About applicability of the winkler model for contact interaction of cylindrical elastoplastic shells with an elastic filler at external pressure

Представлено сравнение результатов расчетов контактного взаимодействия и потери устойчивости упругопластических цилиндрических оболочек с упругим толстостенным заполнителем, выполненных на основе двух подходов: с позиций механики сплошных сред и теории оболочек типа Тимошенко с основанием Винклера. Оба подхода позволяют решать задачи деформирования и устойчивости непологих оболочек с учетом геометрических нелинейностей. Постановка с позиций механики сплошных сред позволяет аппроксимировать оболочку по толщине рядом слоев конечных элементов. Определяющие соотношения формулируются в переменных Лагранжа с использованием в качестве отсчетной неподвижной декартовой или цилиндрической системы координат. Кинематические соотношения записываются в метрике текущего состояния. Упругопластические свойства оболочек описываются теорией пластического течения с изотропным упрочнением. Уравнения движения следуют из баланса виртуальных мощностей работ. В первом подходе контактное взаимодействие оболочки и упругого тела моделируется условиями непроникания по нормали и свободного проскальзывания вдоль касательной. Во втором подходе контактное взаимодействие упругого заполнителя с оболочкой моделируется основанием Винклера. Оба подхода позволяют описать нелинейное докритическое деформирование оболочек вращения с упругим заполнителем, определить предельные (критические) нагрузки в широком диапазоне скоростей нагружения с учетом геометрических несовершенств формы. Оценивается область применимости гипотезы Винклера при контактном взаимодействии оболочки с упругой средой в зависимости от жесткости и толщины основания. Comparison of the results of calculations of contact interaction and loss of stability of elastoplastic cylindrical shells with an elastic thick-walled filler, performed on the basis of two approaches: from the standpoint of continuum mechanics and the theory of Timoshenko-type shells with a Winkler base is presented. Both approaches allow solving the problems of deformation and stability of non-sloping shells, taking into account geometric nonlinearities. The statement from the perspective of continuum mechanics makes it possible to approximate the shell in thickness by a number of layers of finite elements. The constitutive relations are formulated in Lagrange variables using a fixed Cartesian or cylindrical coordinate system as a reference. Kinematic relations are recorded in the metric of the current state. The elastic-plastic properties of shells are described by the theory of plastic flow with isotropic hardening. The equations of motion follow from the balance of the virtual powers of the jobs. In the first approach, the contact interaction of a shell and an elastic body is modeled by the conditions of nonpenetration along the normal and free slip along the tangent. In the second approach, the contact interaction of the elastic filler with the shell is modeled by the Winkler base. Both approaches allow one to describe the nonlinear subcritical deformation of shells of revolution with an elastic filler, to determine the limiting (critical) loads in a wide range of loading rates, taking into account the geometric imperfections of the shape. The area of applicability of the Winkler hypothesis is estimated for the contact interaction of a shell with an elastic medium, depending on the stiffness and thickness of the base.

Effect of ElasticFiller on Pollutant Removal in Each Compartment of ABR

This study was aimed to explore the effect of elastic filler on pollutant removal in each compartment of anaerobic baffled reactor (ABR), ABR with elastic filler, and ABR without elastic filler were compared. The result showed that elastic filler increased the removal rate of chemical oxygen demand (COD) and suspended solid (SS) in the first compartment, decreased the removal rate of COD and SS in the second and third compartments, and had little effect on the removal rate of COD and SS in the fourth compartment. Elastic filler increased the increase rate of ammonia nitrogen in the first and second compartments, decreased the increase rate of ammonia nitrogen in the third and fourth compartments; elastic filler had little effect on the nitrate nitrogen, nitrite nitrogen, total nitrogen and total phosphorus in each compartment of ABR. In general, elastic filler could improve the removal rate of COD and SS of ABR but had little effect on the increase rate of ammonia nitrogen, the removal rate of nitrate nitrogen, nitrite nitrogen, total nitrogen and total phosphorus. Elastic filler slightly increased the concentration of formic acid, acetic acid, propionic acid, and butyric acid in the first compartment of ABR, and slightly decreased the sum of formic acid and acetic acid in the second, hird and fourth compartments. Elastic filler did not change the composition of dissolved organic matter (DOM)in each compartment of ABR, but changed the kinds and contents of aromatic proteins, soluble microbial products and humic acids in each compartment of ABR. Elastic filler had little effect on ABR in the removal of aromatic proteins, but they could improve the removal rate of soluble microbial products and humicacids. Elastic filler slightly increased the degree of DOM humification (or maturity) in ABR effluent, but did not change the main source of humus like substance and DOM in ABR effluent.

USING LARGE-TONNAGE INDUSTRIAL WASTE TO CREATE BITUMEN COMPOSITES WITH IMPROVED FATIGUE LIFE

With the goal of searching effective methods of industrial wastes recycling, filler systems for bituminous binders in road building have been proposed. For the first time in the world, the product of recycled tire rubbers, which is an active powder of discretely devulcanized type of rubber in addition to waste of sulfur produced in technological processes of oil refining, natural gas, etc., have been tested in order to improve the quality of bitumen binders. The rheological properties and fatigue life of the sulfur-bitumen binder have been investigated according to the linear amplitude sweep test (LAS) by using a Smart Pave dynamic shear rheometer (Physica MCR series, Anton Paar, Austria). A technique for preparing samples of sulfur-containing binders has been developed based on the results of photomicrographs analysis obtained by optical microscopy. It has been done to study their fatigue cracking resistance. The analysis of the influence of sulfur and elastic filler on fatigue life has showed that the rise of the quantity of cycles up to fatigue damage of binder samples by the factor of 3-5 (strain of 5% and 2.5%) is due to crumb rubber concentration. The addition of sulfur to ternary systems bitumen/sulfur/elastic filler enables saving energy resources as a result of the possibility of manufacturing sulfur-extended asphalt at lower temperatures.