Orthotropic Layers Research Articles

Prediction and validation of flanking sound transmission in cross-laminated timber junctions with resilient interlayers

Propelled by its small carbon footprint, low weight and high stiffness, cross-laminated timber (CLT) has experienced a significant commercial growth in the last decade. However, these latter two features potentially contribute to poor acoustic performance. A critical factor is flanking sound, in which vibrational energy is transmitted between two elements connected through a common junction, driving the need to include vibration isolation solutions such as resilient interlayers in the junction design. In this work, the vibration reduction index across CLT junctions is predicted with an analytical wave approach for semi-infinite thin plates. Each CLT panel is modelled as an orthotropic or isotropic equivalent single layer (ESL). Multiple options to determine the ESL properties are compared, including the law of mixtures and the modified gamma method. The interlayer is considered to be a thick, flexible waveguide, whose out-of-plane motion is governed by shear. The prediction model is validated experimentally with on-site measurements for a vertical T-junction with a polyurethane foam interlayer. The predictions are moderately accurate in the entire frequency range, with deviations below 10 dB across all 1/3 octave bands. Depending on the layer configuration, the orthotropy of the ESL can significantly influence the predictions.

Axisymmetric torsion of an orthotropic layer sandwiched by two orthotropic half-spaces with interfaced cracks

Axisymmetric torsion of an orthotropic layer sandwiched by two orthotropic half-spaces with interfaced cracks

Analytical approach to contact mechanics of functionally graded orthotropic layers with gravitational considerations

Analytical approach to contact mechanics of functionally graded orthotropic layers with gravitational considerations

Frictional receding contact problem of a functionally graded orthotropic layer / orthotropic interlayer / isotropic half plane system

Frictional receding contact problem of a functionally graded orthotropic layer / orthotropic interlayer / isotropic half plane system

Love-like wave fields at the interface of sliding contact with non-local elastic heterogeneous fluid-saturated fractured poro-viscoelastic layer

The investigation delves into the propagation of Love-like waves within a stratified medium incorporating the impact of non-local elasticity and a sliding interface. The medium is characterized by an orthotropic viscoelastic layer with fractures and matrix porosity saturated with fluid positioned over an orthotropic viscoelastic half-space under initial stresses. The media is vertically heterogeneous with a binomial function of depth featuring a real positive exponent. Two distinct non-local parameters are considered for the layer and half-space, along with a sliding parameter accounting for interface sliding. The particle displacement components are expressed using modified Bessel functions of first and second kinds. A finite number of terms of the asymptotic representation of the modified Bessel functions and their derivatives have been used and compared with the exact solution. The dispersion equation is derived by neglecting fourth and subsequent powers of non-local parameters under suitable boundary conditions. Various cases are explored based on welded, partially, and fully sliding interfaces and compared with classical Love wave propagation. An interesting phenomenon has been found that under a fully sliding interface, the existence of Love-like wave vanishes, and the medium behaves as a separate layer and half-space with shear wave propagation.

Multi-method examination of contact mechanics in orthotropic layers under gravity

Analyzing the behavior of intelligent unconventional materials under diverse contact scenarios, in comparison to conventional materials, is a critical step in the initial design of engineering systems. This paper presents the development of analytical and numerical approaches for analyzing contact mechanics in a system comprising an orthotropic layer resting on a rigid foundation. Parametric analyses include the consideration of cylindrical and flat punch profiles. Analytical formulation utilizes integral transform methods to convert planar elasticity equations into a Cauchy-type singular integral equation of the second kind. A detailed description of the solution technique for the integral equation is provided, encompassing both the analytical formulation and the required discretization for obtaining the solution. Subsequently, a finite element approach (FEA) is employed to approximate contact bodies using a collection of finite elements, while contact boundaries are approximated by utilizing a set of polygons. Alternatively, the problem is addressed using the Multilayer Perceptron approach, a form of artificial neural network frequently applied in diverse machine learning applications, including scenarios involving contact problems. Finally, the resolution to the problem is achieved by employing the multilayer perceptron (MLP) method. The study yields determinations of contact stresses under the punch, the critical separation load resulting in the detachment of the orthotropic layer from the rigid foundation, and the corresponding separation distance. This analysis considers a range of dimensionless parameters and explored the behavior of diverse orthotropic materials. Comparisons between the results of the analytical method and computations from FEA and MLP reveal the exceptional accuracy attained by all three approaches. As the pioneer study employing three distinct approaches to examine continuous contact mechanics within an orthotropic layer under the influence of gravity, this research constitutes a valuable point of reference for upcoming scholars in the field.

On the vibration responses of orthotropic laminated cylindrical panels with non-uniform porosity distributions using higher-order shear deformation theory

The present study investigates free vibration analysis of cylindrical panels made of porous orthotropic layers. Porous material properties are modeled using uniform and two non-uniform porosity distribution patterns through the thickness. The theoretical formulations are expressed based on the higher-order shear deformation theory. The equations of motion of laminated cylindrical panels are established by performing Hamilton’s principle. These fundamental partial differential equations are solved analytically for the laminated cylindrical panels, which are simply supported on all edges. Galerkin’s solution procedure is applied to obtain the natural frequency equation. The natural frequencies are compared to results in the literature to verify the obtained frequency equation. Afterward, novel parametric studies are developed to discuss the influence of porosity parameters, porosity distribution patterns, geometrical parameters, orthotropy, and lamination sequences on the free vibration response of porous laminated cylindrical panels.

Solution of nonlinear vibration problem of shear deformable multilayer nonhomogeneous orthotropic plates using Poincare-Lindstedt method

In this study, one of the first attempts is made to solve the nonlinear (NL) vibration problem of shear-deformable multilayer plates consisting of nonhomogeneous orthotropic layers (NHOLs) using the Poincaré-Lindstedt method. First, the shear deformation theory (SDT) for homogeneous plates is extended to multilayer plates composed of NHOLs. In the framework of von-Karman type nonlinear theory, the basic relations of the plates in question are established and then NL equations of motion based on four functions such as rotation angles, Airy stress and deflection functions are derived. Then, NL-partial differential equations (NL-PDEs) are reduced to NL-ordinary differential equations (NL-ODE) and the solution of NL-ODE is performed for the first time by the modified Poincaré −Lindstedt method, yielding new amplitude dependent expressions for NL frequency, and for the ratio of NL frequency to linear (NL/L) frequency for multilayer plates consisting of NHOLs. Finally, detailed parametric studies are carried out to gain insight into the effects of various factors such as shear strains, non-homogeneity, number and array of layers on the NL frequencies under different rectangular plate characteristics.

Buckling load optimization of sandwich plates with trapezoidal corrugated core and elliptical cutout using vibration correlation techniques and artificial neural network; experimental and numerical analysis

The present research was carried out in order to estimate the buckling load of a sandwich plate with a trapezoidal corrugated core with cut-out using three vibration correlation techniques (VCT). The structure investigated in this research is a sandwich plate with a trapezoidal core and an oval cut-out, which is made of thermoplastic polymer using a 3D printer. By using artificial neural network (ANN) and genetic algorithm (GA), the specific critical buckling load (p¯cr) which is defined as the ratio of critical buckling load (Pcr) to plate weight (gr) has been minimized and the optimal dimensions for cut-out parameters including the ratio of the large diameter of the ellipse (z=20mm) to the small diameter of the ellipse (b) and oval angles with the horizontal axis (a∘) are obtained. Using the method of equivalent properties, the trapezoidal core is transformed into an equivalent orthotropic core and finally the desired structure is transformed into a three-layer sandwich plate including homogeneous upper and lower layers and an orthotropic middle layer. By using the meshless method based on radial and polynomial functions and with the help of the finite element method, the numerical simulation of buckling and free vibration of the sandwich plate has been done. The results showed that the estimation of the buckling load with the vibration correlation technique (VCT) corresponds to the actual condition of the structure, so that due to the high quality of sandwich plate construction and its integrity, the results obtained from the first, second, and third methods of the VCT show the effectiveness of this method for predicting of the buckling load of the structure.

Deformation of an orthotropic layer overlying a rough-rigid base due to surface loads

Deformation of an orthotropic layer overlying a rough-rigid base due to surface loads

High-precision modelling of deformation of sandwich structures under bilateral symmetric and oblique-symmetric loading

The analysis and assessment of the stress-strain state (STS) of multilayer plates with orthotropic layers under the action of stationary transverse and tangential loads is an urgent task. It includes calculations on the strength and deformability of various homogeneous and multi-layered plates with layers of constant thickness but arbitrary structure according to the thickness of the plate. 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 unflexural components, it is proposed to optimize the design scheme of deformation of a rectangular multilayer plate. This significantly simplifies its modeling. For unflexural and exclusively flexural SSS, a two-dimensional, high-degree iterative approximation, but three-dimensional models of deformation of multilayer rectangular plate on a rigid foundation with isotropic, transverse-isotropic and orthotropic layers are constructed in an elastic formulation. That models takes full account deformation of transverse shear and transverse compression at transverse and the tangential loading of a plate. The model is continuous, that is, the number of equations and the order of differentiation of the calculation system of equations does not depend on the number of layers in the slab. This order of differentiation and the number of calculation equations can depend only on the order of iterative approximation of the model. A way of precise satisfaction of all defining correlations of the layers of material under keeping the conditions of their contact is found, while in the known continual models the dependence between the cross normal stress and cross deformation is only integral.The results of the analytical solution of the problem of deformation of a rectangular plate under boundary conditions of the Navier type under the action of transverse and tangential loads are given. By solving the test problems of the deformation of two-layer plates with transversally isotropic layers and three-layer plates with orthotropic layers and comparing the solutions with the exact three-dimensional solutions of these problems obtained by known methods, an assessment of the accuracy of the proposed refined models is given. The limits of admissible parameters of elastic characteristics of transversely isotropic and orthotropic plates for application of the offered models are established.

Moving contact problem of a functionally graded orthotropic coated half plane

This paper develops a frictional moving contact model for a functionally graded (FG) orthotropic layer pressed by a rigid cylindrical punch. The FG orthotropic layer is fully bonded to the isotropic half-plane. The punch moves to the left on the layer at a constant subsonic velocity and a shear stress arises in the contact zone according to the Coulomb friction law. General expressions of displacements and stresses are derived with the help of the Fourier transform and Galilean transformation. Using boundary conditions, the moving contact problem is reduced to a Cauchy-type singular integral equation, the unknowns of which are contact stress and contact width. Gauss–Jacobi integration formula is used to solve the obtained singular integral equation. The effect of some parameters and material properties on the contact width, contact stress and in-plane stress are given in graphical forms and detailed numerical interpretations are presented.

Couple-stress elasticity of intrinsic and extrinsic dislocations in three-dimensional multilayered materials

This work investigates the influence of couple stresses on intrinsic and extrinsic dislocations within three-dimensional heterogeneous multilayered structures. The materials consist of orthotropic and dissimilar layers with different elastic properties, incorporating the microstructural lengths from a special version of the anisotropic couple-stress elasticity. Double Fourier series expansions are used to describe extended displacements and tractions, considering rotation and couple-stress components and accounting for arbitrary displacement and rotation discontinuities associated with dislocation and disclination loops as well as periodic dislocation and disclination networks at semi-coherent interfaces. The dual-variable and position technique is used to recursively determine the field responses at any point in the multilayered laminate. The application examples focus on dislocation problems with couple stresses, revealing the effects of the core-spreading dislocation technique, free surfaces, anisotropic elasticity, and couple stresses on the field solutions. The analysis also uncovers pressure and von Mises stress amplitudes, non-zero rotation, and non-symmetric stress profiles due to couple stresses in copper/niobium bimaterials. Changes in the sign and magnitude of the Peach-Koehler forces are observed when couple stresses are introduced, which deviate from the classical theory of dislocations. The investigation finds a significant 29% reduction in energy per unit area at a semi-coherent interface between copper and niobium influenced by couple stresses. These results deepen our understanding of how couple stresses affect dislocation behavior in multilayered materials, and provide prospects for future discrete dislocation and disclination dynamics simulations with engineering applications in various nano- and micro-structured materials.

Magnetoelastic effect on semi‐infinite moving crack in an orthotropic structure influenced by anti‐plane wave

AbstractA two dimensional boundary value problem of magnetoelasticity for a semi‐infinite moving crack situated between an orthotropic half‐space and an orthotropic layer has been considered. Also, it has been considered that the crack is agitated by an anti‐plane shear wave. The contemplated problem has been reduced to a typical Wiener–Hopf equation by employing Fourier integral transform to the convenient boundary condition. The accomplished Wiener–Hopf equation has been solved only for asymptotic case to get the analytical expression of stress intensity factor (SIF) and crack tearing displacement (CTD). The dependence of several parameters including the magnetoelastic coupling factor, material constants, crack propagation velocity and crack depth from the upper surface on the SIF and CTD have been illustrated using variety of graphs.

Mathematical Investigation of Reflection and Transmission of Plane Wave at the Corrugated Interface of Orthotropic Layer Sandwiched Between Two Distinct Monoclinic Media

Mathematical Investigation of Reflection and Transmission of Plane Wave at the Corrugated Interface of Orthotropic Layer Sandwiched Between Two Distinct Monoclinic Media

The Application of the Modified Lindstedt–Poincaré Method to Solve the Nonlinear Vibration Problem of Exponentially Graded Laminated Plates on Elastic Foundations

The solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young’s modulus and the material density of the orthotropic layers of laminated plates are assumed to vary exponentially in the direction of thickness, and Poisson’s ratio is assumed to be constant. The governing equations are derived as equations of motion and compatibility using the stress–strain relationship within the framework of KLT and von Karman-type nonlinear theory. NL partial differential equations are reduced to NL ordinary differential equations by the Galerkin method and solved by using the modified Lindstedt–Poincaré method to obtain unique amplitude-dependent expressions for the NL frequency. The proposed solution is validated by comparing the results for laminated plates consisting of exponentially graded orthotropic layers with the results for laminated homogeneous orthotropic plates. Finally, a series of examples are presented to illustrate numerical results on the nonlinear frequency of rectangular plates composed of homogeneous and exponentially graded layers. The effects of the exponential change in the material gradient in the layers, the arrangement and number of the layers, the elastic foundations, the plate aspect ratio and the nonlinearity of the frequency are investigated.

Dynamic indentation of viscoelastic orthotropic layer supported by a Winkler–Pasternak foundation

AbstractIn this study, the two-dimensional dynamic contact problem between a rigid flat punch and a viscoelastic orthotropic layer is investigated. The motivation of the study is to provide a better understanding of the vertical vibration of the two-parameter Winkler–Pasternak foundation, which has not yet been investigated. For the contact problem, the mixed boundary conditions on the top and bottom surfaces are transformed into linear equations using the Fourier transform technique and Helmholtz functions. Based on the Gauss–Chebyshev integration formula, the singular integral equation is obtained and solved numerically. As a result of the solutions, the effects of various parameters on the contact stresses are analyzed and examples are given. It was found that the Winkler foundation modulus does not affect the dynamic contact stress, while the Pasternak foundation modulus significantly affects the contact stress.

Stress-strain state of a two-layer orthotropic body under plane deformation

We consider the problem of determining the stresses and strains of a two-layer body consisting of an orthotropic layer of constant thickness connected to an orthotropic half-space. The surface of the layer is subjected to known external loads, such that the deformation of the body is plane. At infinity, the stresses are zero. The stress-strain state of the body is determined using the method of integral Fourier transforms. The features of solutions of the system of differential equations of the problem are investigated. The solutions of a particular problems are obtained and analyzed.

Investigation of the vibration problem of sandwich heterogeneous orthotropic plates

In this study, the solution of the free vibration problem of sandwich plates consisting of heterogeneous orthotropic layers is presented. First, the Kirchhoff-Love theory (KLT) for homogeneous plates is extended to sandwich plates composed of heterogeneous orthotropic layers. Within the framework of Donnell theory, after establishing the basic relations of multilayer plates, governing equations are derived based on Airy stress and deflection functions. The solution of the governing equations is carried out by the Galerkin method and the analytical expression is found for the linear frequency of sandwich plates consisting of heterogeneous orthotropic layers. Finally, the effects of various factors such as heterogeneity, number of layers and their arrangement on the free vibration frequency of sandwich plates are examined.

SOLVING BASIC BOUNDARY VALUE PROBLEMS FOR AN ORTHOTROPIC LAYER

We consider the first, second basic and mixed boundary value problems of the linear theory of elasticity for a homogeneous orthotropic layer of constant thickness. The layer is subjected to a surface load. There are no internal forces. It is required to determine the stresses and displacements at an arbitrary point of the layer, assuming plane deformation. The solutions to the problem are constructed. The solution to the problem is sought in the space of transformants of the one-dimensional integral Fourier transform, where the relationship between the transformants of the stress function and the transformants of displacements and stresses is established. The desired values are expressed through four auxiliary functions that are associated with the stress and displacement transforms at the upper boundary. To obtain the true values of stresses and displacements at the points of the orthotropic layer, the inverse integral Fourier transform is applied to the found stress and displacement transforms. Numerical solutions for specific cases are obtained and the results are analyzed.