The Significance of the Concentrated Load in the Limit Analysis of Conical Shells

1966 ◽  
Vol 33 (1) ◽  
pp. 93-101 ◽  
Author(s):  
John A. DeRuntz ◽  
P. G. Hodge
Keyword(s):  
Yield Condition ◽  
Point Load ◽  
Concentrated Load ◽  
Shallow Shells ◽  
Conical Shells ◽  
Simply Supported ◽  
Tresca Yield Condition ◽  
Wide Range ◽  
Limiting Case ◽  
Yield Conditions

The yield point load of a simply supported conical sandwich shell loaded at its vertex through a rigid central boss is found for a material obeying the Tresca yield condition. Exact solutions are found for a wide range of shell configurations ranging from thick shallow cones to thin steep ones, including large and small boss sizes. The results are compared with those for the limiting case of zero boss radius corresponding to a complete conical shell loaded with a concentrated load at its vertex. It is found that for thick shallow shells the concentrated-load solution is a good approximation to the solution for realistically small boss sizes, but that for thin and/or steep shells the agreement is so poor as to make the concentrated-load solution meaningless. It is shown that such behavior also can be expected for shells obeying more realistic yield conditions.

Analysis of Plastic Shallow Conical Shells

1963 ◽  
Vol 30 (2) ◽  
pp. 199-209 ◽  
Author(s):  
R. H. Lance ◽  
E. T. Onat
Keyword(s):  
Yield Surface ◽  
Digital Computer ◽  
Yield Condition ◽  
Shell Material ◽  
Rigid Plastic ◽  
Conical Shells ◽  
Simply Supported ◽  
State Of Stress ◽  
Load Intensity ◽  
Yield Conditions

The paper is concerned with simply supported shallow conical shells loaded through a central boss. The shell material is rigid-plastic and the relevant stress resultants are subject to a nonlinear yield condition. The critical load intensity at which the shell will begin to deform and the associated fields of stress resultants and plastic flow are to be determined. For this purpose, a problem concerned exclusively with stress resultants is formulated by using the equation of stress compatibility. The resulting nonlinear problem is solved, with the help of a digital computer, in cases where the yield-point state of stress is controlled, over the pertinent intervals covering the entire shell, by three distinct yield conditions, each corresponding to a given face of the appropriate four-dimensional nonlinear yield surface.

scholarly journals Peridynamic Higher-Order Beam Formulation

2020 ◽  
Author(s):  
Zhenghao Yang ◽  
Erkan Oterkus ◽  
Selda Oterkus
Keyword(s):  
Finite Element Method ◽  
Cantilever Beam ◽  
Higher Order ◽  
Point Load ◽  
Transverse Displacement ◽  
Lagrange Equations ◽  
Concentrated Load ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Good Agreement

Abstract In this study, a novel higher-order peridynamic beam formulation is presented. The formulation is obtained by using Euler-Lagrange equations and Taylor’s expansion. To demonstrate the capability of the presented approach, several different beam configurations are considered including simply supported beam subjected to distributed loading, simply supported beam with concentrated load, clamped-clamped beam subjected to distributed loading, cantilever beam subjected to a point load at its free end and cantilever beam subjected to a moment at its free end. Transverse displacement results along the beam obtained from peridynamics and finite element method are compared with each other and very good agreement is obtained between the two approaches.

Optimal Forms of Shallow Shells With Circular Boundary, Part 2: Maximum Buckling Load

1984 ◽  
Vol 51 (3) ◽  
pp. 531-535 ◽  
Author(s):  
R. H. Plaut ◽  
L. W. Johnson
Keyword(s):  
Critical Load ◽  
Elastic Shell ◽  
Material Surface ◽  
Fundamental Vibration ◽  
Uniform Loading ◽  
Concentrated Load ◽  
Shallow Shells ◽  
Simply Supported ◽  
Circular Boundary ◽  
Boundary Part

In Part 1, optimal forms were determined for maximizing the fundamental vibration frequency of a thin, shallow, axisymmetric, elastic shell with given circular boundary. Our objective in this part is to maximize the critical load for buckling under a uniformly distributed load or a concentrated load at the center. Again, the shell form is varied and the material, surface area, and uniform thickness of the shell are specified. Both clamped and simply supported boundary conditions are considered for the case of uniform loading, while one example is presented involving a concentrated load acting on a clamped shell. The optimality condition leads to forms that have zero slope at the boundary if it is clamped. The maximum critical load is sometimes associated with a limit point and sometimes with a bifurcation point. It is often substantially higher than the critical load for the corresponding spherical shell.

Finite Elastic-Plastic Expansion of a Cylindrical Tube

1973 ◽  
Vol 2 (4) ◽  
pp. 216-222
Author(s):  
B. Slevinsky ◽  
J. B. Haddow
Keyword(s):  
Plastic Deformation ◽  
Yield Condition ◽  
Cylindrical Tube ◽  
Flow Rule ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
End Conditions ◽  
Cylindrical Tubes ◽  
Limiting Case ◽  
Plastic Flow Rule

A numerical method for the analysis of the isothermal elastic-plastic expansion, by internal pressure, of cylindrical tubes with various end conditions is presented. The Tresca yield condition and associated plastic flow rule are assumed and both non-hardening and work-hardening tubes are considered with account being taken of finite plastic deformation. Tubes which undergo further plastic deformation on unloading are also considered. Expansion of a cylindrical cavity from zero radius in an infinite medium is considered as a limiting case.

The Resonant Response of a Rectangular Plate With an Elastic Edge Restraint

1972 ◽  
Vol 94 (2) ◽  
pp. 517-525 ◽  
Author(s):  
D. M. Egle
Keyword(s):  
Plate Theory ◽  
Time History ◽  
Resonant Response ◽  
Concentrated Load ◽  
Simply Supported ◽  
Single Term ◽  
Thin Plate Theory ◽  
Wide Range ◽  
Mode Solution ◽  
Elastically Restrained

An analysis of a plate, simply supported on three edges and elastically restrained on the fourth, excited by a concentrated load with a harmonic time history, is used to study the peak resonant response of the plate for several configurations and a wide range of edge restraint. Classical thin plate theory is employed with a complex elastic modulus to account for energy dissipation. An approximate method, based on a single term normal mode solution, is developed for calculating the limits of the peak resonant response for arbitrary edge restraint.

Limits of Economy of Material in Plates

1955 ◽  
Vol 22 (3) ◽  
pp. 372-374
Author(s):  
H. G. Hopkins ◽  
W. Prager
Keyword(s):  
Yield Condition ◽  
Transverse Load ◽  
Constant Thickness ◽  
Flow Rule ◽  
Plate Material ◽  
Uniform Thickness ◽  
Simply Supported ◽  
Varying Thickness ◽  
Limiting Case ◽  
Associated Flow Rule

Abstract The paper is concerned with the limits of economy of material in a simply supported circular plate under a uniformly distributed transverse load. The plate material is supposed to be plastic-rigid and to obey Tresca’s yield condition and the associated flow rule. The criterion of failure adopted is that used in limit analysis. It is shown that the plate of uniform thickness has a weight efficiency of about 82 per cent. Stepped plates of segmentwise constant thickness are discussed, and the plate of continuously varying thickness is treated as the limiting case obtained by letting the number of steps go to infinity.

The Elastic, Plastic Bending of a Simply Supported Plate

1961 ◽  
Vol 28 (3) ◽  
pp. 395-401 ◽  
Author(s):  
G. Eason
Keyword(s):  
Yield Condition ◽  
Constant Load ◽  
Flow Rule ◽  
Plastic Bending ◽  
Simply Supported ◽  
Elastic Plastic ◽  
Tresca Yield Condition ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this paper the problem of the elastic, plastic bending of a circular plate which is simply supported at its edge and carries a constant load over a central circular area is considered. The von Mises yield condition and the associated flow rule are assumed and the material of the plate is assumed to be nonhardening, elastic, perfectly plastic, and compressible. Stress fields are obtained in all cases and a velocity field is presented for the case of point loading. Some numerical results are given comparing the results obtained here with those obtained when the Tresca yield condition is assumed.

On the gravitational displacement of three-dimensional fluid droplets from inclined solid surfaces

1999 ◽  
Vol 395 ◽  
pp. 181-209 ◽  
Author(s):  
P. DIMITRAKOPOULOS ◽  
J. J. L. HIGDON
Keyword(s):  
Optimization Problem ◽  
Numerical Solutions ◽  
Contact Angle Hysteresis ◽  
Normal Component ◽  
Three Dimensional ◽  
Yield Condition ◽  
Contact Angles ◽  
Solid Surfaces ◽  
Wide Range ◽  
Yield Conditions

The yield conditions for the gravitational displacement of three-dimensional fluid droplets from inclined solid surfaces are studied through a series of numerical computations. The study considers both sessile and pendant droplets and includes interfacial forces with constant surface tension. An extensive study is conducted, covering a wide range of Bond numbers Bd, angles of inclination β and advancing and receding contact angles, θA and θR. This study seeks the optimal shape of the contact line which yields the maximum displacing force (or BT ≡ Bd sin β) for which a droplet can adhere to the surface. The yield conditions BT are presented as functions of (Bd or β, θA, Δθ) where Δθ = θA − θR is the contact angle hysteresis. The solution of the optimization problem provides an upper bound for the yield condition for droplets on inclined solid surfaces. Additional contraints based on experimental observations are considered, and their effect on the yield condition is determined. The numerical solutions are based on the spectral boundary element method, incorporating a novel implementation of Newton's method for the determination of equilibrium free surfaces and an optimization algorithm which is combined with the Newton iteration to solve the nonlinear optimization problem. The numerical results are compared with asymptotic theories (Dussan V. & Chow 1983; Dussan V. 1985) and the useful range of these theories is identified. The normal component of the gravitational force BN ≡ Bd cos β was found to have a weak effect on the displacement of sessile droplets and a strong effect on the displacement of pendant droplets, with qualitatively different results for sessile and pendant droplets.

The Finite Beam With a Moving Load

1967 ◽  
Vol 34 (1) ◽  
pp. 111-118 ◽  
Author(s):  
C. R. Steele
Keyword(s):  
Moving Load ◽  
Steady State Solution ◽  
Fourier Integral ◽  
Method Of Images ◽  
Asymptotic Results ◽  
Lateral Velocity ◽  
Concentrated Load ◽  
Simply Supported ◽  
Asymptotic Evaluation ◽  
Limiting Case

A “method of images” series solution is obtained which converges rapidly for a simply supported, long beam with a high-velocity, moving concentrated load. Each term of the series is a Fourier integral solution for an appropriate semi-infinite beam problem. The integrals are evaluated in closed form for the beam without a foundation and have a simple asymptotic evaluation for the beam with an elastic foundation. In particular, the asymptotic results provide a solution for the “critical” load velocity, for which a “steady-state” solution does not exist, and for the limiting case of infinite load velocity, for which the beam is given an initial uniform lateral velocity.

Yield Conditions for Rotationally Symmetric Shells Under Axisymmetric Loading

1960 ◽  
Vol 27 (2) ◽  
pp. 323-331 ◽  
Author(s):  
P. G. Hodge
Keyword(s):  
Yield Surface ◽  
Yield Condition ◽  
Uniform Pressure ◽  
Stress Space ◽  
Reasonable Accuracy ◽  
Spherical Cap ◽  
Axisymmetric Loading ◽  
Tresca Yield Condition ◽  
Rotationally Symmetric ◽  
Yield Conditions

The yield condition for a rotationally symmetric shell may be represented as a surface in a four-dimensional stress space. The exact yield surface according to the Tresca yield condition is compared with various approximations. A new approximation is suggested which combines the advantages of mathematical simplicity and reasonable accuracy. The theory is illustrated with reference to a spherical cap under uniform pressure.

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