Effect Of Orthotropy Research Articles

Anisotropy and magnetoelasticity effects on the propagation of the SH-wave-induced semi-infinite crack in a magnetoelastic orthotropic medium

The crux of the present study is to investigate semi-infinite crack propagation in magnetoelastic strip influenced by propagating SH-wave under orthotropic geometrical configurations. The Wiener-Hopf (WH) technique and two-sided Fourier integral transforms (FIT) are applied in the proposed analytical model. A closed-form expression of the stress intensity factor (SIF) has been established for the constant concentrated force. The SIF in a magnetoelastic orthotropic strip is shown to be significantly affected by the crack length and crack speed, medium anisotropy, and magnetoelastic parameter. The proposed model is compared to the case of a magnetoelastic isotropic strip in order to demonstrate the effect of orthotropy as well as other anomalies. Among other observations, it is noted that regardless of whether orthotropy exists in the strip or not, the value of the SIF rises along with the crack speed until it reaches its maximum, at which point it rapidly declines.

Non-linear vibration analysis of specially orthotropic tapered micro-plates with arbitrary located crack: A non-classical analytical approach

The present work aims to study the non-linear vibrations in a cracked orthotropic tapered micro-plate. Linear and parabolic variation in the plate thickness is assumed in one as well as two directions. The partial crack is located in the centre, and it is continuous; this crack’s location is arbitrary and can be varied within the centre-line. Based on classical plate theory, the equilibrium principle is applied, and the governing equation of tapered orthotropic plate is derived. Additionally, the microstructure’s effect has been included in the governing equation using the non-classical modified couple stress theory. The simplified line spring model is used to consider the impact of partial crack on the plate dynamics and is incorporated using in-plane forces and bending moments. The introduction of Berger’s formulation brings the non-linearity in the model in terms of in-plane forces. Here, Galerkin’s method has been chosen for converting the derived governing equation into time-dependent modal coordinates, which uses an approximate solution technique to solve the non-linear Duffing equation. The crack is considered along the fibres and across the fibres to show the effect of orthotropy. Results are presented for an orthotropic cracked plate with non-uniform thickness. The effects of the variation of taper constants, crack location, crack length, internal material length scale parameter on the fundamental frequency are obtained for two different boundary conditions. The non-linear frequency response curves are plotted to show the effect of non-linearity on the system dynamics using the method of multiple scales, and the contribution of taper constants and crack parameters on non-linearity is shown with bending-hardening and bending-softening phenomenon. It has been found that vibration characteristics are affected by the taper parameters and fibre direction for a cracked orthotropic plate.

On thermal-expansion properties of more-orthotropic prepreg laminates with and without interleaf layers

More-orthotropic laminates are increasingly used in today’s carbon-fiber-epoxy composite airframe structures. A recent study reported on a considerable discrepancy between measured and calculated coefficients of thermal expansion (CTEs) for M21E/IMA prepreg laminates, which was found to increase with the laminates’ degree of orthotropy ξ=Ex/Ey. In this paper it is analyzed whether the observed effect is related to more-orthotropic laminate stackings in general or to the particular inner laminate architecture of M21E/IMA laminates, which is characterized by discrete interleaf layers. Therefore, a quasi-isotropic and three more-orthotropic laminates, made from 8552/AS4 and M21E/IMA prepreg, were analyzed by means of thermo-mechanical analysis (TMA) and classical-laminate theory (CLT). Calculated and measured CTEs are compared and the effect of orthotropy is quantified. Potential affectations of TMA measurements and CTE determination due to edge effects and sample size are examined by means of finite-element analyses.

Effect of specimen configuration and orthotropy on the Young’s modulus of solid wood obtained from a longitudinal vibration test

Abstract Young’s modulus in the longitudinal direction was measured by a longitudinal vibration (LV) test on western hemlock specimens with various length/width ratios. The effects of the configuration and orthotropy of the specimen on the measurement of Young’s modulus was investigated through subsequent finite element (FE) calculations. The experimental results suggested that Young’s modulus could not be obtained accurately when the length/width ratio of the specimen was in a certain range. The FE calculations revealed that Young’s modulus in the transverse direction and Poisson’s ratio in the length-width plane, as well as the length/width ratio, affected the Young’s modulus value. However, the results showed that when the length/width ratio of the specimen was larger than 10, Young’s modulus could be measured accurately with the LV test with a reduction in the effect of orthotropy.

Mode I J-integral of extruded polystyrene measured by the four-point single-edge notched bending test

Four-point single-edge-notched bending (4SENB) tests were conducted using specimens from four kinds of extruded polystyrene (XPS) panels to determine the Mode I critical J-integrals. The cracks parallel with and perpendicular to the length direction of the panel are the so-called TL- and LT-systems, respectively, and the initial crack length was varied during the test. Because of the effect of orthotropy, the Mode I critical J-integral values of the TL- and LT-systems’ specimens were different from each other. Additionally, the dependence of the critical J-integral on the initial crack length was more significant in LT-systems than in TL-systems. However, this dependence could be reduced by introducing an additional crack length due to the fracture process zone (FPZ) ahead of the crack tip.

Local buckling analysis of periodic sinusoidal corrugated composite panels under uniaxial compression

The critical local buckling of simply-supported sinusoidal panels subjected to uniaxial compression using the Rayleigh-Ritz method is investigated. With increased applications of thin-walled composite structures in engineering, these corrugated panels are especially popular due to their high stiffness to weight ratio and high out-of-plane rigidities. Failure of such thin-walled panels occurs mainly in buckling rather than material failure; thus, it leads to the importance of buckling failure analysis. Conventional methods are limited when analyzing these panels in local buckling because of its unique geometries. Hence, a semi-analytical solution is developed to predict the local buckling based on classical shell theory with a unit cell approach, and it shows excellent correlation with the results based on the numerical finite element analysis. A parametric study is conducted to evaluate the effects of the thickness, aspect ratio, and the corrugated amplitude of the panel on buckling. It is revealed that the derived solution can accurately capture the local buckling behavior at high thickness/radius of curvature ratios, any aspect ratios, and high corrugated amplitudes. Additionally, the effects of orthotropy, Poisson’s ratios and twisting capacities on the buckling behavior are explored. The proposed semi-analytical solution can be effectively used to aid in the efficient and accurate design analysis and optimization of corrugated panels.

Bending analysis of laminated plate via polynomial RBF

The present novel work deals with the investigation of bending response of laminated plate using five variable higher order shear defor-mation theory (HSDT). Governing differential equation (GDE) of the plate is acquired by energy principle. Polynomial radial basic function based on Meshfree method is used for discretizing the GDE. A MATLAB code is developed to obtain the results. Convergence and validation for the code is obtained using already published results. The effect of orthotropy and span to thickness ratio on the response of the plate is studied.

Analysis of transient plane thermal stresses in functionally graded orthotropic strip

This research is concerned with the transient plane thermoelastic problems in functionally graded orthotropic materials. The material properties such as the specific heat c, the density ρ, the thermal conductivities λx and λy, the coefficients of linear thermal expansion αx and αy, Young’s moduli Ex and Ey in x and y directions, respectively, are assumed to be functions of position (x). Laplace transform and separation of variables are used to analyze the temperature field in functionally graded orthotropic strips. The stress function is used for the plane thermoelastic problem in the functionally graded orthotropic materials. As a specific example, functionally graded orthotropic strip was analyzed. Numerical results are shown for the effects of orthotropy of material properties on temperature and thermal stresses. They show that the effects of orthotropy on temperature and thermal stresses are very large. The proposed analytical method is useful in the design of structures exposed to severe temperature environment. As a specific example, functionally graded orthotropic strip was analyzed.

Orthotropy in Annular fins: A Collocation based solution

The effect of orthotropy in 2D temperature distribution in annular fins is reported using collocation method. Point Collocation Method (PCM) gives results for insulated tip boundary condition problem along with contact resistance at the base. The problem is solved assuming the non-dimensional 4th order polynomial temperature distribution and forcing the residue to zero at Gauss quadrature points. The fin material is assumed to be aluminium (Kr =200w/m k). The fin is orthotropic in nature and thermal conductivity effect has been governed by thermal conductivity ratio (K). The analysis has been done by considering different coefficients of convective heat transfer at fin base (hc), surface (hs) and tip (he) and is reported for three different aspect ratios (α) of fin. The results presented demonstrate the viability for design and optimization of fins of different sizes under a range of convection conditions, applied to many practical applications encountered in engineering industry.

Material orthotropy effects on progressive damage analysis of open-hole composite laminates under tension

The sizes effects on the strengths of open-hole fibre-reinforced composite laminates subjected to tensile loading (OHT) have been investigated widely. However, little attention has been paid to the influence of material orthotropy. This paper presents a progressive damage model for the model failure of notched laminates under tensile loading based on continuum damage mechanics and cohesive elements. The effects of orthotropy on the failure of notched laminates with seven different ply sequences are investigated by our proposed model. The prediction results adopting the Hoffman and Pinho failure criterions to determine matrix damage initiation are compared with the results of experiments. Our proposed models are able to predict the strong influence of orthotropy on strengths of open-hole laminate under tension, and model using Pinho criterion can predict the open-hole tension strength most accurately.

Analysis of stress distribution near a blunt surface notch tip in an orthotropic fiber under tension

The intrinsic strength of carbon fiber is determined from tensile tests of carbon fibers with a blunt surface notch using a point stress criterion. A stress distribution around the blunt surface notch tip is needed for the carbon fiber with cylindrical shape and orthotropic mechanical properties. In this study, the stress distribution around a blunt surface notch in a fiber with various orthotropy under tension were calculated using a finite element method. An effect of orthotropy on the stress distribution is investigate. To predict the stress distribution for various notch and various orthotropy, an approximate stress distribution equation was proposed.

Effect of Orthotropy on the Stress State of Longitudinally Corrugated Hollow Cylinders

The effect of orthotropy on the stress state of longitudinally corrugated orthotropic hollow cylinders is analyzed using a three-dimensional problem formulation, the analytical variable-separation and Fourier-series methods, and the numerical discrete-orthogonalization method. The results obtained are presented in the form of graphs of displacement and stress fields

The Influence of Orthotropy and Taper Angle on the Compressive Strength of Composite Laminates with Scarfed Holes

The residual strengths of laminated composites containing notches or holes depend on the characteristic dimension of the notches as well as the laminate properties. This paper presents an experimental and computational investigation of the effect of orthotropy as well as scarf notch angles on the compressive strength of composite laminates made of seven different stacking sequences with the number of plies ranging between 20 and 24. Specimens containing scarfed holes of different scarf angles (6° and 10°) and straight holes of two different diameters (3.175mm and 6.35mm) were tested for comparison. Experimental results of the compressive strengths, normalised by the respective un-notched compressive strength show that the extent of orthotropy, defined as the laminate stiffness ratio along and perpendicular to the main loading direction, has a major effect. Computational modelling was carried out using the finite element method to quantify the residual strength; in which ply fracture is modelled using the continuum damage mechanics approach.

Stress Concentration for In-Plane Stressed Orthotropic Plate with Elliptic Opening

The paper discusses the analytical calculation procedure of stress at points along the elliptic opening boundary in an in-plane stressed infinite orthotropic plate. The presented procedure is a first step in the strength analysis of such plates. The stress dependence on material elasticity characteristics and a multilayer plate stacking sequence as well as on a position of the ellipse semi-axes for prescribed stress conditions has been presented on numerical examples while the calculation results have been illustrated by diagrams and numeric data. The specific attention is paid on the case of equal or close values of complex parameters of the orthotropic plate. The derived conclusions, pointing out a danger of stress concentration and orthotropy effects, can be very useful in engineering practice.

Stability of beam-like fracture mechanics specimens

Test specimens used to determine the interlaminar strength of composites as well as the strength of adhesive layers are known to occasionally suffer from instability. Thus, even though the experiments are performed under controlled load-point displacement, the experiments are terminated prematurely by unstable crack propagation. Often there exists a critical crack length which must be exceeded in order to obtain stable crack propagation. In this paper, a general method to assess the stability of beam-like fracture mechanics specimens is developed. Both systems subjected to a single load and the more general situation with several independent loads are treated. A simple formula is derived for the critical crack length for one-parameter loading. The only parameter necessary as input is the compliance of the un-cracked specimen. For the case of non-proportional loading, stability is determined by studying the eigenvalues of a symmetric matrix. Other findings quantified in the paper are the effect of orthotropy, the influence of a flexible interphase layer and the influence of the compliance of the loading device.

Modelling and Analysis of Infilled Frame Structures Under Seismic Loads

In-filled frame structures are commonly used in buildings, even in those located in seismically active regions. Precent codes unfortunately, do not have adequate guidance for treating the modelling, analysis and design of in-filled frame structures. This paper addresses this need and first develops an appropriate technique for modelling the infill-frame interface and then uses it to study the seismic response of in-filled frame structures. Finite element time history analyses under different seismic records have been carried out and the influence of infill strength, openings and soft-storey phe- nomenon are investigated. Results in terms of tip deflection, fundamental period, inter-storey drift ratio and stresses are presented and they will be useful in the seismic design of in-filled frame structures. interface condition, friction coefficient, size of the mesh, relative stiffness of beam to column, relative size of infill wall have significant influence on the response of infilled frame, while the effect of orthotropy of infill material was insignificant. When the mesh density was made finer the stress pattern within the infill also improved, with maximum values of stresses at the compressive corners. The existence of friction coefficient at the interface was reported to in- crease the lateral stiffness of the system. However, friction coefficient is dependent on the quality of material and the workmanship CEB 1996 (6) which is difficult to define ac- curately, hence codes do not provide any guidance.

The Effects of Orthotropic Materials on the Vibration Characteristics of Structural Systems#

The rapid growth in anisotropic material (such as composite materials) usage marks a new era in material science. Obviously, in order to understand the physical behavior of structural systems constituted by composite materials, several parameters, such as natural frequencies, mode shapes, and transmissiblities, must be incorporated into anisotropic elastic analyses. Orthotropy, as a special case of anisotropy, is common in almost all fields of civil and mechanical engineering. The objective of this effort is to investigate the effect of orthotropy on the behavior of vibrating plate systems near degenerate modes. A degenerate plate may be lack of geometric stability since the plate may exhibit a qualitatively different behavior under an arbitrarily small change in special parameters. The special parameters considered in this study are orthotropy and the location of additional mass, which have the effect of removing the system symmetry. The method, which depends on a variational procedure in conjunction with a finite difference method, is employed to examine free vibration characteristics as well as to characterize steady state response to a sinusoidally varying force applied to orthotrophic elastic rectangular plate. The problem is reduced to the solution of a system consisting of algebraic equations by using the variational difference method (VDM). In order to sort the effect of orthotropy on the vibration behavior from other factors, locations of external force, and mass are treated as additional parameters in the analyses. Furthermore, supports are constituted as elastic so as to be able to obtain force transmissibility curves. Finally, plate systems having two different boundary conditions, namely elastically supported and elastically point supported, are utilized to observe the generalization of the outcomes. Results reveal that in case of material orthotropy existence in a plate system, there are several keynote issues that must be taken into account in vibration analyses, which are not important under isotropic conditions. Obviously, these effects are of theoretical importance and should be considered in practical applications.

Heat Conduction in Microwave Devices With Orthotropic and Temperature-Dependent Thermal Conductivity

This paper deals with steady-state heat conduction in integrated circuits due to surface heating. Temperature-dependent and orthotropic thermal conductivities are assumed, and an exact formula is obtained for the temperature field in the integrated circuit due to arbitrary surface flux loading. These general results are then specialized to specific forms of surface flux representative of multifingered FETs of arbitrary gate length, gatewidth, and pitch. Numerical results are presented for a representative transistor on a gallium-arsenide substrate and comparisons are made, where possible, to existing approximate solutions, as well as to finite-element results. The examples are chosen to highlight the effects of orthotropy and temperature dependence of thermal conductivity on the junction temperature of devices on integrated circuits

Effects of orthotropy and variation of Poisson's ratio on the behaviour of tubes in pure flexure

The behaviour of tubes under conditions of pure bending is investigated for the cases where the material of which they are constructed is either orthotropic or of various Poisson's ratios. Large deflections and moderate nonlinear strains are considered and the modelling incorporates Timoshenko beam theory thereby allowing non-zero shear strains to develop. This in turn makes axially inhomogeneous deformation of the cross-section possible and, in particular, the compressed side can develop wrinkling. Numerical solutions are presented for various material types and tube dimensions and some interesting phenomena, such as mode interaction and jumping, are demonstrated.

Application of A Microstructural Constitutive Model of the Pulmonary Artery to Patient-Specific Studies: Validation and Effect of Orthotropy

We applied a statistical mechanics based microstructural model of pulmonary artery mechanics, developed from our previous studies of rats with pulmonary arterial hypertension (PAH), to patient-specific clinical studies of children with PAH. Our previous animal studies provoked the hypothesis that increased cross-linking density of the molecular chains may be one biological remodeling mechanism by which the PA stiffens in PAH. This study appears to further confirm this hypothesis since varying molecular cross-linking density in the model allows us to simulate the changes in the P-D loops between normotensive and hypertensive conditions reasonably well. The model was combined with patient-specific three-dimensional vascular anatomy to obtain detailed information on the topography of stresses and strains within the proximal branches of the pulmonary vasculature. The effect of orthotropy on stressstrain within the main and branch PAs obtained from a patient was explored. This initial study also puts forward important questions that need to be considered before combining the microstructural model with complex patient-specific vascular geometries.