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.

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.

Buckling of elastic plates by the method of constant deflection lines

1972 ◽  
Vol 13 (1) ◽  
pp. 91-103 ◽  
Author(s):  
J. Mazumdar
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Large Class ◽  
Arbitrary Shape ◽  
Elastic Stability ◽  
Buckling Analysis ◽  
Mathematical Treatment ◽  
Elastic Plates ◽  
Bent Plate ◽  
Thin Elastic Plates

In a previous paper of this series – hereinafter to be referred to as [1] – the author introduced a new method for a large class of boundary value problems connected with the flexure analysis of elastic plates of arbitrary shape where the concept of ‘Lines of Equal Deflection’, i.e. lines which are obtained by intersecting the bent plate by planes parallel to the original plane of the plate, was introduced. The present paper extends this analysis to the buckling analysis of thin elastic plates with various forms of boundary conditions. It is shown that the proposed method appears to be a powerful tool for the investigation of those problems of elastic stability which could not be solved by conventional methods because of the difficulty of the mathematical treatment.

The analysis of singularly loaded and rigidly clamped thin elastic slabs with curvilinear boundaries. I

1959 ◽  
Vol 55 (1) ◽  
pp. 121-136 ◽  
Author(s):  
W. A. Bassali
Keyword(s):  
Exact Solutions ◽  
Complex Variable ◽  
Elastic Plates ◽  
Complex Variable Methods ◽  
Isotropic Plates ◽  
Special Cases ◽  
Concentrated Forces ◽  
Quartic Curves ◽  
Thin Elastic Plates

ABSTRACTIn this paper complex variable methods are used to derive exact solutions in closed forms for the small deflexions of certain thin elastic plates due to transverse concentrated forces or couples applied at arbitrary or specified points. The isotropic plates considered are bounded by curvilinear edges of certain types along which the plates are rigidly clamped. Plates bounded by quartic curves having the forms of the inverses of an ellipse with respect to its centre or its focus are included as special cases.

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