

For $\beta>1$, consider the $\beta$-transformation $T_\beta$. When $\beta$ is an integer, the natural extension of $T_\beta$ can be represented explicitly as a map on the unit square with an invariant measure: the corresponding two-dimensional Lebesgue measure. We show that, under certain conditions on $\beta$, the natural extension is defined on a simply connected region and an invariant measure is a constant multiple of the Lebesgue measure.We characterize those $\beta$ in terms of the $\beta$-expansion of one, and study the structure and size of the set of all such $\beta$.

Bounds for the Torsional Rigidity of Isotropic Beams

1962 ◽  
Vol 58 (2) ◽  
pp. 417-419 ◽  
Author(s):  
L. M. Milne-Thomson
Keyword(s):  
Cross Section ◽  
Isotropic Material ◽  
Torsional Rigidity ◽  
Connected Region ◽  
Closed Contour ◽  
Prismatic Beam ◽  
The Cross ◽  
Simply Connected Region ◽  
Simply Connected

Consider a cylindrical or prismatic beam of isotropic material. Let the cross-section of the beam be a simply-connected region S bounded by the closed contour C.

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