Engineering Transactions, 13, 2, pp. 247-268, 1965

Zastosowanie Metody Kollokacji do Obliczenia Sprężysto-Plastycznych Ugięć Belek o Skrepowanej Przesuwności Podpór

Z. Waszczyszyn


The used collocation method consists in assuming the form of the deflected beam i.g. in assuming the distribution function of the slope ϕ =Aϕ. In addition to the constant A the collocation function has three free parameters which can to be determined from the boundary conditions and two collocation conditions. The first condition is that of agreement between the curvature as computed by exact equations (based on the theory of finite deflections for a beam with strechable axis) and by means of the collocation function assumed. The other collocation condition is that of agreement of the shear forces above the support. The satisfaction of both conditions is called the method of two-point collocation while the satisfaction of the first condition alone is called the method of one-point collocation. A solution for an elastic beam with restricted displacement of the supports is obtained by means of one- and two-point collocation. Confrontation of results shows good agreement with the exact method within 3 much greater range than with the perturbation method [21]. The introduction of a single collocation function facilitates considerably the computation of the elastic-plastic deflection because the assumption of a single function for the entire beam enables to avoid the difficulty of joining the regions of different types of stress distribution. The solution obtained for a rectangular beam made of a perfect elastic-plastic material is illustrated by a numerical example.

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