scholarly journals NON-STATIONARY AXISYMMETRIC PROBLEM OF INVERSE PIEZOEFFECT FOR CIRCULAR BIMORPHOUS PLATE OF STEPPED VARIABLE THICKNESS AND RIGIDITY

2017 ◽  
Vol 19 (6) ◽  
pp. 133-140
Author(s):  
D.A. Shlyakhin
Keyword(s):  
Variable Thickness ◽  
Arbitrary Function ◽  
Axisymmetric Problem ◽  
Elastic System ◽  
Integral Transformation ◽  
Variable Rigidity ◽  
Closed Solution ◽  
Finite Integral Transformation ◽  
Finite Integral ◽  
Deformed State

Non-stationary axisymmetric problem for a thin circular bimorphous plate under the action on the end surfaces of electric potential, which is an arbitrary function of time is viewed. On the basis of the theory of Tymoshenko by method of finite integral transformation a new closed solution for the viewed electricity and elastic system of stepped variable rigidity and thickness is built. The obtained calculated correlations allow to explore the frequency characteristics and stress-deformed state of bimorphous elements.

scholarly journals New finite integral transform for the Laplace equation in an arbitrary domain

2020 ◽  
Vol 3 ◽  
pp. 115-124
Author(s):  
M.G. Berdnyk ◽  
◽  
Keyword(s):  
Analytical Solution ◽  
Laplace Equation ◽  
Integral Transformation ◽  
Boundary Value ◽  
Inverse Transformation ◽  
Maximum Deviation ◽  
Arbitrary Domain ◽  
First Order ◽  
Finite Integral Transformation ◽  
Finite Integral

Reliability, survivability, as well as the optimal operating mode of operation of the supercomputer will depend on the architecture and efficiency of the cooling system of the hot components of the supercomputer. That is why the number of problems, of great theoretical and practical interest, is the problem of studying the temperature fields arising in elements of arbitrary configuration, cooling a supercomputer. To solve this class of heat conduction problems, the method of finite integral transformations turned out to be the most convenient. This article is the first to construct a new finite integral transformation for the Laplace equation in an arbitrary domain bounded by several closed piecewise-smooth contours. An inverse transformation formula is given. Finding the core of the constructed new finite integral transformation by the finite element method in the Galerkin form for simplex first-order elements reduces to solving a system of algebraic equations. To test the operability of the new integral transformation, calculations were carried out of solutions of the boundary value problem for the Laplace equation obtained using the developed new integral transformation and the well-known analytical solution. The results of comparison the calculations of the solution of the Laplace equation are presented. In the case of a square with a side length equal to one and on one side of the square, the temperature is unity, and on the other, the temperature is zero, with a well-known analytical solution and a solution obtained using the new integral transformation. These results were obtained for 228 simplex first-order elements and 135 nodes. The maximum deviation modulo of these solutions is 0,096, the mathematical expectation of deviations is 0,009, and the variance of the type is 0,001. The developed integral transformation makes it possible to obtain a solution to complex boundary value problems of mathematical physics.

scholarly journals Heat Conduction in Hollow Cylinders with Radiation

1964 ◽  
Vol 14 (2) ◽  
pp. 159-164 ◽  
Author(s):  
E. Marchi ◽  
G. Zgrablich
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Hollow Cylinder ◽  
Integral Transformation ◽  
Finite Integral Transformation ◽  
Finite Integral ◽  
Hollow Cylinders ◽  
Radiation Type

AbstractA new finite integral transformation (an extension of those given by Sneddon (1)), whose kernel is given by cylindrical functions, is used to solve the problem of finding the temperature at any point of a hollow cylinder of any height, with boundary conditions of radiation type on the outside and inside surfaces, with independent radiation constants. It is to be noticed that all possible problems on boundary conditions in hollow cylinders can be solved by particularising the method described here.

Dynamic Thermoelastic Analysis of a Slab Using Finite Integral Transformation Method

AIAA Journal ◽  
2010 ◽  
Vol 48 (8) ◽  
pp. 1833-1839 ◽  
Author(s):  
Jianli Ruan ◽  
Xue Feng ◽  
Guobing Zhang ◽  
Yong Wang ◽  
Daining Fang
Keyword(s):  
Integral Transformation ◽  
Transformation Method ◽  
Thermoelastic Analysis ◽  
Finite Integral Transformation ◽  
Finite Integral ◽  
Integral Transformation Method

scholarly journals Asymptotic research of deformations and stresses of the ring that sustains the seam of elliptic bottom and conic shell

2021 ◽  
pp. 153
Author(s):  
B.N. Yakovlev
Keyword(s):  
Elastic System ◽  
Circular Ring ◽  
Arbitrary Load ◽  
Conic Shell ◽  
Deformed State ◽  
Angle Of Rotation

In the paper, we consider stress-deformed state of elastic system that consists of the elliptic bottom, the ring, and the conic shell. The ring is under arbitrary load, which acts in its plane.On the base of the principal differential dependencies of design of the planar circular ring, we obtain the expressions for tensions, momentum, and the angle of rotation of lateral section.

New Analytical Solutions of Buckling Problem of Rotationally-Restrained Rectangular Thin Plates

2019 ◽  
Vol 11 (10) ◽  
pp. 1950101 ◽  
Author(s):  
Salamat Ullah ◽  
Jinghui Zhang ◽  
Yang Zhong
Keyword(s):  
Boundary Conditions ◽  
Integral Transform ◽  
Integral Transformation ◽  
Solution Procedure ◽  
Thin Plates ◽  
Algebraic Equations ◽  
Transform Method ◽  
Linear Algebraic Equations ◽  
Title Problem ◽  
Finite Integral

A double finite sine integral transform method is employed to analyze the buckling problem of rectangular thin plate with rotationally-restrained boundary condition. The method provides more reasonable and theoretical procedure than conventional inverse/semi-inverse methods through eliminating the need to preselect the deflection function. Unlike the methods based on Fourier series, the finite integral transform directly solves the governing equation, which automatically involves the boundary conditions. In the solution procedure, after performing integral transformation the title problem is converted to solve a fully regular infinite system of linear algebraic equations with the unknowns determined by satisfying associated boundary conditions. Then, through some mathematical manipulation the analytical buckling solution is elegantly achieved in a straightforward procedure. Various edge flexibilities are investigated through selecting the rotational fixity factor, including simply supported and clamped edges as limiting situations. Finally, comprehensive analytical results obtained in this paper illuminate the validity of the proposed method by comparing with the existing literature as well as the finite element method using (ABAQUS) software.

scholarly journals Certain multiple integral relations involving multivariable $ H $-function and general polynomials

2001 ◽  
Vol 32 (4) ◽  
pp. 259-269
Author(s):  
O. P. Garg ◽  
Virendra Kumar
Keyword(s):  
Arbitrary Function ◽  
Multiple Integral ◽  
Finite Integral ◽  
Multiple Integrals ◽  
Integral Relations

In this paper, first we obtain a finite integral involving multivariable $ H $-function and general classes of polynomials. Next, with the application of this and a lemma due to Srivastava et al. (1981) we obtain two general multiple integral relations involving the multivariable $ H $-function, general classes of polynomials and two arbitrary function $ f $ and $ g $. Again, by suitably specializing the functions $ f $ and $ g $ occurring in the main integral relations, we have also evaluated multiple integrals which are new and quite general in nature.

scholarly journals Analyzing calculation results of non-stationary axisymmetric thermoelasticity task for a circular isotropic plate

2018 ◽  
Vol 196 ◽  
pp. 01007
Author(s):  
Dmitriy Shlyahin
Keyword(s):  
Temperature Change ◽  
High Speed ◽  
Isotropic Plate ◽  
Integral Transformation ◽  
Adjoint System ◽  
Thin Plates ◽  
Movement Vector ◽  
Calculation Results ◽  
Finite Integral ◽  
Separation Of Variable

The paper releases results of numerical calculation of axisymmetric dynamic thermoelasticity task for a fixed circular isotropic plate in case of temperature change on its front faces (boundary conditions of the 1st type). The calculated ratios are obtained by using the GL-theory of thermoelasticity (classical theory), which determines the dependence of the vector of heat flux on the velocity of change and temperature gradient. The mathematical model of the task in question includes differential equations of axisymmetric motion and thermal conductivity, formulated as regard to the component of the movement vector and the function of temperature change. Not self-adjoint system is investigated independently. For its solution, a mathematical apparatus technique of separation of variable in the form of finite integral transformations is used, that is transformations of Fourier, Hankel and generalized integral transformation (GIT). The constructed calculation ratios give an opportunity to define stress and strain state and character of distribution of a thermal field of rigidly fixed circular plate with arbitrary axially symmetrical temperature external influence. It is shown, that elastic inertial characteristics of a plate influence the law of change of movement over time only while investigating very thin plates at high-speed temperature impact.

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