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 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 Longitudinal waves in an elastic rod caused by sudden damage to the foundation

2021 ◽  
pp. 1-1
Author(s):  
Ivan Shatskyi ◽  
Vasyl Perepichka ◽  
Maksym Vaskovskyi
Keyword(s):  
Gordon Equation ◽  
Integral Transformation ◽  
Initial Boundary ◽  
Transformation Method ◽  
Elastic Rod ◽  
Longitudinal Waves ◽  
Initial Boundary Problem ◽  
Klein Gordon ◽  
Integral Transformation Method ◽  
Thin Elastic Layer

We study the problem of propagating longitudinal waves in an elastic rod connected to a locally damaged foundation through a thin elastic layer. The motion of the rigid foundation blocks is considered predetermined. We formulated the initial-boundary problem for the Klein-Gordon equation with a discontinuous right-hand side. The nonstationary fields of displacements, velocities, and deformations were investigated by the Laplace integral transformation method. Examples of sudden divergence of fragments of the foundation by a given value and their mutual separation at a constant speed are considered.

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.

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.

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