On the solution of plane boundary-value problems of elasticity in a rectangle

Golovchan, V. T.

doi:10.1007/s10778-006-0061-8

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2015

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“…Golovchan in Ref. [4] proposed an algorithm based on a complex-valued representation of the general solution to the differential equations of the plane problem and on the use of Lagrange polynomials to satisfy the boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Deformation for a Rectangle by a Finite Fourier Transform

Dhaba¹,

Abou-Dina²,

Ghaleb³

2015

j comput theor nanosci

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In this paper, we introduce a simple method to solve a static, plane boundary value problem in elasticity for an isotropic rectangular region. The method depends on finite Fourier transform to transfer the biharmonic equation to a nonhomogeneous ordinary differential equation of the fourth order. Also, by transfering the boundary conditions, one can find the general solution for the nonhomogeneous ordinary differential equation. Finally, the inverse Fourier transfer allows to get the analytical solution for the biharmonic equation. Using expressions for displacements proved by two of the authors [MSA and AFG], one can obtain the displacements for the rectangular domain.

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Section: Introductionmentioning

confidence: 99%