1887

n Journal of the South African Institution of Civil Engineers - The numerical solution of the biharmonic plate-bending equation on an irregular mesh by the finite difference method : technical paper

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Abstract

This paper proposes an extension to the classical method of finite differences for the analysis of thin plates, bending in conformance with the so-called Kirchhoff assumptions, to allow for irregular mesh intervals. By the arbitrary variation of grid sizes, the analysis of any shape of plate with a wide variety of boundary conditions becomes possible. The subject is simplified if the biharmonic plate equation is considered in terms of two Poisson equations. The irregular mesh is handled by the determination of approximations to the derivatives of the function describing the deflection in terms of the values of the function at discrete points on the plate by using Taylor series. It is found that these Taylor expansions correspond to a certain second-degree polynomial approximation. Only uniformly distributed loads are considered and the paper is illustrated with the results of appropriate examples.

Hierdie verhandeling stel 'n uitbreiding van die tradisionele metode van eindigverskille vir die analise van dun plate in buiging volgens die sogenaamde Kirchhoff-aannames voor, om ook vir die geval van 'n onreelmatige rooster voorsiening te maak. Deur die roostergrootte willekeurig te verander, is dit moontlik om enige vorm van plaat met 'n wye verskeidenheid randvoorwaardes te ontleed. Die onderwerp word vergemaklik indien die biharmoniese vergelyking in terme van twee Poisson-vergelykings beskou word. Die onreelmatige rooster word hanteer deur benaderings tot die afgeleides van die defleksiefunksie in terme van die waardes van die funksie by diskrete punte op die plaat te skryf met behulp van Taylorreekse. Daar word gevind dat hierdie Taylorreeksbenadering ooreenkom met 'n sekere tweedegraadse polinoompassing. Slegs gelykverspreide las word beskou, en die stuk word geillustreer met behulp van die resultate van toepaslike voorbeelde.

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/content/civileng1/35/2/EJC26709
1993-01-01
2016-12-07
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