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Erschienen in:
2010 | OriginalPaper | Buchkapitel
4. Optimal Design of Beams and Plates with Uncertainties
verfasst von : N. V. Banichuk, Pekka Neittaanmäki
Erschienen in: Structural Optimization with Uncertainties
Verlag: Springer Netherlands
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Abstract
The equilibrium state of a simply supported beam of length l, situated in the x − y plane, with its axis lying on the x-axis and loaded by exterior distributed load q(x) parallel to the y axis, is given by the following system of equations and boundary conditions 4.1 $$\frac{\mathit{dM}} {\mathit{dx}} = Q,\ \frac{\mathit{dQ}} {\mathit{dx}} = -q,$$ 4.2$$M(0) = M\left (l\right ) = 0,$$ where M = M(x) and Q = Q(x) denote, respectively, bending moment and shear load acting on the cross section of the beam, perpendicular to the x-axis. The beam has a rectangular cross-sectional area of width b and height h.