Engineering Transactions,
19, 2, pp. 333–341, 1971
Tarcza Kwadratowa Obciążona na Konturze Siłami Skupionymi
This paper contains the solution for an elastic and isotropic square disk loaded by a system of m condensed forces Pk = Xk + iYk acting on the points tk = xk + iyk on the edge of the disk.
The solution is based on the book by L. Martini [3], containing a development of the method of N. I. Muschelishvili [4] for the basic biharmonic problem with discontinuous boundary conditions.
Obtaining of the solution – that it, the Goursat’s function φ (ζ) and ψ(ζ) – formulae (1.1) and (3.15) – involves calculation of the coefficients aj according to the formulae (3.8) and hj according to the formulae (3.14). These coefficients depend on the loading forces Pk and mapped on a unit circle of the points of their application pk.
The transformation of points of the unit circle to a square proceeds according to formula (2.10).
The solution is based on the book by L. Martini [3], containing a development of the method of N. I. Muschelishvili [4] for the basic biharmonic problem with discontinuous boundary conditions.
Obtaining of the solution – that it, the Goursat’s function φ (ζ) and ψ(ζ) – formulae (1.1) and (3.15) – involves calculation of the coefficients aj according to the formulae (3.8) and hj according to the formulae (3.14). These coefficients depend on the loading forces Pk and mapped on a unit circle of the points of their application pk.
The transformation of points of the unit circle to a square proceeds according to formula (2.10).
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References
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L. MARTINI, Płaskie zagadnienie teorii sprężystości, PWN, Warszawa 1957.
H. И. Мусхелйшвияи, Некоторые основные задачи математической теории упругости, Наука, Москва 1966.
W. I. SMIRNOW, Matematyka wyższa, 3, cz. 2, PWN, Warszawa 1967.