Treatment of Body-Force Volume Integrals in Bem by Exact Transformation for 2-D Anisotropic Elasticity

SUMMARYA new approach which allows solving the elastic problems by the boundary integral equation (BIE) methods is presented. The solution of the integral equation is presented in the form of Neumann series and in order to accelerate its convergence the Shanks transform was applied in a modified form. Usage of this transform allows essentially the decrease of the number of Neumann series terms for complex geometrical forms of the bodies boundary. The BIE method to the class of problems characterized by mass potential forces (i.e. thermal, gravitational or centrifugal) is applied. The comparison with the known solution for the disturbed flow around a aerofoil shows good agreement. The method is demonstrated through an example of the stress analysis of a centrifugal high-speed compressor working wheel.

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The modified Shanks transform for the solution of elastic problems by boundary integral equation (BIE) method

Antes

Karinski

Yankelevsky

2006

Commun. Numer. Meth. Engng.

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Exact boundary integral transformation of the thermoelastic domain integral in BEM for general 2D anisotropic elasticity

Shiah¹,

Tan²

1999

Computational Mechanics

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In the direct formulation of the boundary element method, body-force and thermal loads manifest themselves as additional volume integral terms in the boundary integral equation. The exact transformation of the volume integral associated with body-force loading into surface ones for two-dimensional elastostatics in general anisotropy, has only very recently been achieved. This paper extends the work to treat two-dimensional thermoelastic problems which, unlike in isotropic elasticity, pose additional complications in the formulation. The success of the exact volume-to-surface integral transformation and its implementation is illustrated with three examples. The present study restores the application of BEM to two-dimensional anisotropic elastostatics as a truly boundary solution technique even when thermal effects are involved.

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A 3D SPH-based entirely Lagrangian meshfree hydroelastic FSI solver for anisotropic composite structures

Khayyer

Shimizu

Gotoh

et al. 2022

Applied Mathematical Modelling

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Treatment of Body-Force Volume Integrals in Bem by Exact Transformation for 2-D Anisotropic Elasticity

Cited by 17 publications

References 11 publications

The modified Shanks transform for the solution of elastic problems by boundary integral equation (BIE) method

The modified Shanks transform for the solution of elastic problems by boundary integral equation (BIE) method

Exact boundary integral transformation of the thermoelastic domain integral in BEM for general 2D anisotropic elasticity

A 3D SPH-based entirely Lagrangian meshfree hydroelastic FSI solver for anisotropic composite structures

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