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1
Content available An initial stability of plates in various conservative load conditions by the Boundary Element Method
Guminiak M.
Journal of Applied Mathematics and Computational Mechanics
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2015
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Vol. 14, nr 3
25--36
EN
An initial stability of Kirchhoff plates by the Boundary Element Method (BEM) is presented in the paper. A plate is subjected by external in-plane normal and tangential conservative loadings acting in two perpendicular directions. The Betti’s theorem is used to derive the boundary-domain integral equations. The direct version of the Boundary Element Method is presented with combination to simplified boundary conditions. The singular and non-singular approach of the boundary integrals derivation is used.
2
Content available Static analysis of circular and elliptic plates resting on internal flexible supports by the Boundary Element Method
Guminiak M., Szajek K.
Journal of Applied Mathematics and Computational Mechanics
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2014
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Vol. 13, nr 2
21--32
EN
A static analysis of circular and elliptic Kirchhoff plates resting on internal elastic supports by the Boundary Element Method is presented in the paper. Elastic support has the character of Winkler-type elastic foundations. Bilateral and unilateral internal constraints are taken into consideration. The Betti’s theorem is used to derive the boundary domain integral equation. The direct version of the boundary element method is presented and simplified boundary conditions, including curvilinear boundary elements, are introduced. The collocation version of boundary element method with non-singular approach is presented.
3
Content available remote Boundary Integral Equations Formulation for Fractional Order Thermoelasticity
Tiwari R., Mukhopadhyay S.
Computational Methods in Science and Technology
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2014
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Vol. 20, No. 2
49--58
EN
The present work is concerned with the boundary integral equation formulation for the solutions of equations under fractional order thermo elasticity in a three dimensional Euclidean space. A mixed initial-boundary value problem is considered and the fundamental solutions of the corresponding coupled differential equations are obtained in the Laplace transform domain. We employ one reciprocal relation in the present context and formulate the boundary integral equations on the basis of our fundamental solutions.Then the formulation is illustrated with a suitable example.
4
Content available remote Fundamental solutions in the full coupled theory of elasticity for solid with double porosity
Svanadze M., De Cicco S.
Archives of Mechanics
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2013
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Vol. 65, nr 5
367--390
EN
This paper discusses the full coupled linear theory of elasticity for solids with double porosity. The system of the governing equations is based on the equations of motion, conservation of fluid mass, the constitutive equations and Darcy’s law for material with double porosity. Four spatial cases of the dynamical equations are considered: equations of steady vibrations, equations in Laplace transform space, equations of quasi-static and equations of equilibrium. The fundamental solutions of the systems of these partial differential equations (PDEs) are constructed by means of elementary functions and finally, the basic properties of these solutions are established.
5
Selected problems of thin and thick plates theory in terms of BEM. Theoretical foundations and numerical comparison
Guminiak M., Litewka B.
Foundations of Civil and Environmental Engineering
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2012
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No. 15
41--90
EN
A static analysis of Kirchhoff and Reissner plates by the boundary element method has been presented in the paper. The Betti’s theorem has been used to derive the boundary integral equation. The direct version of the boundary element method has been presented.
6
Content available remote Weighted least-squares algorithms of the method of fundamental solutions
Smyrlis Y. S., Karageorghis A.
Vibrations in Physical Systems
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2004
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Vol. 21
339--348
EN
We Study the Method of Fundamental Solutions (MPS) for the solution of certain elliptic boundary value problems. We propose least squares algorithms, when the number of collocation points is larger the number of singularities as well as in "the case in which the number of singularities is larger than the number of collocation points.
7
Content available remote Maysel's formula in the generalized linear micropolar thermoviscoelasticity
El-Karamany A. S.
Archives of Mechanics
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2004
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Vol. 56, nr 5
357-376
EN
Generalizations of Maysel's formula to generalized linear micropolar thermoviscoelasticity is given. Fundamental solutions in the Laplace transform domain are obtained. The results are applicable to the following generalized thermoelasticity theories: Lord-Shulman theory with one relaxation time, Green-Lindsay theory with two relaxation times, Green-Naghdi theory of type III, and the Chandrasekharaiah and Tzou theory with dual-phase lag, as well as to the dynamic coupled theory. The cases of generalized linear micropolar thermoviscoelasticity of the Kelvin-Voigt model, and the generalized linear micropolar thermoelasticity can be obtained from the given results.
8
Content available remote Matrix of fundamental solutions for the coupled parabolic system of partial differential equations
Łazuka J., Szymaniec A.
Biuletyn Wojskowej Akademii Technicznej
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2000
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Vol. 49, nr 1
19-31
EN
The aim of this paper is to construct the matrix of fundamental solutions for linear coupled parabolic system in the three-dilinensional space, consisting of two equations. The matrix of the fundamental solutions has been constructed using the Fourier transform. Basing of the matrix of fundamenal solutions we represent the solution of the Cauchy problem for this system of equations by the convolution type represntation.
PL
Celem pracy jest konstrukcja macierzy rozwiązań podstawowych dla liniowego sprzężonego parabolicznego układu równań w przestrzeni trójwymiarowej zawierającego dwa równania. Macierz rozwiązań podstawowych skonstruowano używając transformacji Fouriera. Bazując na macierzy rozwiązań podstawowych przedstawiono rozwiązanie zagadnienia Cauchy'ego dla takiego układu równań za pomocą splotu z danymi początkowymi.
9
Content available Fundamental matrix of the generalized thermoelastic system
Pyryev Y.A., Mokryk R.I.
Journal of Theoretical and Applied Mechanics
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1998
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nr 4
919-936
EN
The fundamental matrix of the generalised thermoelastic system is constructed with interaction between temperature and displacement fields as well as finite rate of heat propagation taken into account. Components of the considered matrix are represented in terms of Laplace transforms of the corresponding functions. These functions are represented as integrals over the segments which connect singular points of their Laplace transforms. The characteristic properties of these functions are investigated.
PL
Macierz podstawowa uogólnionej teorii termosprężystości została skonstruowana dla oddziaływań temperatury, przemieszczeń oraz propagacji ciepła. Elementy macierzy są przedstawione w formie transformat Laplace'a odpowiednich funkcji. Właściwości charakterystyczne tych funkcji zostały zbadane.
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