Abstract We study how three-dimensional linearized elasticity for thin plates can be approximated by a two-dimensional projection. The classical approach using formal asymptotic expansions in powers of the thickness in the Hellinger-Reissner formulation, only provides error estimates in the H1 norm for the displacements, assuming at least L2 regularity for the applied forces, plus additional re...

In this work we consider bubbles that can form spontaneously when a two-dimensional (2D) crystal is transferred to substrate with gases or liquids trapped at the crystal–substrate interface. The underlying mechanics may be described by thin sheet on an adhesive fluid applying uniform transverse pressure. What makes apparently simple problem complex rich interplay among geometry, interface, elas...

In this article, we review a dual-primal FETI (FETI-DP) method with mortar methods. The mortar matching condition is used as the continuity constraints for the FETI-DP formulation. A Neumann-Dirichlet preconditioner is investigated and it is shown that the condition number of the preconditioned FETI-DP operator for the two-dimensional elliptic problem is bounded by C maxi=1,...,N{(1 + log (Hi/h...

Open-Pit Production Scheduling (OPPS) problem focuses on determining a block sequencing and scheduling to maximize Net Present Value (NPV) of the venture under constraints. The scheduling model is critically sensitive to the economic value volatility of block, block weight, and operational capacity. In order to deal with the OPPS uncertainties, various approaches can be recommended. Robust opti...

The problem of computing numerically the boundary exact control for the system of linear elasticity in 2D is addressed. A numerical method which has been recently proposed in [Stud. Appl. Math. 121 (2008), no. 1, 27–47] is implemented. Two cases are considered: first, a rectangular domain with Dirichlet controls acting on two adjacent edges, and secondly, a circular domain with Neumann controls...

Abstract The discovery of two-dimensional (2D) iron monolayer in graphene pores stimulated experimental and computational material scientists to investigate low-dimensional elemental metals. There have been many advances their synthesis, stability, properties the last few years. Inspired by these advancements, we investigated electronic structure elasticity free-standing monolayers group 10 met...

We consider the plane elasticity problem of two asymmetrical edge cracks emanating from an elliptical hole in two-dimensional decagonal quasicrystals (QCs) under remotely uniform tensile stress. A complex variation method QCs is developed to solve containing defects. The analytical solutions for stress field and intensity factors near crack tip are expressed by using a conformal mapping techniq...