Mathematical model of deformation of orthotropic reinforced shells of revolution

Abstract

In recent years there are more and more structures made of composite materials, especially in the form of thin-walled shells, being applied in various fields of technology. When using composite materials such as concrete or fiberglass, reinforcing elements are often placed along the axes of the curvilinear coordinate system of the shell, and in this case, the structure can be considered as orthotropic. There are a lot of papers on the calculation of orthotropic shells, but they do not adequately investigate a number of important factors that influence the stress-strain state of the shell and its stability. In particular, the calculation of reinforced shells does not take into account such factors as in-plane shear, shear and torsional stiffness of ribs, etc. The paper presents the mathematical model of deformation of thin orthotropic shells of revolution, based on the model of Timoshenko – Reissner. The model takes into account the design of reinforcement with the shear and torsional stiffness of the ribs, geometric nonlinearity and also the irregular shape of the shell. Possibility of application of methods and algorithms which are used in the study of isotropic shells is shown. The presented model investigates the stress-strain state and stability of thin orthotropic reinforced shells of revolution more adequate

Strength and stability of geometrically nonlinear orthotropic shell structures

“…xy xy xz x yz y 12 1 2 Functionality of total potential energy of deformation [44] is written as follows: …”

Stress–Strain State of Flexible Orthotropic Cylindrical Shells with a Reinforced Circular Hole

“…Therefore, the development of a theory that describes the SSS of shells with reinforced holes involves difficulties associated with the necessity of describing the combined action of components with different dimensionality and satisfying the interface conditions [4,7]. Note that the same difficulties are encountered in studying the SSS of ribbed shells [3,6,12,17].…”

“…Therefore, the development of a theory that describes the SSS of shells with reinforced holes involves difficulties associated with the necessity of describing the combined action of components with different dimensionality and satisfying the interface conditions [4,7]. Note that the same difficulties are encountered in studying the SSS of ribbed shells [3,6,12,17].Most results on stress concentration in isotropic and anisotropic shells with reinforced holes were obtained by solving linear elastic problems with analytic, variational, and numerical methods and are reviewed in [4,7,11,16].Much fewer studies are concerned with nonlinear boundary-value problems of stress concentration, but mainly for shells of revolution under an axisymmetric load [4, 10, 13].Very few publications report on solution of nonlinear two-dimensional problems for shells with reinforced holes. For example, the effect of plastic strains and finite deflections on the SSS of isotropic shells with a reinforced curved hole was analyzed in [7,20].…”

“…Such an approach to the design of ribbed shells was proposed in [1] in the late 1960s. Later, a similar approach was used to develop a geometrically nonlinear theory of shallow and deep shells of discretely variable thickness [2,3].…”

Асимптотический Анализ Решения Нелинейной Задачи Нестационарной Теплопроводности Слоистых Анизотропных Неоднородных Оболочек При Граничных Условиях Первого Рода На Лицевых Поверхностях

“…Допустимость полученного решения задачи тепло-проводности в практических расчетах на прочность можно обосновать еще и тем, что в инженерной практике, как правило, используются приближенные теории изгиба оболочек и пластин (Кирхгофа Лява, Тимошенко Рейснера и др. [20][21][22]), которые дают приемлемую точность лишь на некотором уда-лении от кромок тонкостенных конструкций, т. е. за пределами пограничных слоёв и локальных эффектов, распространяющихся в глубину конструкции на расстояние порядка её толщины [20,21].…”