Anticlastic Curvature of Elastically Bent Crystals for Sagittal Focusing

1993 ◽  
Vol 307 ◽  
Author(s):  
J. P. Quintana ◽  
V. I. Kushnir ◽  
P. Georgopoulos
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Width Ratio ◽  
Crystal Length ◽  
Poisson Coefficient ◽  
Anticlastic Curvature ◽  
Bent Crystals

ABSTRACTFinite element results are presented for the case of an elastically bent isotropic rectangular crystal with clamped boundary conditions. Results show that the anticlastic curvature can be eliminated in the center of the crystal provided the crystal length to width ratio fits a “golden aspect ratio” which is dependent on the Poisson coefficient ν. For ν=0.262 (appropriate for Si(111)), this ratio is approximately equal to 1.42.

scholarly journals Analysis of Combined Convection in an Open Cavity under Constant Heat Flux Boundary Conditions and Magnetic Field Using Finite Element Method

2014 ◽  
Vol 6 (2) ◽  
pp. 243-256 ◽  
Author(s):  
A. Kalam ◽  
J. H. Munshi ◽  
M. Rahman ◽  
M. M. K. Chowdhury
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Length Change ◽  
Constant Heat Flux ◽  
Open Cavity ◽  
Maximum Temperature ◽  
Fluid Temperature ◽  
Rayleigh Numbers

This study investigated the effects of the aspect ratio of the cavity for average fluid temperature at exit port, average Nusselt number, maximum temperature of the fluid in the domain, drag coefficient, isotherms and streamlines on behalf of different Hartmann numbers and Rayleigh numbers. Solution of governing equations of momentum and energy has been made by finite element technique. Above mentioned parameters such as an aspect ratio which is cavity height to cavity length change from Ar = 0.5 to 2 for different Rayleigh numbers and Hartmann numbers which change from Ra = 103 to 105 and Ha = 0 to 50 respectively. Prandtl number Pr = 7 and Reynolds number Re = 100 is fixed in this simulation. It is found that variation of the aspect ratio makes an important effect for higher values of Rayleigh numbers. Heat transfer enhances with increasing of aspect ratio. Increasing of Hartmann number decreases the heat transfer inside the cavity.  Keywords: Temperature boundary conditions; Open cavity; Aspect ratio; Finite element methods.  © 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.  doi: http://dx.doi.org/10.3329/jsr.v6i2.14505 J. Sci. Res. 6 (2), 243-256 (2014)

Investigation of the vibration and buckling of graphynes: A molecular dynamics-based finite element model

2016 ◽  
Vol 231 (6) ◽  
pp. 1162-1178 ◽  
Author(s):  
Saeed Rouhi ◽  
Tayyeb Pour Reza ◽  
Babak Ramzani ◽  
Saeed Mehran
Keyword(s):  
Molecular Dynamics ◽  
Finite Element ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Finite Element Model ◽  
Molecular Dynamics Simulations ◽  
Element Model ◽  
Side Length ◽  
Aspect Ratios ◽  
Dynamics Simulations

Molecular dynamics simulations are used to investigate the mechanical properties of graphynes. To study the effect of atomic structure and graphyne size on Young’s and bulk modulus, armchair and zigzag nanosheets with different side lengths and aspect ratios are considered. It is observed that at a constant aspect ratio (the ratio of height to side length), variation of side length has no significant effect on Young’s modulus of graphynes. Besides, using the obtained results by molecular dynamics simulations, a finite element model is proposed to study the vibrational and buckling behaviors of graphynes. The effects of different parameters such as nanosheet geometry and boundary conditions on the fundamental natural frequency and critical buckling force of graphynes are explored. It is shown that increasing side length has an inverse effect on the frequency and buckling force. Increasing aspect ratio results in decreasing the frequency. However, this effect reduces for longer sheets. Increasing aspect ratio results in converging the vibration curves associated with graphynes under different boundary conditions. Moreover, by increasing aspect ratio, the sensitivity of buckling force to aspect ratio variation decreases.

scholarly journals The Effect of Various Fiber Orientations and Boundary Conditions on Natural Frequencies of Laminated Composite Beam

2018 ◽  
Vol 7 (3.11) ◽  
pp. 67 ◽  
Author(s):  
M Arif Mat Norman ◽  
M Amiruddin Zainuddin ◽  
Jamaluddin Mahmud
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Composite Beam ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Mode Shapes ◽  
Laminated Composite Beam

This paper investigates the free vibration characteristics of laminate composite beam for various lamination schemes and under various boundary conditions. A beam model with the aspect ratio (length to thickness) of 25 to 150 made of carbon/ epoxy laminates under free vibration were constructed using a commercially available finite element software (ANSYS). The varied parameters are the lamination schemes (cross ply, angle ply and unidirectional ply) and boundary conditions (Clamp-Free (C-F), Clamp-Clamp (C-C), Clamp-Hanger (C-H), Free-Free (F-F) and Hanger-Hanger (H-H) ). For each case, finite element simulations were performed and the natural frequencies were determined. Mode shapes were also analyzed to observe the beam’s deformation behavior. Results showed that increasing aspect ratio will decrease natural frequencies for the first seven mode shapes. In terms of lamination scheme, the unidirectional ply produced the highest frequency (34.26 Hz), followed by cross ply (34.05 Hz) and angle ply (13.60 Hz) at the aspect ratio of 25. In terms of boundary conditions, the Hanger-Hanger boundary condition produced the highest natural frequency (2272.52  Hz) at the aspect ratio of 25, while Clamped-Free boundary condition produced the lowest frequency (2.28 Hz) at the aspect ratio of 150. In general, it can be concluded that the current study is useful and has contributed significant knowledge to better understand of effect of various fiber orientations and boundary conditions on the natural frequencies of laminated composite beam. 

Equilibrium Profile of Modern Belted Radial Ply Tires: Its Determination and Performance Benefits

2013 ◽  
Vol 41 (2) ◽  
pp. 127-151
Author(s):  
Rudolf F. Bauer
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Finite Element Methods ◽  
Mathematical Analysis ◽  
Internal Stresses ◽  
Stress Concentrations ◽  
Equilibrium Profiles ◽  
Equilibrium Profile ◽  
And Performance ◽  
Beneficial Property

ABSTRACT The benefits of a tire's equilibrium profile have been suggested by several authors in the published literature, and mathematical procedures were developed that represented well the behavior of bias ply tires. However, for modern belted radial ply tires, and particularly those with a lower aspect ratio, the tire constructions are much more complicated and pose new problems for a mathematical analysis. Solutions to these problems are presented in this paper, and for a modern radial touring tire the equilibrium profile was calculated together with the mold profile to produce such tires. Some construction modifications were then applied to these tires to render their profiles “nonequilibrium.” Finite element methods were used to analyze for stress concentrations and deformations within all tires that did or did not conform to equilibrium profiles. Finally, tires were built and tested to verify the predictions of these analyses. From the analysis of internal stresses and deformations on inflation and loading and from the actual tire tests, the superior durability of tires with an equilibrium profile was established, and hence it is concluded that an equilibrium profile is a beneficial property of modern belted radial ply tires.

Upon Impact Numerical Modeling of Foam Materials

2017 ◽  
Vol 54 (2) ◽  
pp. 195-202
Author(s):  
Vasile Nastasescu ◽  
Silvia Marzavan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Numerical Analysis ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
General Character ◽  
Foam Material ◽  
Various Boundary Conditions ◽  
Specific Behaviour

The paper presents some theoretical and practical issues, particularly useful to users of numerical methods, especially finite element method for the behaviour modelling of the foam materials. Given the characteristics of specific behaviour of the foam materials, the requirement which has to be taken into consideration is the compression, inclusive impact with bodies more rigid then a foam material, when this is used alone or in combination with other materials in the form of composite laminated with various boundary conditions. The results and conclusions presented in this paper are the results of our investigations in the field and relates to the use of LS-Dyna program, but many observations, findings and conclusions, have a general character, valid for use of any numerical analysis by FEM programs.

scholarly journals Stiffness Estimation and Equivalence of Boundary Conditions in FEM Models

2021 ◽  
Vol 11 (4) ◽  
pp. 1482
Author(s):  
Róbert Huňady ◽  
Pavol Lengvarský ◽  
Peter Pavelka ◽  
Adam Kaľavský ◽  
Jakub Mlotek
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Boundary Conditions ◽  
Model Updating ◽  
Element Model ◽  
Computational Time ◽  
Stiffness Coefficients ◽  
First Case ◽  
Numerical Approaches

The paper deals with methods of equivalence of boundary conditions in finite element models that are based on finite element model updating technique. The proposed methods are based on the determination of the stiffness parameters in the section plate or region, where the boundary condition or the removed part of the model is replaced by the bushing connector. Two methods for determining its elastic properties are described. In the first case, the stiffness coefficients are determined by a series of static finite element analyses that are used to obtain the response of the removed part to the six basic types of loads. The second method is a combination of experimental and numerical approaches. The natural frequencies obtained by the measurement are used in finite element (FE) optimization, in which the response of the model is tuned by changing the stiffness coefficients of the bushing. Both methods provide a good estimate of the stiffness at the region where the model is replaced by an equivalent boundary condition. This increases the accuracy of the numerical model and also saves computational time and capacity due to element reduction.

scholarly journals Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1388
Author(s):  
Daniele Oboe ◽  
Luca Colombo ◽  
Claudio Sbarufatti ◽  
Marco Giglio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Strain Field ◽  
Element Analysis ◽  
Inverse Finite Element Method ◽  
Shape Sensing ◽  
Definition Of ◽  
High Level ◽  
Element Method

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

High length-to-width aspect ratio lead bromide microwires via perovskite-induced local concentration gradient for X-ray detection

CrystEngComm ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 2215-2221
Author(s):  
Emma Dennis ◽  
Soumya Kundu ◽  
Deepak Thrithamarassery Gangadharan ◽  
Jingjun Huang ◽  
Victor M. Burlakov ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Concentration Gradient ◽  
Width Ratio ◽  
Local Concentration ◽  
X Ray ◽  
Lead Bromide ◽  
High Length

Well-oriented PbBr2 microwires with a length-to-width ratio of up to 5000 were grown using a concentration gradient in co-crystallization with perovskite. Planar-integrated microwires showed a response to X-ray photons.

scholarly journals Numerical Solution of Nonlinear Schrödinger Equation with Neumann Boundary Conditions Using Quintic B-Spline Galerkin Method

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 469 ◽  
Author(s):  
Azhar Iqbal ◽  
Nur Nadiah Abd Hamid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Spline Method ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
B Spline

This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank Nicolson and finite difference schemes are applied for nodal parameters and for time integration. Two numerical problems are discussed to demonstrate the accuracy and feasibility of the proposed method. The error norms L 2 , L ∞ and conservation laws I 1 ,   I 2 are calculated to check the accuracy and feasibility of the method. The results of the scheme are compared with previously obtained approximate solutions and are found to be in good agreement.

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