Signorini-Type Problems over Non-Convex Sets for Composite Bodies Contacting by Sharp Edges of Rigid Inclusions

A new type of non-classical 2D contact problem formulated over non-convex admissible sets is proposed. Specifically, we suppose that a composite body in its undeformed state touches a wedge-shaped rigid obstacle at a single contact point. Composite bodies under investigation consist of an elastic matrix and a rigid inclusion. In this case, the displacements on the set, corresponding to a rigid inclusion, have a predetermined structure that describes possible parallel shifts and rotations of the inclusion. The rigid inclusion is located on the external boundary and has the form of a wedge. The presence of the rigid inclusion imposes a new type of non-penetration condition for certain geometrical configurations of the obstacle and the body near the contact point. The sharp-shaped edges of the obstacle effect such sets of admissible displacements that may be non-convex. For the case of a thin rigid inclusion, which is described by a curve and a volume (bulk) rigid inclusion specified in a subdomain, the energy minimization problems are formulated. The solvability of the corresponding boundary value problems is proved, based on analysis of auxiliary minimization problems formulated over convex sets. Qualitative properties of the auxiliary variational problems are revealed; in particular, we have found their equivalent differential formulations. As the most important result of this study, we provide justification for a new type of mathematical model for 2D contact problems for reinforced composite bodies.

Analysis of Embankment Supported by Rigid Inclusions Using Plaxis 3D

A rigid inclusion-supported embankment is used to overcome the problems of soft soils. This system is considered complex due to the various interactions between its elements, namely the embankment body, load transfer platform, geogrid layers, piles, and soft soils. The load transfer mechanism is based on the phenomenon of soil arching, the tension in the geogrid layers, support of the soft soils, and friction between piles and soft soil. In this paper, the first part highlights the behaviour of a rigid inclusion-supported embankment validated by field measurements, and the contribution of rigid inclusions technology to the reduction of settlement and creep settlement. In addition, the effect of geogrid in improving the load efficiency and reducing the settlements is presented. In the second part, a comparison is made between many analytical design methods and a three-dimensional finite element analysis method. The results show the inconsistencies between the analytical methods in calculating the load efficiency and the tension in the geogrid.