The Generalized Conforming Element (GCE) — Theory and Applications

1997 ◽  
Vol 1 (1) ◽  
pp. 63-70 ◽  
Author(s):  
Yuqiu Long ◽  
Zhifei Long ◽  
Yin Xu
Keyword(s):  
Weighted Residual Method ◽  
Energy Principle ◽  
Structural Problems ◽  
Combined Application ◽  
Plate And Shell ◽  
Continuous Problems ◽  
Refined Meshes ◽  
Generalized Conforming Element ◽  
Coarse Meshes ◽  
Limiting Case

The concept of generalized conforming elements and their applications to membrane, plate and shell problems are introduced in this paper. The generalized conforming element method proposed by the first author in 1987 provides a simple and efficient means to deal with structural problems, especially the C1 continuous problems. In the first part of this paper, the theoretical basis of GCE is presented. GCE is a limiting-conforming element which is non-conforming in coarse meshes but tends to be conforming in the limiting case of refined meshes. It is formulated based on the modified potential energy principle and the concept of generalized compatibility conditions. It is a new way to construct the finite elements — combined application of the energy method and the weighted residual method. In the second part of this paper, various models of GCE are illustrated. A series of generalized conforming elements with excellent performance have been constructed, that is, thin and thick plate bending GCE, membrane GCE with drilling freedoms and thin shell GCE.

scholarly journals On The Vibration of a Cracked Rotating Blade

1998 ◽  
Vol 5 (5-6) ◽  
pp. 317-323 ◽  
Author(s):  
Ming-Chuan Wu ◽  
Shyh-Chin Huang
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Weighted Residual Method ◽  
Energy Principle ◽  
Discrete Equations ◽  
Rotating Blade ◽  
On Line ◽  
Released Energy ◽  
Blade Frequency

The dynamic behavior of a rotating blade containing a transverse crack was investigated. First, the local flexibility of the cracked blade was obtained by using the method of the released energy. An energy principle, in conjunction with a weighted residual method, was then applied to yield the discrete equations of motion. The equations of motion were further utilized to study the influences of the crack depth and location on the bending natural frequencies under various of rotation speeds. The numerical calculation showed that the crack effects the natural frequencies and the response appreciably only if it is relatively deep and locates near the root of the blade. However, the effects increase exponentially with the depth increases. In addition to the natural frequencies, the displacement responses of the blade with a crack under a constant lateral forces were discussed as well. This was done by calculating the deflections at the tip of the blade for various crack depths and locations. Similar to the rotation speed of the blade frequency, the deflection was offset by the increase of the rotation. However, the centrifugal effects increased significantly such that the crack’s effects became relatively insignificant. Nevertheless, the study showed that the changes on the natural frequency and the tip-deflection of the blade due to a crack may be used as indices for on-line detection of cracks.

MHD Natural Convective Flow in an Isosceles Triangular Cavity Filled with Porous Medium due to Uniform/Non-Uniform Heated Side Walls

2015 ◽  
Vol 70 (11) ◽  
pp. 919-928 ◽  
Author(s):  
Tariq Javed ◽  
Muhammad Arshad Siddiqui ◽  
Ziafat Mehmood ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Nusselt Number ◽  
Bottom Wall ◽  
Physical Parameters ◽  
Uniform Heating ◽  
Weighted Residual Method ◽  
Flow And Heat Transfer ◽  
Side Walls ◽  
Limiting Case

AbstractIn this article, numerical simulations are carried out for fluid flow and heat transfer through natural convection in an isosceles triangular cavity under the effects of uniform magnetic field. The cavity is of cold bottom wall and uniformly/non-uniformly heated side walls and is filled with isotropic porous medium. The governing Navier Stoke's equations are subjected to Penalty finite element method to eliminate pressure term and Galerkin weighted residual method is applied to obtain the solution of the reduced equations for different ranges of the physical parameters. The results are verified as grid independent and comparison is made as a limiting case with the results available in literature, and it is shown that the developed code is highly accurate. Computations are presented in terms of streamlines, isotherms, local Nusselt number and average Nusselt number through graphs and tables. It is observed that, for the case of uniform heating side walls, strength of circulation of streamlines gets increased when Rayleigh number is increased above critical value, but increase in Hartmann number decreases strength of streamlines circulations. For non-uniform heating case, it is noticed that heat transfer rate is maximum at corners of bottom wall.

Nonlinear Instability Modeling of a Nonlocal Strain Gradient Functionally Graded Capacitive Nano-Bridge in Thermal Environment

2018 ◽  
Vol 10 (08) ◽  
pp. 1850083 ◽  
Author(s):  
Ilgar Jafarsadeghi-Pournaki ◽  
Ghader Rezazadeh ◽  
Rasool Shabani
Keyword(s):  
Strain Gradient ◽  
Thermal Environment ◽  
Electrostatic Force ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Weighted Residual Method ◽  
Energy Principle ◽  
Nonlocal Strain Gradient

This paper develops a theoretical model directed towards investigation of the static pull-in instability of a functionally graded (FG) electrostatically actuated nano-bridge via nonlocal strain gradient theory (NLSGT) of elasticity and Euler–Bernoulli beam theory in thermal environment. The nano-beam is under the influence of electrostatic and van der Waals (vdW) forces. In addition to the nonlinear nature of the electrostatic force, the other type of nonlinearity namely geometric nonlinearity resulting from the mid-plane stretching is considered. Material properties of FG nano-beam are assumed to vary gradually along the thickness direction according to simple power-law form. With the purpose of eliminating the coupling between the stretching and bending due to the asymmetrical material variation along the thickness, a new surface reference is introduced. The nonlinear integro-differential governing equation is derived utilizing minimum total potential energy principle, linearized by means of the step-by-step linearization method (SSLM) and solved by Galerkin-based weighted residual method. The numerical investigations are performed while the emphasis is placed on studying the effect of various parameters including: nonlocal parameter, material characteristic length scale, material gradient index, thermal effect and intermolecular force on the static pull-in instability of FG nano-beam. To establish the validity of the present formulation, a comparison is conducted with experimental and numerical results reported in previous studies.

Encultured minds, not error reduction minds

2020 ◽  
Vol 43 ◽  
Author(s):  
Robert Mirski ◽  
Mark H. Bickhard ◽  
David Eck ◽  
Arkadiusz Gut
Keyword(s):  
Free Energy ◽  
Error Reduction ◽  
Energy Principle ◽  
Free Energy Principle ◽  
Current Article

Abstract There are serious theoretical problems with the free-energy principle model, which are shown in the current article. We discuss the proposed model's inability to account for culturally emergent normativities, and point out the foundational issues that we claim this inability stems from.

Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

1983 ◽  
Vol 41 ◽  
pp. 646-647
Author(s):  
Joseph A. Zasadzinski
Keyword(s):  
Liquid Crystalline ◽  
Freeze Fracture ◽  
Continuum Theory ◽  
Closed Surfaces ◽  
Straight Line ◽  
Low Weight ◽  
Concentric Spheres ◽  
Membrane Geometry ◽  
Dupin Cyclides ◽  
Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

Suppression of γ’ Precipitation in a Laser-Melted Nickel-Base Alloy

1977 ◽  
Vol 35 ◽  
pp. 270-271
Author(s):  
J. M. Walsh ◽  
J. C. Whittles ◽  
B. H. Kear ◽  
E. M. Breinan
Keyword(s):  
Cooling Rate ◽  
Base Alloy ◽  
Material Surface ◽  
Intimate Contact ◽  
Absorbed Power ◽  
Perfect Contact ◽  
Nickel Base ◽  
Rapidly Solidified ◽  
Limiting Case ◽  
The Heat Transfer Coefficient

Conventionally cast γ’ precipitation hardened nickel-base superalloys possess well-defined dendritic structures and normally exhibit pronounced segregation. Splat quenched, or rapidly solidified alloys, on the other hand, show little or no evidence for phase decomposition and markedly reduced segregation. In what follows, it is shown that comparable results have been obtained in superalloys processed by the LASERGLAZE™ method.In laser glazing, a sharply focused laser beam is traversed across the material surface at a rate that induces surface localized melting, while avoiding significant surface vaporization. Under these conditions, computations of the average cooling rate can be made with confidence, since intimate contact between the melt and the self-substrate ensures that the heat transfer coefficient is reproducibly constant (h=∞ for perfect contact) in contrast to the variable h characteristic of splat quenching. Results of such computations for pure nickel are presented in Fig. 1, which shows that there is a maximum cooling rate for a given absorbed power density, corresponding to the limiting case in which melt depth approaches zero.

Cartesian Fingerprints in Beckett's Imagination Dead Imagine

2012 ◽  
Vol 21 (2) ◽  
pp. 223-243
Author(s):  
Irit Degani-Raz
Keyword(s):  
The Self ◽  
Levels Of Abstraction ◽  
The Media ◽  
The Mind ◽  
Limiting Case

The idea that Beckett investigates in his works the limits of the media he uses has been widely discussed. In this article I examine the fiction Imagination Dead Imagine as a limiting case in Beckett's exploration of limits at large and the limits of the media he uses in particular. Imagination Dead Imagine is shown to be the self-reflexive act of an artist who imaginatively explores the limits of that ultimate medium – the artist's imagination itself. My central aim is to show that various types of structural homologies (at several levels of abstraction) can be discerned between this poetic exploration of the limits of imagination and Cartesian thought. The homologies indicated here transcend what might be termed as ‘Cartesian typical topics’ (such as the mind-body dualism, the cogito, rationalism versus empiricism, etc.). The most important homologies that are indicated here are those existing between the role of imagination in Descartes' thought - an issue that until only a few decades ago was quite neglected, even by Cartesian scholars - and Beckett's perception of imagination. I suggest the use of these homologies as a tool for tracing possible sources of inspiration for Beckett's Imagination Dead Imagine.

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