Analytical Puncture Study of Circular Metal Plates

1980 ◽  
Vol 102 (3) ◽  
pp. 242-248 ◽  
Author(s):  
R. C. Shieh
Keyword(s):  
Large Deflection ◽  
Plate Thickness ◽  
Closed Form Solution ◽  
Analytical Techniques ◽  
Correlation Study ◽  
Form Solution ◽  
Punch Force ◽  
Perfectly Plastic ◽  
Static Responses ◽  
Metal Plates

An existing closed-form solution for large-deflection static responses of centrally loaded, rigid, perfectly plastic circular metal plates (with emphasis on steel plate cases) that are clamped (built-in) or simply supported at the edges is first modified to take into account the effects of elastic deformation and material strainhardening in an approximate manner. The modified theoretical solution is first shown to correlate very well with experimental results. Then it is applied in solving the quasi-static plate puncture problem in which the punch bar penetrates slowly into the plate. An analytical/experimental correlation study on punch force-deflection relationship and incipient plate puncture energy is made on newly obtained experimental data. Effects of variation of strainhardening parameter, boundary conditions and shear deformation on incipient puncture energy are studied, and plate puncture design curves are developed in the form of nondimensional incipient plate puncture energy as a function of punch diameter/plate thickness ratio for various values of punch diameter/plate diameter ratio. Application of these analytical techniques/design curves to the design of nuclear shipping cask plate components subject to regulatory puncture drop loading is also discussed.

Finite Deformations of a Rigid Perfectly Plastic Arch

1962 ◽  
Vol 29 (3) ◽  
pp. 549-553 ◽  
Author(s):  
E. T. Onat ◽  
L. S. Shu
Keyword(s):  
Closed Form ◽  
Yield Point ◽  
Finite Deformation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Finite Deformations ◽  
Deformation History ◽  
Rigid Plastic ◽  
Perfectly Plastic ◽  
History Of

The quasi-static postyield deformation of a rigid-plastic arch in the presence of geometry changes is considered. The problem is formulated in terms of a series of boundary-value problems concerned with rates of stress and velocities. In the present simple case, the consideration of the rate problem associated with the yield-point state of the structure enables one to construct a closed-form solution which describes the entire deformation history of the arch. However, the principal aim of the present study is to stress the central role played by the rate problem in the investigation of the finite deformation of structures.

scholarly journals Axisymmetric Large Deflection Elastic Analysis of Hollow Annular Membranes under Transverse Uniform Loading

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1770
Author(s):  
Jun-Yi Sun ◽  
Qi Zhang ◽  
Xue Li ◽  
Xiao-Ting He
Keyword(s):  
Closed Form ◽  
Circular Plate ◽  
Large Deflection ◽  
Closed Form Solution ◽  
Circular Ring ◽  
Form Solution ◽  
Elastic Response ◽  
Geometrically Nonlinear ◽  
Closed Form Solutions ◽  
Annular Membrane

The anticipated use of a hollow linearly elastic annular membrane for designing elastic shells has provided an impetus for this paper to investigate the large deflection geometrically nonlinear phenomena of such a hollow linearly elastic annular membrane under transverse uniform loads. The so-called hollow annular membranes differ from the traditional annular membranes available in the literature only in that the former has the inner edge attached to a movable but weightless rigid concentric circular ring while the latter has the inner edge attached to a movable but weightless rigid concentric circular plate. The hollow annular membranes remove the transverse uniform loads distributed on “circular plate” due to the use of “circular ring” and result in a reduction in elastic response. In this paper, the large deflection geometrically nonlinear problem of an initially flat, peripherally fixed, linearly elastic, transversely uniformly loaded hollow annular membrane is formulated, the problem formulated is solved by using power series method, and its closed-form solution is presented for the first time. The convergence and effectiveness of the closed-form solution presented are investigated numerically. A comparison between closed-form solutions for hollow and traditional annular membranes under the same conditions is conducted, to reveal the difference in elastic response, as well as the influence of different closed-form solutions on the anticipated use for designing elastic shells.

Large Deflection Behavior of Composite Laminated Plates under End-Shortening and Normal Pressure Loading Using a Semi-Energy Finite Strip Method

2011 ◽  
Vol 471-472 ◽  
pp. 432-437
Author(s):  
Hamid Reza Ovesy ◽  
Mohammad Homayoun Sadr-Lahidjani ◽  
Mohammad Hajikazemi ◽  
Hassan Assaee
Keyword(s):  
Large Deflection ◽  
Closed Form Solution ◽  
Normal Pressure ◽  
Form Solution ◽  
Laminated Plates ◽  
Pressure Loading ◽  
Finite Strip ◽  
Composite Laminated Plates ◽  
Strip Method ◽  
Finite Strip Method

In this paper, the application of previously the semi energy finite strip method (FSM) for the non-linear post-buckling analysis of rectangular anti-symmetric laminates is extended to include the effects of normal pressure loading in addition to the progressive end-shortening. One of the main advantages of the semi-energy FSM is that it is based on the closed form solution of von Kármán’s compatibility equation. The developed finite strip method is applied to analyze the large deflection behavior of anti-symmetric angle ply composite laminated plates with simply supported boundary conditions at its loaded ends. To validate the results, they are compared with those obtained from finite element method (FEM) of analysis.

scholarly journals Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure Loading

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1238
Author(s):  
Bin-Bin Shi ◽  
Jun-Yi Sun ◽  
Ting-Kai Huang ◽  
Xiao-Ting He
Keyword(s):  
Closed Form ◽  
Plane Stress ◽  
Large Deflection ◽  
Closed Form Solution ◽  
Form Solution ◽  
Gas Pressure ◽  
Circular Membrane ◽  
Pressure Loading ◽  
Out Of Plane ◽  
Large Deflection Problem

The large deflection phenomenon of an initially flat circular membrane under out-of-plane gas pressure loading is usually involved in many technical applications, such as the pressure blister or bulge tests, where a uniform in-plane stress is often present in the initially flat circular membrane before deflection. However, there is still a lack of an effective closed-form solution for the large deflection problem with initial uniform in-plane stress. In this study, the problem is formulated and is solved analytically. The initial uniform in-plane stress is first modelled by stretching or compressing an initially flat, stress-free circular membrane radially in the plane in which the initially flat circular membrane is located, and based on this, the boundary conditions, under which the large deflection problem of an initially flat circular membrane under in-plane radial stretching or compressing and out-of-plane gas pressure loading can be solved, are determined. Therefore, the closed-form solution presented in this paper can be applied to the case where the initially flat circular membrane may, or may not, have a uniform in-plane stress before deflection, and the in-plane stress can be either tensile or compressive. The numerical example conducted shows that the closed-form solution presented has satisfactory convergence.

scholarly journals Large Deflection of Prismatic Cantilever Beam Exposed to Combination of End Inclined Force and Tip Moment

2017 ◽  
Vol 12 (1) ◽  
pp. 98 ◽  
Author(s):  
Ibrahim Abu-Alshaikh ◽  
Hashem S. Alkhaldi ◽  
Nabil Beithou
Keyword(s):  
Numerical Solution ◽  
Cantilever Beam ◽  
Large Deflection ◽  
Elliptic Integral ◽  
Geometrical Nonlinearity ◽  
Closed Form Solution ◽  
Form Solution ◽  
Integration Constant ◽  
Computational Time ◽  
Special Cases

The large deflection of a prismatic Euler-Bernoulli cantilever beam under a combination of end-concentrated coplanar inclined force and tip-concentrated moment is investigated. The angle of inclination of the applied force with respect to the horizontal axis remains unchanged during deformation. The cantilever beam is assumed to be naturally straight, slender, inextensible and elastic. The large deflection of the cantilever beam induces geometrical nonlinearity; hence, the nonlinear theory of bending and the exact expression of curvature are used. Based on an elliptic integral formulation, an accurate numerical solution is obtained in terms of an integration constant that should satisfy the boundary conditions associated with the cantilever beam. For some special cases this integration constant is exactly found, which leads to closed form solution. The numerical solution obtained is quite simple, accurate and involves less computational time compared with other techniques available in literature. The details of elastica and its corresponding orientation curves are presented and analyzed for extremely large load combinations. A comparative study with pre-obtained results has been made to verify the accuracy of the presented solution; an excellent agreement has been obtained.

DEFLECTION OF A FLEXURAL CANTILEVER BEAM

1993 ◽  
Vol 17 (1) ◽  
pp. 29-43 ◽  
Author(s):  
A.N. Sherbourne ◽  
F. Lu
Keyword(s):  
Cantilever Beam ◽  
Large Deflection ◽  
Standard Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Relative Depth ◽  
Algebraic Equations ◽  
Unknown Variable ◽  
Small Deflection ◽  
Yield Behaviour

The behaviour of a flexural elasto-plastic cantilever beam is investigated in which geometric nonlinearities are considered. The result of an elastica analysis by Frisch-Fay [1] is extended to include post-yield behaviour. Although a closed-form solution is not possible, as in the elastic case, simple algebraic equations are derived involving only one unknown variable, which can also be expressed in the standard form of elliptic integrals if so desired. The results, in comparison with those of the small deflection analyses, indicate that large deflection analyses are necessary when the relative depth of the beam is very small over the length. The present exact solution can be used as a reference by those who resort to a finite element method for more complicated problems. It can also serve as a building block to other beam problems such as a simply supported beam or a beam with multiple loads.

scholarly journals A Closed Form Solution for Nonlinear Oscillators Frequencies Using Amplitude-Frequency Formulation

2012 ◽  
Vol 19 (6) ◽  
pp. 1415-1426 ◽  
Author(s):  
A. Barari ◽  
A. Kimiaeifar ◽  
M.G. Nejad ◽  
M. Motevalli ◽  
M.G. Sfahani
Keyword(s):  
Closed Form ◽  
Numerical Solutions ◽  
Closed Form Solution ◽  
Analytical Techniques ◽  
Nonlinear Oscillators ◽  
Form Solution ◽  
Closed Form Expression ◽  
System Response ◽  
Classical Dynamics ◽  
Analytical Technique

Many nonlinear systems in industry including oscillators can be simulated as a mass-spring system. In reality, all kinds of oscillators are nonlinear due to the nonlinear nature of springs. Due to this nonlinearity, most of the studies on oscillation systems are numerically carried out while an analytical approach with a closed form expression for system response would be very useful in different applications. Some analytical techniques have been presented in the literature for the solution of strong nonlinear oscillators as well as approximate and numerical solutions. In this paper, Amplitude-Frequency Formulation (AFF) approach is applied to analyze some periodic problems arising in classical dynamics. Results are compared with another approximate analytical technique called Energy Balance Method developed by the authors (EBM) and also numerical solutions. Close agreement of the obtained results reveal the accuracy of the employed method for several practical problems in engineering.

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