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SUMMARYThe well-known problem of the height limit of a Tresca or von Mises vertical slope of height h, subjected to the action of gravity stems naturally from Limit Analysis theory under the plane strain condition. Although the exact solution to this problem remains unknown, this paper aims to give new precise bounds using both the static and kinematic approaches and an Interior Point optimizer code. The constituent material is a homogeneous isotropic soil of weight per unit volume . It obeys the Tresca or von Mises criterion characterized by C cohesion. We show that the loading parameter to be optimized, h=C, is found to be between 3.767 and 3.782, and ÿnally, using a recent result of Lyamin and Sloan (Int. J. Numer. Meth. Engng. 2002; 55:573), between 3.772 and 3.782. The proposed methods, combined with an Interior Point optimization code, prove that linearizing the problem remains e cient, and both rigorous and global: this point is the main objective of the present paper.

This study is aimed to evaluate the influence of a number of parameters within the context of composite structure optimization. In particular, the nature of the component materials and all of the possible orientations were studied. Problems optimizing elementary plates and structures modeled using finite elements were treated using a genetic algorithm. The results were used to define the relative importance of these parameters and to derive simple design rules that would reliably obtain a high-performance configuration.

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SUMMARYUsing the "nite element method, the static and kinematic methods of limit analysis provide tools to solve many stability problems in mechanics of continuous media. The classic problem of the height limit of a Tresca or Mises vertical slope subjected to the action of gravity stems naturally from this theory in plane strain. Although the exact solution to this problem remains unknown, the present work has produced precise bounds using the static and kinematic approaches conjointly: the height limit is now between 3)760 and 3)786 C/ , being the weight per unit volume and C the soil cohesion. These tests also show that both methods, used on current workstations with industrial optimization codes such as XPRESS or OSL, are capable of solving any plane problem of limit loads in geotechnics or in structural calculus.

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