Influences of Elastic Foundations and Material Gradient on the Dynamic Response of Polymer Cylindrical Pipes Patterned by Carbon Nanotube Subjected to Moving Pressures

Composite materials are frequently used in the construction of rail, tunnels, and pipelines as well as in the construction of aircraft, ships, and chemical pipelines. When such structural elements are formed from new-generation composites, such as CNT-reinforced composites, and their interaction with the ground, there is a need to renew the dynamic response calculations under moving pressures and to create new mathematical solution methods during their design. The aim of this study was to analyze the influences of elastic foundations (EFs) and material gradient on the dynamic response of infinitely long carbon nanotube (CNT)-based polymer pipes under combined static and moving pressures. The CNT-based polymer pipes resting on the EFs were exposed to the axial and moving pressures. The uniform and heterogeneous reinforcement distributions of CNTs, which varied linearly throughout the thickness of polymer pipes, were considered. After setting the problem, the fundamental equations derived to find new analytical expressions for dynamic coefficients and critical velocity, which are dynamic characteristics of cylindrical pipes reinforced by the uniform and linear distributions of CNTs, were solved in the framework of the vibration theory. Finally, numerical computations were performed to examine the effects of EFs on the critical parameters depending on the characteristics of the pipes, the speed of moving pressures, the shape of the distribution of CNTs, and the change in volume fractions.

CONTACT PROBLEM FOR ORTHOTROPIC PLATES OF VARIABLE THICKNESS WITH A SPATIALLY INHOMOGENEOUS BASE

В работе приведено численное моделирование пространственной задачи контактного взаимодействия ортотропных плит переменной жесткости с упругими основаниями. Используемая методика расчета пригодна в случае любых известных контактных моделей упругих оснований. В качестве примера приведены численные результаты для пространственно-неоднородных оснований типа упругих слоев постоянной и переменной толщины. Система интегро-дифференциальных уравнений, к которой сводится задача, решается численно, сочетанием методов конечных разностей типа сквозного счета и граничных элементов. Найдены прогибы, изгибающие моменты и распределения контактных давлений прямоугольной плиты переменной жесткости, полностью примыкающей к основанию. Приводится анализ влияния на напряженно-деформированное состояние плиты, изменения ортотропных свойств ее материала и степень неравномерной сжимаемости толщи грунта. Разработанная методика позволяет эффективно моделировать работу плитных фундаментных конструкций, когда необходим учет неоднородности грунтов сжимаемой толщи в пределах габарита зданий или сооружений. The paper presents a numerical simulation of the spatial problem of contact interaction of orthotropic slabs of variable stiffness with elastic foundations. The calculation technique used is suitable for any known contact models of elastic foundations. As an example, numerical results are given for spatially inhomogeneous foundations such as elastic layers of constant and variable thickness. The system of integrodifferential equations, to which the problem is reduced, is solved numerically by a combination of finite difference methods such as end-to-end counting and boundary elements. Deflections, bending moments and contact pressure distributions of a rectangular slab of variable stiffness, completely adjacent to the base, are found. An analysis of the influence on the stress-strain state of the slab of changes in the orthotropic properties of its material and the degree of uneven compressibility of the soil thickness is given. The developed technique makes it possible to effectively simulate the operation of slab foundation structures when it is necessary to take into account the heterogeneity of the soil of the compressible strata within the dimensions of buildings or structures.