Vlasov 和 Kerr 地基模型

Acta Mechanica 25, 45--49 (1976)@ by Springer-Verlag 1976

On the Vlasov and Kerr Foundation

Models

By It. Jones and J. Xenophontos, H a w t h o r n, Victoria

With 2 Figures (Received J u n e 2, 1975)

S u m m a r y - Zusammenfassung On the Vlasov and Kerr Foundation Models. By studying the response of a two layered foundation to surface loading, the Kerr foundation model is shown to be identical to a Vlasov foundation model. _As a consequence of the analysis, expressions for the shear and spring constants of the Kerr foundation, are obtained.

Zu den Griindungs-Modellen yon Wlassew und Kerr. Durch Untcrsuchung des Verhaltens einer zweischichtigen Griindung unter Oberfl~chenbelastung wird gezeigt, dab das Kerrschc Modell mit dem yon Wlassow identisch ist. Daraus werden Ausdriicke ftir Schubund Fcderkonstanten des Kerrschen Modelles erhalten. 1. Introduction One of the most advantageous models, which has recently been used for the analysis of an elastic foundation, is the K e r r foundation model[1],[2],[3]. This model is an extension of the usual P a s t e r n a k model and consists of two spring layers, with spring constants c and k respectively, interconnected b y a shear layer with shear constant G (Fig. 1). The response of this foundation when subjected to a continuously distributed surface load p(x, y) is governed b y: 1 -{P -- c W2p= k W - - GIV2w.

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W h e n c= 3k this model is identicle with a similar foundation model proposed b y REISSlgEI~[4]. An alternative extension of the P a s t e r n a k model was suggested b y VLASOV and L:~o~T~v[5],[6]. T h e y considered a two layered foundation assuming t h a t the upper layer is very thin so t h a t its shear interaction is negligable. Being a continuum model the Vlasov model has the a d v a n t a g e t h a t the foundation moduli are expressable in terms of k n o w n functions. U n f o r t u n a t e l y the K e r r and Vlasov models differ. The major a d v a n t a g e of the Kerr model over the Vlasov, and other models (such as the isotropic, elastic continuum, P a s t e r n a k foundation, etc.), is that.

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