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1

Eigenvalue approach to two dimensional problem of generalized thermoelasticity for a half - space with body-force

Lahiri A., Das B.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 2

419-437

EN

The theory of generalized thermoelasticity is applied to a two-dimensional problem for a half-space under the action of body forces. The surface is stress free with thermal shock. Double integral transforms (Laplace transform for time variable and Fourier transform for space variable) are used and the resulting equations are written in the form of a vector-matrix differential equation. The solution of the vector-matrix differential equation in the transformed domain are obtained by eigenvalue approach. The inversion of the Laplace transform is carried out numerically by the Bellman method and computations are done by Mathematica software. Finally, numerical computations of the temperature distribution, displacement and stress components are made and represented graphically.

2

A new hybrid finite element approach for three-dimensional elastic problems

Cao C., Qin Q. H., Yu A.

Archives of Mechanics

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2012

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Vol. 64, nr 3

261-261

EN

A new fundamental solution based finite element method (HFS-FEM) is presented for analyzing three-dimensional (3D) elastic problems with body forces in this paper. It begins with deriving formulations of 3D HFS-FEM for elastic problems without body force and then the body force term is handled by means of the method of particular solution and radial basis function approximation. In our analysis, the homogeneous solution is obtained using the proposed HFS-FEM and the particular solution associated with the body force is approximated by radial basis functions. Several standard tests and numerical examples are considered to assess the capability and performance of the proposed method and elements. It is found that, comparing with conventional FEM (ABAQUS), the proposed method can achieve higher accuracy and efficiency when same element meshes are used. It is also found that the elements associated with this method are not very sensitive to mesh distortion and can be employed for problems involving nearly incompressible materials. This new method seems to be promising to deal with problems involving generalized body force, complex geometry, stress concentration and multi-materials.

3

Numerical simulation of electrowetting using electric body force density and surface tension

Sung T. Il

Prace Instytutu Elektrotechniki

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2011

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Z. 252

107-116

EN

The electrowetting is a phenomenon in which the shape of a droplet is deformed by external electric field. The most of electrowetting studies have been presented by researchers from the mechanical viewpoint. In this paper, we present a numerical method to calculate the droplet shape by taking into account the effects of external electric field, surface tension and gravity. The numerical analysis for shape calculation is formulated by using the equilibrium condition of hydrostatical pressure in the coupled system of external electric field and surface tension in the presence of gravity. The model is numerically implemented and coupled using a standard finite element procedure. The proposed method is numerically tested and validated in a shaping problem of water droplet placed above a conductor coated by dielectric material in external electric field. The electrowetting phenomenon was successfully modeled and analyzed by the proposed approach.

PL

Nawilżanie elektryczne polega na tym, że kształt kropli jest odkształcany poprzez zewnętrzne pole elektryczne. Większość prac dotyczących nawilżania elektrycznego została dokonana przez badaczy z mechanicznego punktu widzenia. Artykuł przedstawia numeryczną metodę obliczania kształtu kropli z uwzględnieniem wpływu zewnętrznego pola elektrycznego, naprężenia powierzchniowego i grawitacji. Numeryczna analiza obliczania kształtu wykorzystuje warunki równowagi ciśnienia hydrostatycznego w sprzężonym układzie zewnętrznego pola elektrycznego i naprężenia powierzchniowego w obecności grawitacji. Model jest wdrożony numerycznie i sprawdzony przy użyciu standardowej procedury elementów skończonych.Proponowana metoda jest numerycznie testowana i sprawdzana poprzez problem kropli wody umieszczonej ponad przewodnikiem pokrytym dielektrykiem w zewnętrznym polu magnetycznym. Zjawisko nawilżania elektrycznego jest z powodzeniem modelowane i analizowane przy użyciu proponowanego podejścia do zagadnienia