A Space-Time Adaptive Algorithm to Illustrate the Lack of Collision of a Rigid Disk Falling in an Incompressible Fluid

A space-time adaptive algorithm to solve the motion of a rigid disk in an incompressible Newtonian fluid is presented, which allows collision or quasi-collision processes to be computed with high accuracy. In particular, we recover the theoretical result proven in [M. Hillairet, Lack of collision between solid bodies in a 2D incompressible viscous flow, Comm. Partial Differential Equations 32 2007, 7–9, 1345–1371], that the disk will never touch the boundary of the domain in finite time. Anisotropic, continuous piecewise linear finite elements are used for the space discretization, the Euler scheme for the time discretization. The adaptive criteria are based on a posteriori error estimates for simpler problems.

Anti-Seismic Bracing in a Hollow-Core Slab of Formwork-Free Shaping for The Possibility of Creating a Rigid Disk in a Building Floor Slab

Building codes and regulations for construction in seismic regions of many countries (including Uzbekistan) require that the floors slabs and elements of a building should possess resistance to seismic impacts, have such functions that not only distribute seismic load between the supporting elements of the building (walls, crossbars and frame columns), but also ensure the spatial operation of the building as a result of reliable bracing of these elements. Therefore, floor slabs made of reinforced concrete prefabricated elements must present rigid horizontal diaphragms (disks) that uniformly distribute seismic loads between load-bearing structures. To fulfill the above requirements, the building standards of Uzbekistan KMK 2.01.03-96 “Construction in seismic areas” oblige designers to provide the strength and rigidity of floors slabs of buildings (structures) by installation the anti-seismic bracings in inter-slab joints between the side surfaces of adjacent slabs; between the end supporting sections of slabs and the frame elements or the anti-seismic belts of stone buildings. The same standards require the presence of free lengths of reinforcement bars or concrete inserts at the ends of slabs for connecting floor slabs with each other and with an anti-seismic belt (or a framing beam); these requirements apply to the production of floor slabs using the aggregate-flow technology. An installation of bracing elements for hollow-core slabs of formwork-free shaping with adjacent structures is not provided since the slabs of a set length are fabricated on a production line by cutting a molded monolithic tape on the line. In this regard, hollow-core slabs of formwork-free shaping must have anti-seismic joint units that provide the bearing capacity of building structures of various systems at the stages of their life cycle. Typical solutions of such units for hollow-core slabs of formwork-free shaping have not been developed. An anchor node with a unit in the void at the end section of the slab has been developed for the anti-seismic bracing of a hollow-core floor slab of formwork-free shaping with adjacent building structures (through a seismic belt or a framing beam). For anti-seismic bracing in inter-slab joints between the lateral surfaces of adjacent floor slabs, a constructive solution is proposed for the cross section of a hollow-core slab of formwork-free shaping with a widened lower flange relative to the upper flange to install a reinforced concrete framing beam in the inter-slab joints. This creates a rigid disk in the building floors. Tests for pulling out anchor rods from nodes arranged in voids at the end sections of a hollow-core slab of formwork-free shaping assessed the strength and serviceability of the proposed antiseismic coupling units. The pulling out of the anchor rods in all tested units occurred before the loss of cohesive strength in the contact zone “concrete of the body of anchor unit - concrete of the slab”. The use of hollow-core slabs of formwork-free shaping with a widened lower flange relative to the upper flange greatly simplifies the installation of reinforced concrete framing beams in the inter-slab joints of buildings. A useful model was patented in the Intellectual Property Agency of the Republic of Uzbekistan; a constructive solution was proposed for a hollow-core slab of formwork-free shaping with a widened lower flange relative to the upper flange, application number FAP20180174 with priority date 11/08/2018. The proposed solutions for the anti-seismic ties of a hollow-core slab of formwork-free shaping with a building structure meet the requirements of the building codes of Uzbekistan KMK 2.01.03-96 “Construction in seismic areas” for transforming a floor slab made from prefabricated plates into a continuous beam slab to create a rigid horizontal diaphragm. The arrangement of the proposed anti-seismic connecting units in a hollow-core slab of formwork-free shaping does not change the manufacturing technology of this type of slabs, and allows the creation of a wide range of products for buildings and structures with various architectural, planning and structural solutions that increase the possibilities of housing, civil and industrial construction in seismic areas.