Buckling Behavior of Thick Porous FGM Toroidal Shell Segments Under External Pressure and Elevated Temperature Including Tangential Edge Restraint

Owing to mathematical and geometrical complexities, there is an evident lack of stability analyses of thick closed shell structures with porosity. The present work aims to analyze the effects of porosities, elasticity of edge constraint and surrounding elastic media on the buckling resistance capacity of thick functionally graded material (FGM) toroidal shell segments subjected to external pressure, elevated temperature and the combined action of these loads. The volume fractions of constituents are varied across the thickness according to power law functions and effective properties of the FGM are determined using a modified rule of mixture. The porosities exist in the FGM through even and uneven distributions. Governing equations are based on a higher order shear deformation theory taking into account interactive pressure from surrounding elastic media. These equations are analytically solved and closed-form expressions of buckling loads are derived adopting the two-term form of deflection along with Galerkin method. Parametric studies indicate that the porosities have beneficial and deteriorative influences on the buckling resistance capacity of thermally loaded and pressure loaded porous FGM toroidal shell segments, respectively. Furthermore, tangential constraints of edges lower the buckling resistance capacity of the shells, especially at elevated temperatures.

The generalized stokes integral theorem for a covariant pseudotensor field

Ориентируемые континуумы играют важную роль в микрополярной теории упругости, все реализации которой возможны только в рамках псевдотензорного формализма и представления об ориентируемом многообразии. Особенно это касается теории микрополярных гемитропных упругих сред. В настоящей работе рассматриваются различные формулировки интегральной теоремы Стокса для асимметричного ковариантного пседотензорного поля, заданного веса. Тем самым достигается распространение известной интегральной формулы Стокса на случай псевдотензоров. Последнее обстоятельство позволяет использовать, указанное обобщение для микрополярных континуумов. Исследование существенно опирается на класс специальных координатных систем. Oriented continua play an important role in the micropolar theory of elasticity, all realizations of which are possible only within the framework of the pseudotensor formalism and the orientable manifold concept. This especially concerns the theory of micropolar hemitropic elastic media. In this paper, we consider various formulations of the Stokes integral theorem for an asymmetric covariant pseudotensor field of a given weight. This extends the well-known Stokes integral formula to the case of pseudotensors. The latter circumstance makes it possible to use the manifistated generalization for micropolar continua. The study relies heavily on the class of special coordinate systems.

Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions

We consider a family of variational problems on the equilibrium of a composite Kirchhoff–Love plate containing two flat rectilinear rigid inclusions, which are connected in a hinged manner. It is assumed that both inclusions are delaminated from an elastic matrix, thus forming an interfacial crack between the inclusions and the surrounding elastic media. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual nonpenetration of opposite crack faces. The problems of the family depend on a parameter specifying the coordinate of a connection point of the inclusions. For the considered family of problems, we formulate a new inverse problem of finding unknown coordinates of a hinge joint point. The continuity of solutions of the problems on this parameter is proved. The solvability of this inverse problem has been established. Using a passage to the limit, a qualitative connection between the problems for plates with flat and bulk hinged inclusions is shown.

Monte Carlo simulations of coupled body- and Rayleigh-wave multiple scattering in elastic media

Summary Seismic coda waves are commonly used in estimation of subsurface Q values and monitoring subsurface changes. Coda waves mainly consist of multiply scattered body and surface waves. These two types of waves interact with each other in the multiple scattering process, which thus leads to a spatiotemporal evolution of the body- and surface-wave energies. One cannot characterize the evolution because one has not fully understood the multiple scattering of the two types of waves. Thus one commonly assumes only one type of waves exists or ignores their interaction while studying the coda waves. However, neglecting the interaction leads to an incorrect energy evolution of the two types of waves and consequently biases the Q estimation or interpretation of coda-wave changes for monitoring. To better understand the interaction between these waves during multiple scattering and to model the energy evolution correctly, we propose a Monte Carlo algorithm to model the multiple scattering process. We describe the physics of the scattering for the two types of waves and derive scattering properties like cross sections for perturbations in elastic properties (e.g. density, shear modulus and Lamé parameters). Our algorithm incorporates this knowledge and thus physically models the body- and surface-wave energy evolution in space and time. The energy partitioning ratios between surface and body waves provided by our algorithm match the theoretical prediction based on equipartition theory. In the equipartition state, our simulation results also match Lambert’s cosine law for body waves on the free surface. We discuss how the Rayleigh-to-body-wave scattering affects the energy partitioning ratios. Our algorithm provides a new tool to study multiple scattering and coda waves in elastic media with a free surface.