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.

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.

scholarly journals Theoretical prediction by DFT and experimental observation of heterocation-doping effects on hydrogen adsorption and migration over the CeO2(111) surface

2021 ◽  
Author(s):  
Kota Murakami ◽  
Yuta Mizutani ◽  
Hiroshi Sampei ◽  
Atsushi Ishikawa ◽  
Yuta Tanaka ◽  
...  
Keyword(s):  
Theoretical Prediction ◽  
Experimental Observation ◽  
Ionic Radius ◽  
Hydrogen Adsorption ◽  
Strong Binding ◽  
Doping Effects ◽  
Small Ionic Radius ◽  
And Migration

The addition of dopants with a small ionic radius led to strong binding of H atoms, and the balance of H+ reactivity (mobility) and H+ coverage was fundamentally important for high H+ conductivity and catalysis involving surface protonics.

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. 

Dynamic Buckling of Shallow Spherical Shells

1973 ◽  
Vol 40 (2) ◽  
pp. 411-416 ◽  
Author(s):  
R. E. Ball ◽  
J. A. Burt
Keyword(s):  
Computer Program ◽  
Dynamic Analysis ◽  
Digital Computer ◽  
Large Range ◽  
Dynamic Buckling ◽  
Geometrically Nonlinear ◽  
Shells Of Revolution ◽  
Spherical Shells ◽  
Static And Dynamic Analysis ◽  
Nonlinear Static

The dynamic behavior of clamped shallow spherical shells subjected to axisymmetric and nearly axisymmetric step-pressure loads is examined using a digital computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution. A criterion for dynamic buckling under the nearly axisymmetric load is proposed and critical buckling pressures are determined for a large range of shell sizes.

Nonlinear Dynamic Response and Active Control of Piezoelastic Laminated Shallow Spherical Shells with Damage

2011 ◽  
Vol 21 (6) ◽  
pp. 783-809 ◽  
Author(s):  
Mao Yiqi ◽  
Fu Yiming ◽  
Tian Yanping
Keyword(s):  
Dynamic Response ◽  
Spherical Shell ◽  
Vibration Control ◽  
Analytical Model ◽  
Constitutive Relations ◽  
Collocation Point ◽  
Shallow Spherical Shell ◽  
Geometrical Parameters ◽  
Orthogonal Collocation ◽  
Spherical Shells

Based on Talreja’s damage model with tensor valued internal state variables and geometric nonlinear theory, the constitutive relations for a moderately thick shallow spherical shell with damage are derived. The distribution of electric potential along the thickness direction in the piezoelectric layer is simulated by a sinusoidal function, and accordingly the dynamic analytical model for the cross-ply laminated moderately thick piezoelectric shallow spherical shell is established. Using the negative velocity feedback control algorithm, an analytical model for active vibration control of the piezoelectric laminated moderately thick piezoelectric shallow spherical shell is built when the damage effect is considered. And the solutions to the whole problem are obtained with synthetical utilization of the orthogonal collocation point method and the Newark method. In numerical examples, the effects of damage, piezoelectric effect, and the structure’s geometrical parameters on the dynamic response and vibration control of the piezoelastic laminated shallow spherical shells with damage are investigated.

Design of Large-Range XY Compliant Parallel Manipulators Based on Parasitic Motion Compensation

2013 ◽  
Author(s):  
Guangbo Hao ◽  
Qiaoling Meng ◽  
Yangmin Li
Keyword(s):  
Large Range ◽  
Coupling Effect ◽  
Parallel Manipulators ◽  
Geometrical Parameters ◽  
Element Analysis ◽  
Parasitic Motion ◽  
Prior Art ◽  
Characteristics Analysis ◽  
Optimization Function ◽  
Cross Axis

This paper presents a large-range decoupled XY compliant parallel manipulator (CPM) with good dynamics (no under-constrained/non-controllable mass). The present XY CPM is composed of novel parallelogram flexure modules (NPFMs) that are parallel four-bar mechanisms as prismatic (P) joints with four identical monolithic cross-spring flexural pivots, flexure revolute (R) joints. The parasitic translation of the NPFM is compensated via the rotational centre shift of the flexure R joint thereof based on the prior art. The optimization function and optimised geometrical parameters are investigated for the NPFM at first to achieve the largest translation. The design of a large-range XY CPM is then implemented according to the fully symmetrical 4-PP parallel kinematic mechanism (PKM) and through using the optimised NPFMs. Finally, the simplified analytical stiffness modelling and finite element analysis (FEA) are undertaken for the static and/or dynamic characteristics analysis of the 4-PP XY CPM. It is shown from FEA in the example case that the present 4-PP XY CPM has good performance characteristics such as large-range motion space (10 mm × 10 mm with the total dimension of 465 mm× 465 mm), no non-controllable mass, monolithic configuration, maximal kinematostatic decoupling (cross-axis coupling effect less than 1.2%), maximal actuator isolation (input coupling effect less than 0.13%) and well-constrained parasitic rotation (less than 0.4 urad). In addition, the stiffness-enhanced NPFM using over-constraint is proposed to produce a first/second modal frequency of about 100 Hz for the resulting XY CPM.

Water Jump Reorientation: From Theoretical Prediction to Experimental Observation

2011 ◽  
Vol 45 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Damien Laage ◽  
Guillaume Stirnemann ◽  
Fabio Sterpone ◽  
James T. Hynes
Keyword(s):  
Theoretical Prediction ◽  
Experimental Observation
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