TRANSVERSE BENDING AND FREE VIBRATIONS OF ELASTIC ISOTROPIC PLATES IN THE FORM OF ISOSCELES TRIANGLES

2021 ◽  
Vol 98 (6) ◽  
pp. 20-27
Author(s):  
А.V. KOROBKO ◽  
◽  
N.G. KALASHNIKOVA ◽  
Е.G. ABASHIN ◽  
◽  
...  
Keyword(s):  
Form Factor ◽  
Free Vibrations ◽  
Arbitrary Form ◽  
Maximum Deflection ◽  
Isotropic Plates ◽  
Unloaded State ◽  
Theory Of Plates ◽  
Technical Theory ◽  
Hinged Support ◽  
Isosceles Triangles

This paper considers elastic isotropic plates in the form of isosceles triangles with combined boundary conditions (a combination of hinged support and rigid restraint conditions along the sides of the contour). Calculations were performed using FEM to determine the integral physical characteristics in the considered problems F (the maximum deflection of uniformly loaded plates w0 and the fundamental frequency of oscillations in the unloaded state ω). On the basis of the obtained numerical results, approximating functions have been constructed: "maximum deflection - form factor of plates", "basic frequency of oscillations - form factor of plates", the structure of which corresponds to the structure of similar formulas obtained when presenting known exact solutions in the corresponding problems of technical theory of plates in isoperimetric form. Based on the properties of the form factor of plates, these approximating functions limit the whole set of considered integral physical quantities and therefore can be used as reference solutions for the calculation of triangular plates of arbitrary form applying the method of interpolation by form factor (MIFF). We consider an example of calculation of a plate in the form of a rectangular triangle with hinged support of the sides.

scholarly journals Poisson’s Theory for Analysis of Bending of Isotropic and Anisotropic Plates

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
K. Vijayakumar
Keyword(s):  
Boundary Conditions ◽  
Transverse Shear ◽  
Shear Stresses ◽  
Anisotropic Plates ◽  
Root Cause ◽  
Total Potential ◽  
Isotropic Plates ◽  
Theory Of Plates ◽  
Transverse Shear Stresses ◽  
Transverse Stresses

Sixteen-decade-old problem of Poisson-Kirchhoff’s boundary conditions paradox is resolved in the case of isotropic plates through a theory designated as “Poisson’s theory of plates in bending.” It is based on “assuming” zero transverse shear stresses instead of strains. Reactive (statically equivalent) transverse shear stresses are gradients of a function (in place of in-plane displacements as gradients of vertical deflection) so that reactive transverse stresses are independent of material constants in the preliminary solution. Equations governing in-plane displacements are independent of the vertical (transverse) deflection w0(x,y). Coupling of these equations with w0 is the root cause for the boundary conditions paradox. Edge support condition on w0 does not play any role in obtaining in-plane displacements. Normally, solutions to the displacements are obtained from governing equations based on the stationary property of relevant total potential and reactive transverse shear stresses are expressed in terms of these displacements. In the present study, a reverse process in obtaining preliminary solution is adapted in which reactive transverse stresses are determined first and displacements are obtained in terms of these stresses. Equations governing second-order corrections to preliminary solutions of bending of anisotropic plates are derived through application of an iterative method used earlier for the analysis of bending of isotropic plates.

scholarly journals The approximate method of determining the integral physical characteristics in some problems of technical theory of plates

2018 ◽  
Vol 251 ◽  
pp. 04018
Author(s):  
Viktor Korobko ◽  
Natalia Kalashnikova ◽  
Stanislav Shlyakhov
Keyword(s):  
Numerical Experiment ◽  
Approximate Method ◽  
Elementary Function ◽  
Geometric Characteristic ◽  
Theory Of Elasticity ◽  
Free Oscillations ◽  
Integral Characteristics ◽  
Theory Of Plates ◽  
Technical Theory ◽  
Geometric Analogue

The paper considers the dimensionless geometric characteristic R/r (R is the maximum radius of a circle inscribed in a given region, r is the minimum radius of a circle circumscribed around it), which is used as a geometric analogue of integral characteristics in problems of the technical theory of plates and theory of elasticity. By numerical experiment the authors showed that using this characteristic as the only argument made it possible to approximate with one elementary function all the solutions for short plates, which satisfied the condition (0.5 < R/r < 1) in problems of trans-verse bending, free oscillations and stability of plates.

scholarly journals The Nonlinear Instability Modes of Dished Shallow Shells under Circular Line Loads

2011 ◽  
Vol 2011 ◽  
pp. 1-21
Author(s):  
Liu Chang-Jiang ◽  
Zheng Zhou-Lian ◽  
Huang Cong-Bing ◽  
He Xiao-Ting ◽  
Sun Jun-Yi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Shallow Shell ◽  
Nonlinear Instability ◽  
Maximum Deflection ◽  
Shallow Shells ◽  
Instability Modes ◽  
Theory Of Plates ◽  
Circular Line ◽  
Line Loads ◽  
Dished Shallow Shells

This paper investigated the nonlinear stability problem of dished shallow shells under circular line loads. We derived the dimensionless governing differential equations of dished shallow shell under circular line loads according to the nonlinear theory of plates and shells and solved the governing differential equations by combing the free-parameter perturbation method (FPPM) with spline function method (SFM) to analyze the nonlinear instability modes of dished shallow shell under circular line loads. By analyzing the nonlinear instability modes and combining with concrete computational examples, we obtained the variation rules of the maximum deflection area of initial instability with different geometric parameters and loading action positions and discussed the relationship between the initial instability area and the maximum deflection area of initial instability. The results obtained from this paper provide some theoretical basis for engineering design and instability prediction and control of shallow-shell structures.

Miniature MEMS Interface Circuits Using Nanoparticle Conductors and Embedded Components

2011 ◽  
Vol 2011 (DPC) ◽  
pp. 001674-001706
Author(s):  
C. Paul Christensen
Keyword(s):  
Form Factor ◽  
Sensor Nodes ◽  
Smooth Transition ◽  
Arbitrary Form ◽  
Mems Devices ◽  
Interface Circuits ◽  
Communication Interface ◽  
Thermally Conductive ◽  
Cad Cam ◽  
Component Assembly

MEMS devices are typically used in subsystems comprising the MEMS component and the infrastructure required to support it. This infrastructure – signal processing, communication interface, power supply, and system packaging – often determines the size and cost of the subsystem. This paper describes a new approach to fabrication of highly miniaturized electronic circuitry and packaging that is well-suited to interfacing and support of MEMS components. The fabrication process utilizes nanoparticle silver conductors to connect miniature embedded surface-mount components. Interconnect conductors are produced by filling laser-ablated channels with nanoparticle silver pastes that cure at low temperatures. This laser-based approach allows production of very fine line interconnect structures (&lt; 10 micron trace widths), which simplifies conductor routing and reduces layer count. Avoiding subtractive copper processes significantly reduces capital equipment and facilities costs and minimizes waste streams. After interconnection, the component assembly is encapsulated in a thermally conductive epoxy to produce a robust, stackable electronic module. Techniques also have been developed for stacking and interconnection of these circuit modules to form 3D electronic systems of nearly arbitrary form factor. All fabrication processes are CAD/CAM controlled, providing fast adaptability to design change and a smooth transition to production in both small and large volumes. The new fabrication technology has been applied to the challenge of miniaturization of wireless sensor nodes with the goal of constructing complete nodes of sugar-cube size (including an advanced battery). Node form factor can be easily adapted to specific applications.

The effect of temperature on high-resolution TEM image contrast

1995 ◽  
Vol 53 ◽  
pp. 640-641
Author(s):  
T. Geipel ◽  
W. Mader ◽  
P. Pirouz
Keyword(s):  
Form Factor ◽  
Inelastic Scattering ◽  
Accurate Method ◽  
Waller Factor ◽  
Effect Of Temperature ◽  
Specimen Thickness ◽  
Influence Of Temperature ◽  
Debye Waller Factor ◽  
Influence Of Temperature On ◽  
Atomic Form Factor

Temperature affects both elastic and inelastic scattering of electrons in a crystal. The Debye-Waller factor, B, describes the influence of temperature on the elastic scattering of electrons, whereas the imaginary part of the (complex) atomic form factor, fc = fr + ifi, describes the influence of temperature on the inelastic scattering of electrons (i.e. absorption). In HRTEM simulations, two possible ways to include absorption are: (i) an approximate method in which absorption is described by a phenomenological constant, μ, i.e. fi; - μfr, with the real part of the atomic form factor, fr, obtained from Hartree-Fock calculations, (ii) a more accurate method in which the absorptive components, fi of the atomic form factor are explicitly calculated. In this contribution, the inclusion of both the Debye-Waller factor and absorption on HRTEM images of a (Oll)-oriented GaAs crystal are presented (using the EMS software.Fig. 1 shows the the amplitudes and phases of the dominant 111 beams as a function of the specimen thickness, t, for the cases when μ = 0 (i.e. no absorption, solid line) and μ = 0.1 (with absorption, dashed line).

MAGNETIC FORM FACTOR MEASUREMENTS IN CERIUM HEXABORIDE

1982 ◽  
Vol 43 (C7) ◽  
pp. C7-273-C7-278 ◽  
Author(s):  
P. Burlet ◽  
J. X. Boucherle ◽  
J. Rossat-Mignod ◽  
J. W. Cable ◽  
W. C. Koehler ◽  
...  
Keyword(s):  
Form Factor ◽  
Magnetic Form Factor
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