Thermal force loading of an orthotropic cylindrical shell made of a deformationally anisotropic material

Объектами рассмотренных исследований послужил частный случай оболочечных конструкций, а именно оболочка вращения - замкнутая круговая цилиндрическая, так как подобные сооружения весьма часто встречаются при проектировании и строительстве промышленных и гражданских объектов, а также в энергетике. Особенностью конструкции исследуемых оболочек являются материалы, из которых они выполнены, обладают анизотропией двоякого характера. Рассмотрена структурная анизотропия материала уровня ортотропии в совокупности с деформационной, появляющейся в зависимости жесткостных и прочностных свойств от вида напряженного состояния. Оболочка загружается внутренним давлением, которое сводится к равномерно распределенной осесимметричной нагрузки. Кроме того, при постановке задачи строительной механики учтено, что конкретные сооружения эксплуатируются не в идеальном стационаром изолированном пространстве, а в среде с изменяющимися температурными параметрами. При этом учтена вероятность проявления температурного перепада между внутренней загруженной поверхностью оболочки и наружной - свободной от силового воздействия. Известно, что в общем случае температурные и силовые поля взаимосвязаны, а распределение температуры в материале конструкции зависит от напряженного состояния, но как показали многочисленные исследования, связанность термомеханической задачи заметно проявляется только в короткий начальный период температурного изменения до возникновения установившегося перепада. Поэтому в представленной статье задача по термосиловому нагружению цилиндрической оболочки рассматривается в несвязанной постановке, когда общую задачу можно разделить на две независимые: строительной механики и термодинамики. Учитывая, что классические теории термомеханики оболочек, выполненных из материалов, обладающих анизотропией двоякого характера, не позволяют получить достаточно надежные результаты, а большинство известных моделей, предназначенных для указанных материалов, обладают серьезными недостатками, здесь использована методика нормированного тензорного пространства напряжений. В статье представлена система дифференциальных уравнений задачи термоупругости цилиндрической оболочки из материалов с усложненными термомеханическими свойствами. Приведены отдельные решения с наиболее характерными результатами расчета напряженно-деформированного состояния оболочки с их анализом. The objects of the considered studies were a special case of shell structures, namely, the shell of rotation - a closed circular cylindrical one, since such structures are very often found in the design and construction of industrial and civil facilities, as well as in the energy sector. A special feature of the design of the studied shells is the materials, which have anisotropy of a twofold nature. The structural anisotropy of the material of the orthotropy level is considered in conjunction with the deformation one, which appears depending on the stiffness and strength properties of the type of stress state. The shell is loaded with internal pressure, which is reduced to a uniformly distributed axisymmetric load. In addition, when setting the problem of construction mechanics, it is taken into account that specific structures are operated not in an ideal stationary isolated space, but in an environment with changing temperature parameters. At the same time, the probability of a temperature difference between the inner loaded surface of the shell and the outer surface - free from force action-is taken into account. It is known that in the general case, the temperature and force fields are interrelated, and the temperature distribution in the material of the structure depends on the stress state, but as numerous studies have shown, the connectivity of the thermomechanical problem is noticeable only in the short initial period of temperature change before the occurrence of a steady drop. Therefore, in the present article, the problem of thermal force loading of a cylindrical shell is considered in an unrelated formulation, when the general problem can be divided into two independent ones: structural mechanics and thermodynamics. Given that the classical theories of thermomechanics of shells made of materials with anisotropy of a twofold nature do not allow us to obtain sufficiently reliable results, and most of the known models designed for these materials have serious drawbacks, the method of normalized tensor stress space is used here. The article presents a system of differential equations for the problem of thermoelasticity of a cylindrical shell made of materials with complicated thermomechanical properties. Separate solutions with the most characteristic results of calculating the stress-strain state of the shell and their analysis are presented.

Application of various uncertainty measures in the problem of critical force searching for orthotropic shell in conditions of the carrying capacity

The questions of measures calculation of events containing uncertain quantities of random, fuzzy and rough nature are considered. The algorithms of determination of measures of events, based on methods of statistical simulation, are proposed. The "chances" of realization an uncertain event - the simultaneous fulfillment of the conditions of the bearing capacity of a cylindrical orthotropic shell compressed by an axial force, which can be presented in a random, fuzzy or rough manner, are investigated. The stochastic uncertainty is given by the distribution density of the random variable. Fuzzy data are defined by the membership function, and rough data are defined by a deterministic upper and lower approximation. Each type of uncertainty is characterized by its own measures: the probability - for the description of the modality - "probably", the possibility - for the description of the modality is "fuzzy", trust - to describe the modality "rough". The paper proposes procedures for calculating the listed measures. Also numerical illustrations of the calculation of modalities as "probably", "fuzzy", "rough" for the analysis of the limit force of carrying capacity in the problem of optimal design of the compressed orthotropic cylindrical shell made of fiberglass in conditions of uncertainty of the problem of geometrical parameters, such as thickness and radius, and description of the corresponding degree of implementation of an uncertain event are shown. Uncertain event is to fulfill the limitations of general and local stability and durability. The results of the calculations are compared with the solution of the problem with deterministic data. The results show the "reaction" of the values of the critical force to the possible presence of uncertain factors in the problem and the degree of uncertainty. Thus, the bearing capacity of the shell decreases significantly more in the presence of factors of random and rough nature in comparison to the fuzzy data.

VIBRATIONS OF A LONGITUDINALLY STIFFENED, LIQUID-FILLED CYLINDRICAL SHELL IN LIQUID

In the paper we study free vibrations of a longitudinally stiffened, viscous liquid-filled orthotropic cylindrical shell in ideal liquid. The Navier – Stokеs linearized equation is used to describe the motion of the internal viscous liquid, the motion of the external liquid is described by a wave equation written in the potential by perturbed velocity. Frequency equation of a longitudinally stiffened orthotropic, viscous liquid-contacting cylindrical shell is obtained on the basis of the Hamilton – Ostrogradsky principle of stationarity of action. Characteristic curves of dependence are constructed.

FORCED VIBRATIONS OF A INHOMOGENEOUS ORTHOTROPIC CYLINDRICAL SHELL STIFFENED WITH A CROSS-SYSTEM OF RIBS IN LIQUID

In the paper we study forced vibrations of an orthotropic cylindrical shell inhomogeneous in thickness and stiffened with a cross-system of ribs in liquid under the action of inner radial pressure pulsating in time. Based on Hamilton – Ostrogradsky variational principle, we construct a system of equations to determine the displacements of the mid-surface points of an orthotropic cylindrical shell inhomogeneous in thickness and stiffened with a cross-system of ribs under dynamical interaction with liquid. Surface loads acting on the cylindrical shell inhomogeneous in thickness and stiffened with a cross-system of ribs as viewed from liquid are determined from the solutions of liquid motion equations written in potentials. Analytic formulas for finding the displacements of the midsurface points of a liquid-contacting orthotropic cylindrical shell inhomogeneous in thickness and stiffened with a cross-system of ribs, were obtained.

Elastoplastic Solution and Limit Load Analysis of Orthotropic Cylindrical Shell Subjected to Internal Pressure

Cylindrical shell structure is widely used in pressure vessels. In this paper, the orthotropic cylindrical shell structure is analyzed based on the theory of elastoplastic mechanics and the Hill48 yield criterion, the elastoplastic limit load expression of the orthotropic cylindrical shell and the corresponding three-dimensional stress formulas at different stages are obtained. The effect of the radius ratio and the yield strength ratio on the elastic limit load and plastic limit load of the cylindrical shell are also discussed. Finally, the orthotropic cylindrical shell structure is simulated by finite element method, the numerical results verify the correctness of the analytical solutions.