A hybrid-mixed ANS four-node shell element by using the sampling surfaces (SaS) technique is developed. The SaS formulation is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to introduce the displacements of these surfaces as basic shell variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree In − 1 in the thickness direction for each layer permits the presentation of the layered shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that allows one to minimize uniformly the error due to the Lagrange interpolation. To implement the efficient analytical integration throughout the element, the enhanced ANS method is employed. The proposed hybrid-mixed four-node shell element is based on the Hu-Washizu variational equation and exhibits a superior performance in the case of coarse meshes. It could be useful for the 3D stress analysis of thick and thin doubly-curved shells since the SaS formulation gives the possibility to obtain numerical solutions with a prescribed accuracy, which asymptotically approach the exact solutions of elasticity as the number of SaS tends to infinity.

This paper focuses on a finite element implementation of the sampling surfaces (SaS) method for the three-dimensional (3D) stress analysis of functionally graded (FG) laminated elastic and electroelastic shells. The SaS formulation is based on choosing inside the nth layer n I not equally spaced SaS parallel to the middle surface of the shell in order to introduce the electric potentials and displacements of these surfaces as basic shell variables. Such choice of unknowns permits the presentation of the proposed FG shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that improves the convergence of the SaS method significantly. KeywordsFunctionally graded material; laminated piezoelectric shell; sampling surfaces method, exact geometry solid-shell element.

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Disruption of the adhesion of reinforcement to concrete causes significant deformation of the structure, which can subsequently lead to the loss of its bearing capacity. There is a need to study the bonding process between concrete and reinforcement under various influences. The results of a numerical experiment on pulling out reinforcement of periodic profile from concrete are presented. A mathematical model to study the processes taking place in the field of embedding reinforcement in concrete has been built. The results of numerical modeling are described.

Recently, waterproofing systems made of PVC membranes, used in the construction of high-rise buildings with a developed underground part, have gained great popularity. Due to the considerable depth and magnitude of static loads at the foundation level, the complete replacement of such waterproofing with standard methods in case of its damage is practically impossible. To avoid this situation, a multi-layer PVC waterproofing membrane system with a geotextile middle layer was created. To repair such a system it is supposed to inject a polymer composition into it through special tubes, which after curing restores the waterproofness of the membranes. The article presents the results of an experimental assessment of the maintainability of the described waterproofing system. It was proved that the injection of the repair composition into the middle geotextile layer is possible even with external static pressure on the membranes of 146 t/m2. At the same time, the high resistance of PVC membranes to the long-term action of a significant static load and repair composition was found, and the durability of a waterproofing system, predicted from the point of the thermal-fluctuation theory of the destruction of solids, under operating conditions for shear was about 50 years.