Nonlinear Asymmetric Buckling of Truncated Spherical Shells

1970 ◽  
Vol 37 (3) ◽  
pp. 651-660 ◽  
Author(s):  
M. T. Wu ◽  
Shun Cheng
Keyword(s):  
Eigenvalue Problem ◽  
Nonlinear Equations ◽  
Theoretical Study ◽  
Numerical Results ◽  
Equilibrium States ◽  
Geometrical Parameters ◽  
Spherical Shells ◽  
Buckling Loads ◽  
Axisymmetric Equilibrium

This paper is concerned with the theoretical study of buckling of truncated spherical shells. Sander’s nonlinear equations for deep shells are used and the equations of equilibrium are expressed in terms of displacements for spherical shells. Based on these equations, analyses are made for calculating prebuckling axisymmetric equilibrium positions and then examining these equilibrium states for points of bifurcation into asymmetric buckling deformations. An eigenvalue problem is formulated and the buckling loads for truncated spherical shells of different geometrical parameters are obtained numerically. The numerical results for the prebuckling axisymmetric deformations and the points of bifurcation are shown on graphs.

Unsymmetrical Buckling of Thin Shallow Spherical Shells

1964 ◽  
Vol 31 (3) ◽  
pp. 447-457 ◽  
Author(s):  
Nai-Chien Huang
Keyword(s):  
Eigenvalue Problem ◽  
Theoretical Prediction ◽  
Experimental Observation ◽  
Large Range ◽  
Geometrical Parameters ◽  
Spherical Shells

The axisymmetrical snapping of clamped shallow spherical shells has been studied by many authors. There is found to be a discrepancy between the experimental observation of the buckling pressure and their theoretical prediction. In this paper, a study is made of the buckling pressure based on the initiation of unsymmetrical deflection. An eigenvalue problem is formulated and the buckling pressures for shells of a large range of geometrical parameters are obtained numerically. The present work reduces the gap between experiment and theory.

THEORETICAL STUDY OF THE EFFECT OF GEOMETRICAL PARAMETERS AND LOCATION OF ROTOR IMPACT ELEMENTS OF AN IMPACT-CENTRIFUGAL GRINDER ON SPEED AND ANGLES OF CRUSHED PARTICLES FLIGHT

2020 ◽  
Keyword(s):  
Granulometric Composition ◽  
Theoretical Study ◽  
Process Efficiency ◽  
Geometrical Parameters ◽  
Grinding Process ◽  
Main Work ◽  
Impact Element ◽  
The Impact ◽  
Positive Effect ◽  
Efficiency Indicators

One of efficiency indicators of grain grinders is grain granulometric composition. The basis of mixed fodder is crushed grain, the particles of which must have a leveled granulometric composition for subsequent mixing and obtaining a high-quality feed mixture. In agricultural production, hammer crushers are widely used, in which the destruction of grain occurs due to the impact of a hinged hammer. The main disadvantage of these crushers is that not the entire surface of the hammers is involved in grinding, thus reduces grinding process efficiency. A slightly different principle of material destruction is laid down in the basis of the proposed design of the shock-centrifugal grinder. Main work is performed by flat impact elements located on the rotor, which serve to accelerate crushed particles with subsequent impact of them on the bump elements. An important step in the design of new constructions of shock-centrifugal grinders is to determine size and location of the impact elements on the rotor, without which the grinding process is not possible. In the calculation method presented, the dependencies for determining the velocities and angles of a single particle flight from the surface of a flat impact element for its specified dimensions are proposed. Two variants of an impact element location on the rotor are considered and analyzed: radial and at an angle in the direction of rotor rotation. As a result of research carried out, it is noted that in the case of inclined position of an impact element on the rotor an increase in flight speed and flight angles change in crushed particles, which gives the opportunity to have a positive effect on grinding process.

The Bending, Buckling, and Flexural Vibration of Simply Supported Polygonal Plates by Point-Matching

1961 ◽  
Vol 28 (2) ◽  
pp. 288-291 ◽  
Author(s):  
H. D. Conway
Keyword(s):  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Flexural Vibration ◽  
Frequency Equation ◽  
Numerical Results ◽  
Special Technique ◽  
Point Matching ◽  
Buckling Loads ◽  
Simply Supported ◽  
Flexural Vibrations

The bending by uniform lateral loading, buckling by two-dimensional hydrostatic pressure, and the flexural vibrations of simply supported polygonal plates are investigated. The method of meeting the boundary conditions at discrete points, together with the Marcus membrane analog [1], is found to be very advantageous. Numerical examples include the calculation of the deflections and moments, and buckling loads of triangular square, and hexagonal plates. A special technique is then given, whereby the boundary conditions are exactly satisfied along one edge, and an example of the buckling of an isosceles, right-angled triangle plate is analyzed. Finally, the frequency equation for the flexural vibrations of simply supported polygonal plates is shown to be the same as that for buckling under hydrostatic pressure, and numerical results can be written by analogy. All numerical results agree well with the exact solutions, where the latter are known.

A Theoretical Study of Substituted Stepwise Fluorinated Cyclopropanone Keto-Enol System

2003 ◽  
Vol 58 (12) ◽  
pp. 749-755
Author(s):  
Abdullah El-Alali ◽  
Ali A. Marashdeh ◽  
Salim M. Khalil
Keyword(s):  
Theoretical Study ◽  
Dipole Moments ◽  
Heats Of Formation ◽  
Geometrical Parameters ◽  
Free Energies ◽  
Isodesmic Reactions ◽  
Orbital Energies ◽  
Substantial Concentration ◽  
Homo Lumo ◽  
Complete Optimization

MINDO-Forces calculations have been performed with complete optimization of the geometries on stepwise fluorinated cyclopropanones and their enols. Increase in the number of fluorine atoms causes destabilization of cyclopropanone. Perfluorinated enol was found to be present in substantial concentration, as was mentioned in previous work. This is supported by calculations of Gibbs free energies and isodesmic reactions. Geometrical parameters, heats of formation, electron densities, dipole moments and orbital energies (HOMO-LUMO) are reported.

scholarly journals Non-linear buckling analysis of functionally graded shallow spherical shells

2009 ◽  
Vol 31 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Dao Huy Bich
Keyword(s):  
External Pressure ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Governing Equations ◽  
Spherical Shells ◽  
Buckling Loads ◽  
Linear Buckling ◽  
Non Linear ◽  
Linear Buckling Analysis

In the present paper the non-linear buckling analysis of functionally graded spherical shells subjected to external pressure is investigated. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. In the formulation of governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. Using Bubnov-Galerkin's method to solve the problem an approximated analytical expression of non-linear buckling loads of functionally graded spherical shells is obtained, that allows easily to investigate stability behaviors of the shell.

scholarly journals Nonlinear thermo-mechanical stability of shear deformable FGM sandwich shallow spherical shells with tangential edge constraints

2017 ◽  
Vol 39 (4) ◽  
pp. 351-364
Author(s):  
Nguyen Minh Khoa ◽  
Hoang Van Tung
Keyword(s):  
Mechanical Stability ◽  
Effective Properties ◽  
Geometrical Nonlinearity ◽  
Geometrical Parameters ◽  
Boundary Edge ◽  
Power Law Distribution ◽  
Spherical Shells ◽  
Nonlinear Load ◽  
Elastic Foundations ◽  
Thermal Environments

This paper presents an analytical approach to investigate the nonlinear axisymmetric response of moderately thick FGM sandwich shallow spherical shells resting on elastic foundations, exposed to thermal environments and subjected to uniform external pressure. Material properties are assumed to be temperature independent, and effective properties of FGM layer are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Formulations are based on first-order shear deformation shell theory taking geometrical nonlinearity, initial geometrical imperfection, Pasternak type elastic foundations and various degree of tangential constraint of boundary edge into consideration. Approximate solutions are assumed to satisfy clamped boundary condition and Galerkin method is applied to derive closed-form expressions of critical buckling loads and nonlinear load-deflection relation. Effects of geometrical parameters, thickness of face sheets, foundation stiffness, imperfection, thermal environments and degree of tangential edge constraints on the nonlinear stability of FGM sandwich shallow spherical shells are analyzed and discussed. 

scholarly journals An efficient three-term conjugate gradient-type algorithm for monotone nonlinear equations

2020 ◽  
Author(s):  
Jamilu Sabi'u ◽  
Abdullah Shah
Keyword(s):  
Global Convergence ◽  
Nonlinear Equations ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Numerical Results ◽  
Search Direction ◽  
Projection Technique ◽  
Type Algorithm ◽  
Gradient Type

In this article, we proposed two Conjugate Gradient (CG) parameters using the modified Dai-{L}iao condition and the descent three-term CG search direction. Both parameters are incorporated with the projection technique for solving large-scale monotone nonlinear equations. Using the Lipschitz and monotone assumptions, the global convergence of methods has been proved. Finally, numerical results are provided to illustrate the robustness of the proposed methods.

Size-Dependent Geometrically Nonlinear Forced Vibration Analysis of Functionally Graded First-Order Shear Deformable Microplates

2016 ◽  
Vol 32 (5) ◽  
pp. 539-554 ◽  
Author(s):  
R. Ansari ◽  
R. Gholami ◽  
A. Shahabodini
Keyword(s):  
Size Effect ◽  
Nonlinear Equations ◽  
Forced Vibration ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Continuation Method ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Governing Equations ◽  
First Order

AbstractIn this paper, a non-classical plate model capturing the size effect is developed to study the forced vibration of functionally graded (FG) microplates subjected to a harmonic excitation transverse force. To this, the modified couple stress theory (MCST) is incorporated into the first-order shear deformation plate theory (FSDPT) to account for the size effect through one length scale parameter, only. Strong form of nonlinear governing equations and associated boundary conditions are obtained using Hamilton's principle. The solution process is implemented on two domains. The generalized differential quadrature (GDQ) method is first employed to discretize the governing equations on the space domain. A Galerkin-based scheme is then applied to extract a reduced set of the nonlinear equations of Duffing-type. On the second domain, through a time differentiation matrix operator, the set of ordinary differential equations are transformed into the discrete form on time domain. Eventually, a system of the parameterized nonlinear equations is acquired and solved via the pseudo-arc length continuation method. The frequency response curve of the microplate is sketched and the effects of various material and geometrical parameters on it are evaluated.

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