scholarly journals ANALYSIS OF COMBINED PLATES WITH ALLOWANCE FOR CONTACT WITH ELASTIC FOUNDATION

2019 ◽  
Vol 15 (4) ◽  
pp. 83-87
Author(s):  
Elena Koreneva
Keyword(s):  
Bessel Functions ◽  
Outer Part ◽  
Internal Boundary ◽  
Constant Thickness ◽  
Thickness Variation ◽  
Ring Plate ◽  
Plate Of Variable Thickness ◽  
Circular Base ◽  
Elastic Basis ◽  
Cylindrical Reservoir

The paper covers the problems of combined plates with circular base and consisting of a few sections with different laws of thickness variation. Analytical methods of analysis of similar structures are not yet devel­oped. The present work suggests the analytical method for solving of the stated problems, the contact with the elas­tic subgrade is also considered. The above-mentioned approach is shown on the example of the analysis of the bot­tom of the cylindrical reservoir, resting on the elastic subgrade. The inner part of this construction is represented by the ring plate of variable thickness which increases along the direction from the internal boundary. The outer part is represented by the ring plate of the constant thickness. The influence of the elastic basis and the upper part of the reservoir is taken into consideration. The solutions for stresses and deflections of the combined plate are given in closed form in terms of Bessel functions. The conditions of the plate’s sections conjugation are fulfilled.

A Levy-Type Solution for a Rectangular Plate of Variable Thickness

1958 ◽  
Vol 25 (2) ◽  
pp. 297-298
Author(s):  
H. D. Conway
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Variable Thickness ◽  
Thickness Variation ◽  
Type Solution ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Arbitrary Boundary Conditions ◽  
Plate Of Variable Thickness

Abstract A solution is given for the bending of a uniformly loaded rectangular plate, simply supported on two opposite edges and having arbitrary boundary conditions on the others. The thickness variation is taken as exponential in order to make the solution tractable, and thus closely approximates to uniform taper if the latter is small.

Buckling of Rectangular Plates With General Variation in Thickness

1973 ◽  
Vol 40 (3) ◽  
pp. 745-751 ◽  
Author(s):  
D. S. Chehil ◽  
S. S. Dua
Keyword(s):  
Rectangular Plate ◽  
Variable Thickness ◽  
Perturbation Technique ◽  
Thickness Variation ◽  
Rectangular Plates ◽  
Bending Vibration ◽  
Simply Supported ◽  
Buckling Stress ◽  
General Variation ◽  
Plate Of Variable Thickness

A perturbation technique is employed to determine the critical buckling stress of a simply supported rectangular plate of variable thickness. The differential equation is derived for a general thickness variation. The problem of bending, vibration, buckling, and that of dynamic stability of a variable thickness plate can be deduced from this equation. The problem of buckling of a rectangular plate with simply supported edges and having general variation in thickness in one direction is considered in detail. The solution is presented in a form such as can be easily adopted for computing critical buckling stress, once the thickness variation is known. The numerical values obtained from the present analysis are in excellent agreement with the published results.

Sensitivity of Non-Uniform Beams in Depositing Mass Process

2006 ◽  
Author(s):  
Dumitru I. Caruntu
Keyword(s):  
Film Thickness ◽  
Relative Density ◽  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Relative Sensitivity ◽  
Constant Thickness ◽  
Thickness Variation ◽  
Slender Beams ◽  
Beam Dimension

This paper deals with the mass deposition influence on the natural frequencies of nonuniform cantilever resonator sensors of linear and parabolic thickness. Resonator sensitivity, defined as fraction of change in frequency per fraction of change in thickness deposition and relative density, was found. A constant thickness mass deposition on all four lateral surfaces of the cantilever of rectangular cross-section was assumed. Euler-Bernoulli theory was used, so only slender beams were considered. Mass deposition on the free end surface of the beams was neglected. The film thickness was considered very small compared to any beam dimension. The film had no contribution to the beam stiffness, only to the mass. Results show that for the same thickness deposition, the sensitivity in the first mode of beams of linear thickness is 2.5 to 3.5 higher when compared to uniform beams. For beams of parabolic thickness variation the relative sensitivity ranges between 1.5 and 2.1.

scholarly journals Solution of nonaxisymmetric stationary problem of heat conductivity for polar-orthotropic ring plate of variable thickness with account of heat transfer with external environment

2020 ◽  
pp. 47-58
Author(s):  
Uladzimir V. Korolevich
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Heat Conductivity ◽  
External Environment ◽  
Stationary Problem ◽  
Constant Thickness ◽  
Stationary Heat ◽  
Annular Plates ◽  
Ring Plate ◽  
Polar Orthotropic

The solution of the nonaxisymmetric stationary problem of the heat conductivity for profiled polar-orthotropic annular plates considering the heat exchange with external environment through the bases is presented. Thermophysical characteristics of the material of the plate are assumed to be temperature-independent. A constant temperature T1∗ is maintained on the inner contour of the ring plate and on the outer contour N equidistant point sources of heat with the same temperature T2∗ each are applied. Plate temperature is higher than ambient temperature T0 (T0 < T1∗ < T2∗). It is assumed that the temperature does not vary in thickness of a thin ring plate. The temperature values on the contours of the annular plate are given. There are no internal heat sources in the plate. The temperature distribution in such plates will be nonaxisymmetric.  Analytical solutions of the stationary heat conductivity problem for the following anisotropic annular plates are presented: the plate of constant thickness, the back conical and the conical plate. The Volterra integral equation of the second kind corresponding to the given differential equation of the stationary heat conductivity for profiled anisotropic annular plates is written to obtain the solution in the general case. The kernels of the integral equation for anisotropic annular plates of power and exponential profiles are given explicitly. The solution of the integral equation is written by using the resolvent. It is indicated that due to the presence of irrational functions in the kernels of the integral equation it is necessary to apply numerical methods in the calculation of iterated kernels or numerically solve the Volterra integral equation of the second kind. A formula for the calculation of temperatures in anisotropic annular plates of an arbitrary profile is given.

scholarly journals METHOD OF COMPENSATING LOADS FOR SOLVING OF A PROBLEM OF UNSYMMETRIC BENDING OF INFINITE ICE SLAB WITH CIRCULAR OPENING

2017 ◽  
Vol 13 (2) ◽  
pp. 50-55
Author(s):  
Elena B. Koreneva
Keyword(s):  
Closed Form ◽  
Bessel Functions ◽  
Infinite Plate ◽  
Constant Thickness ◽  
Circular Opening ◽  
Opening Method

Unsymmetric flexure of an infinite ice slab with circular opening is under examination. The men-tioned construction is considered as an infinite plate of constant thickness resting on an elastic subgrade which properties are described by Winkler’s model. The plate’s thickness is variable in the area ajoining to the opening. Method of compensating loads is used. Basic and compensating solutions are received. The obtained solutions are produced in closed form in terms of Bessel functions.

Axi-Symmetric Buckling of Orthotopic Circular Plates with Variable Thickness

1967 ◽  
Vol 71 (675) ◽  
pp. 218-223 ◽  
Author(s):  
Sharad A. Patel ◽  
Franklin J. Broth
Keyword(s):  
Circular Plate ◽  
Variable Thickness ◽  
Material Properties ◽  
Radial Direction ◽  
Constant Thickness ◽  
Thickness Variation ◽  
Circular Plates ◽  
Plate Edge ◽  
Simply Supported

Axi-symmetric buckling of a circular plate having different material properties in the radial and circumferential directions was analysed in ref. 1. A plate with constant thickness and subjected to a uniform edge compression was considered. The plate edge was assumed clamped or simply-supported. The analysis of ref. 1 is extended to include plates with thickness variation in the radial direction.

scholarly journals Multi-Objective Optimization of Plastics Thermoforming

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1760
Author(s):  
António Gaspar-Cunha ◽  
Paulo Costa ◽  
Wagner de Campos Galuppo ◽  
João Miguel Nóbrega ◽  
Fernando Duarte ◽  
...  
Keyword(s):  
Evolutionary Algorithms ◽  
Thickness Distribution ◽  
Final Part ◽  
Constant Thickness ◽  
Thickness Variation ◽  
Optimization Strategy ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Successive Generations ◽  
Different Thickness

The practical application of a multi-objective optimization strategy based on evolutionary algorithms was proposed to optimize the plastics thermoforming process. For that purpose, in this work, differently from the other works proposed in the literature, the shaping step was considered individually with the aim of optimizing the thickness distribution of the final part originated from sheets characterized by different thickness profiles, such as constant thickness, spline thickness variation in one direction and concentric thickness variation in two directions, while maintaining the temperature constant. As far we know, this is the first work where such a type of approach is proposed. A multi-objective optimization strategy based on Evolutionary Algorithms was applied to the determination of the final part thickness distribution with the aim of demonstrating the validity of the methodology proposed. The results obtained considering three different theoretical initial sheet shapes indicate clearly that the methodology proposed is valid, as it provides solutions with physical meaning and with great potential to be applied in real practice. The different thickness profiles obtained for the optimal Pareto solutions show, in all cases, that that the different profiles along the front are related to the objectives considered. Also, there is a clear improvement in the successive generations of the evolutionary algorithm.

scholarly journals Effects of Intrinsic Layer Thickness on the Short-Circuit Current Density of Crystalline Silicon-Based Solar Cells

2019 ◽  
Vol 2 (2) ◽  
pp. 72
Author(s):  
Imroatus Soleha ◽  
Endhah Purwandari ◽  
Endang Haryati
Keyword(s):  
Solar Cell ◽  
Current Density ◽  
Crystalline Silicon ◽  
Short Circuit ◽  
Electrical Characterization ◽  
Short Circuit Current ◽  
Short Circuit Current Density ◽  
Constant Thickness ◽  
Thickness Variation ◽  
Pure Silicon

The amount of short-circuits current density (Jsc) shown in the results of the electrical characterization of silicon (c:Si)-based solar cell diodes is one of the determinants of device performance. Efforts to increase Jsc are carried out by adding pure silicon to the diode junction, thereby increasing the magnitude of photoelectron generation in the material. In this paper, the insertion of an intrinsic semiconductor at various thicknesses will be analyzed for its effect on the characteristics of the resulting current-voltage density. By using a 2D simulation based on the finite element method, the solution to the equation of a solar cell semiconductor with a p-i-n junction structure becomes the basis for calculating the resulting electric current density. The thickness variation of the simulated layer i ranges from 1 μm to 15 μm, with a constant thickness of p and n layers of 0.4 m. The simulation results show that the reduced thickness of the intrinsic layer has a significant effect on the decrease in short-circuit current density.

Vibration analysis of non-uniform porous beams with functionally graded porosity distribution

2018 ◽  
Vol 233 (8) ◽  
pp. 1678-1697
Author(s):  
M Heshmati ◽  
F Daneshmand
Keyword(s):  
Mathematical Formulation ◽  
Beam Theory ◽  
Considerable Change ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Constant Thickness ◽  
Thickness Variation ◽  
Porosity Distribution ◽  
Piecewise Constant ◽  
Modes Of Vibration

In this paper, the effect of different profile variations on vibrational properties of non-uniform beams made of graded porous materials is studied. Timoshenko beam theory is used to present the mathematical formulation of the problem including shear deformation, rotary inertia, non-uniformity of the cross-section, and graded porosity of the beam material. Three different variations of porosities through the thickness direction are introduced. The beam is assumed with the clamped condition at both ends. To obtain a numerical solution, finite element formulations of the governing equations are presented. The non-uniform beam is approximated by another beam consisting of n elements with piecewise constant thickness to keep the volume and hence the total mass unchanged for each element. The beam response has been calculated for the first three modes of vibration. In each case, the results for different types of thickness variation and porosity distribution are compared with those obtained for a beam with uniform thickness. The effects of non-uniformity, taper parameters, and porosity distribution on the frequencies and mode shapes are investigated. It is observed that a considerable change in frequencies and mode shapes can be achieved by selection of different thickness variation and porosity distribution.

BUCKLING OF CIRCULAR SANDWICH PLATES OF VARIABLE CORE THICKNESS AND FGM FACE SHEETS

2011 ◽  
Vol 11 (02) ◽  
pp. 273-295 ◽  
Author(s):  
S. K. JALALI ◽  
M. H. NAEI ◽  
A. POORSOLHJOUY
Keyword(s):  
Numerical Solutions ◽  
Volume Fraction ◽  
Sheet Thickness ◽  
Functionally Graded ◽  
Constant Thickness ◽  
Thickness Variation ◽  
Sandwich Plates ◽  
Radial Compression ◽  
Core Thickness ◽  
Circular Sandwich Plates

Presented herein is the buckling response of circular sandwich plates with a homogenous core of variable thickness and constant thickness functionally graded material (FGM) face sheets whose material properties are assumed to be graded in the thickness direction according to a simple power law. The plate is modeled using the first order shear deformation plate theory and subjected to a uniform radial compression. In order to determine the distribution of the prebuckling load along the radius, the membrane equation is solved using the shooting method. Subsequently, by employing the pseudospectral method that makes use of Chebyshev polynomials, the stability equations are solved numerically to evaluate the critical buckling load. Numerical solutions are presented for both clamped and simply supported plates and for linear and parabolic core thickness distributions. The results show that the buckling behavior is significantly influenced by the thickness variation profile, the aspect ratio, the volume fraction index, and the core-to-face sheet thickness ratio. Comparison studies demonstrate that the results obtained using the current method compare very well with those available in the literature.

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