Transverse Isotropic Layer Research Articles

Specified models in the problems of the deformation of multilayer plates on a rigid foundations

The analysis and estimation of the stress-strain state (SSS) of multilayered plates on a rigid foundation under the action of stationary transverse loading is an urgent task. As its includes the calculations of strength and deformability of various homogeneous and multilayer coatings. This is the calculation of pavement on relatively rigid bridge structures, or on a non-deformable underlying layer, protective multilayer coatings of flat elements of structures of greater rigidity than roofing, parts and more. Combining materials with isotropic and transversely isotropic physical characteristics into a multilayer package allows you to create multifunctional structures. The SSS of such structures, due to their structural heterogeneity and relatively low transverse stiffness of the individual layers, is significantly associated with the influence of transverse shear deformations and transverse compression deformations. Therefore, the problem of refined modeling of SSS plates, which would take into account these types of deformations, is urgent. Based on the decomposition of the SSS plate into flexural and unflexuralcomponents, it is proposed to optimize the design scheme of deformation of a rectangular multilayer plate on a rigid foundation. The essence of optimization is to consider such a calculation scheme of the plate, in which the SSS of the plate would be fully described by only one component, namely the unflexural component of SSS. To do this, instead of the actual design of the multilayer plate, which is deformed without separation from the foundation, it is proposed to consider the design scheme of the plate, which is formed by symmetrical completion relative to the contact surface of the plate with the foundation. In this case, the plate will be bilaterally symmetrically loaded relative to the middle surface of the plate, and the thickness of the plate will double. SSS plate will be unflexural, which greatly simplifies its modeling. For unflexural SSS, a two-dimensional, high-degree iterative approximation, but three-dimensional models of deformation of multilayer rectangular plate on a rigid foundation with isotropic and transverse-isotropic layers are constructed in an elastic formulation.That models takes full account deformationof transverseshearand transverse compression at transverse loading of a plate. By solving the test problems of deformation of isotropic and transversely isotropic plates on a rigid foundation with sliding and rigid contact with the foundation, and comparing the solutions with the exact three-dimensional solutions of these problems obtained by known methods, the accuracy of the proposed refined models is estimated.The limits of admissible parameters of elastic characteristics of transversely isotropic plates for application of the offered models are established.

ДОСЛІДЖЕННЯ ДЕФОРМУВАННЯ БАГАТОШАРОВОЇ ТРАНСВЕРСАЛЬНО-ІЗОТРОПНОЇ ПЛИТИ НА ЖОРСТКІЙ ОСНОВІ ЗА БЕЗЗГИНОВОЮ УТОЧНЕНОЮ КОНТИНУАЛЬНОЮ МОДЕЛЛЮ

The high-precision estimation of the stress-strain state (SSS) of multilayered plates on a rigid foundation under the action of stationary transverse loading is an urgent task. As its includes the calculations of strength and deformability of various homogeneous and multilayer coatings. This is the calculation of road surface on relatively rigid bridge structures, or on a non-deformable underlying layer or calculation protective multilayer coatings of flat structural elements of greater rigidity than coatings, etc. The combining of materials with isotropic and transversal-isotropic physical characteristics into a multilayer package allows creating of the multifunctional designs. The SSS of such structures due to their structural heterogeneity and the relatively low transverse stiffness of the individual layers is significantly associated with the effect of transverse shear deformations and transverse compression deformations. Therefore, the problem of refined modelling of SSS of plates, which takes into account these types of deformations, is an urgent one. Based on the decomposition the SSS of plate into the flexural and unflexural components, it is proposed to optimize the design diagram of deformation a rectangular multilayer plate on a rigid foundation. The essence of optimization is to consider such a design diagram of the plate, in which the SSS of plate would be fully described by only one component, namely the unflexural component of SSS. To do this, instead of the actual design of the multilayer plate, which is deformed without separation from the foundation, it is suggested to consider the design diagram of the plate, which is formed by supplementing it with a symmetric one about the contact surface of the foundation. In this case, the plate will be symmetrically loaded with respect to the middle surface of the plate, and the thickness of the plate will double. The SSS of plate will be unflexural, which greatly simplifies its modeling. For unflexural SSS, a twodimensional and high-degree iterative approximation but three-dimensional by the nature reflection of SSS, model of deformation of multilayer rectangular plates on a rigid foundation with isotropic and transverse-isotropic layers is constructed in an elastic formulation. This model takes full account deformations of transverse shear and of transverse compression at transverse loading of a plate. Calculations of homogeneous and two-layer transverse-isotropic plates on a rigid foundation under the action evenly distributed and localized transverse loads on the surface of a plate are performed by the finite difference method.

A spectral global matrix method for modelling the response of a fluid-loaded multilayered cylindrical shell excited by an acoustic plane wave

This paper proposes a numerically stable method for modelling a fluid-loaded multilayered cylindrical shell excited by a plane wave, which solves the fd instability problem that is usually observed when using the well-known transfer matrix method (TMM). In the considered modelling, each layer can be either a viscoelastic coating described by a general three-dimensional (3D) elasticity model or an intermediate perfect fluid layer. The transfer matrix of each layer relating the state vector at the layer's two interfaces is estimated with an appropriate standard method. Instead of multiplying together the layer transfer matrices in order to deduce the transfer matrix of the multilayer cylinder, we propose an alternative approach. This one consists in writing the continuity relations at each interface of the considered systems and in building a global matrix that can be solved to obtain the system response. As shown by numerical applications on typical naval test cases, the proposed global matrix assembly procedure as opposed to the classical TMM provides numerical stability over both a wide range of axial wavenumbers and circumferential orders, but also the ability to consider intermediate fluid layers. Besides, this model is well-suited to describe elastic solid layers of any anisotropy as illustrated by an additional case considering a transverse isotropic layer.

Quantitative analysis of rock stress heterogeneity: Implications for the seismogenesis of fluid-injection-induced seismicity

We compared elastic-rock heterogeneity measured by borehole logging to the occurrence of seismic events caused by hydraulic fracturing of the corresponding rock sections. Our observations made from two hydraulic fracturing case studies suggest that elastic-rock heterogeneity controls the occurrence of fluid-injection-induced seismicity. The seismic events occurred preferentially in rock sections characterized by low Poisson’s ratio and high Young’s modulus. Based on analytic solutions of stress fluctuations in elastically heterogeneous media in equilibrium to a homogeneous far-field stress, we quantified the relation between elastic-rock heterogeneity and stress changes leading to fracture opening and reactivation in two end member models of 1D and 3D heterogeneity. We found that significant fluctuations of rock stress originated from elastic rock heterogeneity. Moreover, we found that stress changes leading to fracture opening and reactivation in rocks undergo scale invariance spatial fluctuations. This gave a possible physical explanation for the observed scale invariance of seismogenic processes. We analyzed the physical meaning of a heterogeneity index of rocks, which indicated rock sections of high Young’s modulus and low Poisson’s ratio. We found that this index can be used to identify rock sections of high differential stress. In addition, our results suggest that it is related to the occurrence probability of brittle rock failure during hydraulic fracturing. Nevertheless, we found that fluctuations of Poisson’s ratio showed an even stronger correlation to critical stress changes which resulted in opening and reactivation of fractures in rocks. We obtained an analytic solution of stress fluctuations in vertical transverse isotropic layers such as shale deposits and applied it to a hydraulic fracturing case study of a shale gas reservoir. Also in this case, we observed strong relations between seismicity and fluctuations of stress in space.

Surface wave propagation in a transversely isotropic elastic layer overlying a liquid saturated porous solid half-space and lying under the uniform layer of liquid

Dispersion of Rayleigh-type surface wave is studied in a homogeneous transversely isotropic elastic layer overlying a nondissipative liquid-saturated porous solid half-space and lying under a uniform layer of homogeneous liquid. The frequency equation in the form of ninth-order determinant is obtained. Special cases have been deduced by reducing the depth of the layers to zero and by changing the transverse isotropic layer to an isotropic layer. Dispersion curves for the phase velocity have been plotted for a particular model.

Compression of a transverse isotropic layer by two heated dies

Compression of a transverse isotropic layer by two heated dies