Principal Directions Of Orthotropy Research Articles

Identification of diffusion properties of composites materials for aircraft applications

The paper deals with the identification of planar anisotropic diffusion properties of carbon-epoxy composite materials for aircraft applications, based on the exploitation of short-time gravimetric tests. The method consists in performing short time gravimetric tests on composites samples and measuring the initial slope of their mass uptake curve with respect to t. The identification is performed by minimizing the sum of squared residuals, the residual being the difference between the measured slope and the analytical slope. The identification protocol allows determining the 2 coefficients of diffusion along the principal directions of orthotropy and the orientation of the orthotropic frame reference with respect to the sample frame. Analysis and discussion of results allow to propose a robust identification protocol.

Identification of Diffusion Properties of Polymer-Matrix Composite Materials with Complex Texture

The paper deals with the identification of three-dimensional anisotropic diffusion properties of polymer-matrix composite materials with complex texture, based on the exploitation of short-time gravimetric tests. According to the Thermodynamics of Irreversible Processes, the diffusion behavior can be isotropic or orthotropic: for many materials, due to the complexity of the microscopic texture, the principal directions of orthotropy are not known a priori and enter the identification issue. After reviewing some identification methods (proper generalized decomposition) for isotropic and orthotropic material whose orthotropy directions are known, the paper proposes an experimental protocol and an identification algorithm for the full three-dimensional diffusion case, aiming at establishing the 3 coefficients of diffusion along the principal directions of orthotropy and the orientation of the orthotropic reference frame with respect to the sample frame. The identification of the physical properties is done through the minimization of a distance in the space of the physical parameters. The problem being non-convex, the numerical strategy used for the search of the global minimum is a particle swarm optimization, the code adaptive local evolution-particle swarm optimization with adaptive coefficients.

Identification of the flexural stiffness parameters of an orthotropic plate from the local dynamic equilibrium without a priori knowledge of the principal directions

This paper proposes an inverse method to characterize orthotropic material properties from vibratory measurements on plate-like structures. The method is an adaptation of the Force Analysis Technique (FAT), which was originally developed to identify the external force distribution acting on a structure using its local discretized equation of motion. This method was recently adapted to the identification of elastic and damping properties of isotropic plates. In the present approach, the equation of motion of an orthotropic plate with respect to an arbitrary set of orthogonal axes is considered. The angle between the axes of the measurement mesh and the principal directions of orthotropy therefore explicitly appears in the equation and constitutes an unknown. A procedure to identify this angle together with the flexural stiffness parameters is proposed, as well as an automatic regularization procedure to overcome the high sensitivity of the inverse problem to measurement noise. The method is illustrated using simulated data. Experimental results shown on various structures demonstrate the ability of the method to simultaneously identify the principal orthotropy directions and the flexural stiffness parameters.

Interface crack problem in layered orthotropic materials under thermo-mechanical loading

In the present paper, the behavior of an interface crack for a homogeneous orthotropic strip sandwiched between two different functionally graded orthotropic materials subjected to thermal and mechanical loading is considered. It is assumed that interface crack is partly insulated, and the temperature drop across the crack surfaces is the result of the thermal resistance due to the heat conduction through the crack region. The elastic properties of the material are assumed to vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the crack orientation. The complicated mixed boundary problems of equations of heat conduction and elasticity are converted analytically into singular integral equations, which are solved numerically. The main objective of the paper is to study the effects of material nonhomogeneity parameters and the dimensionless thermal resistance on the thermal stress intensity factors for the purpose of gaining better understanding of the thermal behavior of graded layer.

Mode I Crack Problem for a Functionally Graded Orthotropic COATING-Substrate Structure

In this paper, the Fourier integral transform-singular integral equation method is presented for the Mode I crack problem of the functionally graded orthotropic coating-substrate structure. The elastic property of the material is assumed vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the boundaries of the strip. Numerical examples are presented to illustrate the effects of the crack length, the material nonhomogeneity and the thickness of coating on the stress intensity factors.

A mixed boundary value problem in orthotropic strip containing a crack

In this study, an orthotropic strip containing a symmetrically located crack whose sides are parallel to the boundaries of strip is considered. It is assumed that the strip is hinged along its boundaries, the crack sides are loaded by distributed pressure and the principal directions of orthotropy are parallel and perpendicular to the boundaries. The problem is solved under plane strain conditions. As a result, the stress concentration characterized by the stress intensity factor (SIF) of mode I arises at the crack tip. By using the boundary conditions and the Fourier transform technique a Cauchy type singular integral equation of first kind is derived to determine the derivative of the function describing vertical displacements of the points on the crack sides. Iterative method is used to construct the approximate solution of this integral equation. A theorem is given to determine the lower bounds of applicable of the iterative method respect to the relative thickness of the strip, which has a geometrical importance. Two loading conditions are considered during the analysis. In this paper, the influence of relative thickness of strip as geometry parameter and the effect of the mechanical orthotropic properties on the SIFs are studied.

The importance of cortical bone orthotropicity, maximum stiffness direction and thickness on the reliability of mandible numerical models

To identify mechanical and geometrical variables affecting the biofidelity of numerical models of human mandible. Computed results sensibility to cortical bone orthotropy and thicknesses is investigated. Two mandible numerical models of different bone complexities are setup. In the low-complexity model, cortical bone is coupled with isotropic materials properties; constant thickness for cortical bone is adopted along the mandible structure. In the higher complexity model, the cortical bone is considered as an orthotropic material according to an independent mechanical characterization performed on fresh human dentate mandibles. Cortical thickness distribution, the values of the principal elastic moduli and principal directions of orthotropy are considered as piecewise heterogeneous. Forces for masseter (10 N), medial pterigoid (6 N), anterior (4 N) and posterior (4 N) temporalis muscles are applied to the models. Computed strains fields are compared with those experimentally measured in an independent test performed on a real human mandible in the same loading conditions. Under closure muscles forces both models shows similar strain distribution. On the contrary, strain fields values are significantly different between the presented models. The mandible structure is sensible to compact bone orthotropy and thickness at the facial side of condylar neck, retro molar area and at the lingual side of middle portion of the corpus in molars area, anterior margin of the ramus. In these areas, it is advisable to use orthotropic properties for cortical bone to accurately describe the strain state.

Frictional instabilities in orthotropic hollow cylinders

This study discusses the implications of obstacle curvature, material orthotropy and friction to the occurrence of flutter and divergence instabilities of elastic media. The analytic solution for the divergence instability problem of a hollow cylinder when its principal directions of orthotropy make constant angles with the circumferential and radial directions is closely approximated by finite element solutions of a complementarity eigenproblem in which the coefficient of friction appears as an eigenvalue, quadratically due to the obstacle curvature. Mechanical systems with a finite number of degrees of freedom illustrate some aspects of the onset of instability. In particular, the presented study shows that, under certain conditions, the increase of the obstacle convexity may favour stability.

Buckling of an orthotropic graded coating with an embedded crack bonded to a homogeneous substrate

To simulate buckling of nonuniform coatings, we consider the problem of an embedded crack in a graded orthotropic coating bonded to a homogeneous substrate subjected to a compressive loading. The coating is graded in the thickness direction and the material gradient is orthogonal to the crack direction which is parallel with the free surface. The elastic properties of the material are assumed to vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the crack orientation. The loading consists of a uniform compressive strain applied away from the crack region. The graded coating is modeled as a nonhomogeneous medium with an orthotropic stress–strain law. Using a nonlinear continuum theory and a suitable perturbation technique, the plane strain problem is reduced to an eigenvalue problem describing the onset of buckling. Using integral transforms, the resulting plane elasticity equations are converted analytically into singular integral equations which are solved numerically to yield the critical buckling strain. The Finite Element Method was additionally used to model the crack problem. The main objective of the paper is to study the influence of material nonhomogeneity on the buckling resistance of the graded layer for various crack positions, coating thicknesses and different orthotropic FGMs.

Dynamic buckling of thin-walled composite plates with varying widthwise material properties

The paper deals with dynamic response of a thin-walled rectangular plate subjected to in-plane pulse loading. The plate is made of orthotropic (fibre composite) material in which the principal directions of orthotropy are parallel to the plate edges. The plate is characterised by a widthwise varying fibre volume fraction. The structures are assumed to be simply supported at the loaded ends and at non-loaded ends with five different boundary conditions (both simply supported, both fixed, simply supported fixed, simply supported free edge, fixed free edge). In order to obtain the equations of motion the non-linear theory of orthotropic thin-walled plates has been modified in such a way that it additionally accounts for all components of inertial forces. The differential equations of motion have been obtained from Hamilton’s Principle. The problem of nonlinear static stability was solved with the second order of the Koiter’s asymptotic stability theory of conservative systems. The results obtained from analytical–numerical method were compared with the results from finite element method (FEM).

Mode I crack problem for a functionally graded orthotropic strip

A theoretical treatment of mode I crack problem is put forward for a functionally graded orthotropic strip. The internal crack and edge crack perpendicular to the boundaries are investigated, respectively. The elastic property of the material is assumed to vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the boundaries of the strip. The singular integral equation for solving the problem and the corresponding asymptotic expression of the singular kernel are obtained. Three different loading conditions, namely crack surface pressure, fixed-grip loading and bending, are considered during the analysis. The influences of parameters such as the material constants and the geometry parameters on the stress intensity factors (SIFs) are studied.

Plane Problem of a Crack on the Interface of Orthotropic Plates with Friction of Crack Lips

We consider a plane problem of a crack on the interface of different orthotropic arbitrarily oriented semiinfinite spaces subjected to the action of uniform tensile and shear forces applied at infinity. In the vicinity of the crack tip, the crack lips smoothly close up to form a contact zone of a priori unknown length in the presence of constant friction between the lips. A transcendental equation for the length of the contact zone is deduced and analyzed. As a result, we obtain the dependences of the relative length of the contact zone and the stress intensity factors on the orientation of the principal directions of orthotropy for different values of the external load and boundary friction.

USE OF ISOTROPIC FUNDAMENTAL SOLUTIONS FOR HEAT CONDUCTION IN ANISOTROPIC MEDIA

A numerical formulation for solving homogeneous anisotropic heat conduction problems based on the use of an isotropic fundamental solution is presented in detail. The analysis is carried out assuming a generic position of the coordinate axes, which may not coincide with the principal directions of orthotropy of the material. The two primary integral equations of the method are derived from the governing differential equation of the problem. Then, the numerical procedure is developed by rewriting the internal degrees of freedom that arise from the domain discretization in terms of the boundary nodes and solving the resulting system of linear equations for the boundary unknowns only. Special attention is given to the differentiation of singular integrals which yields additional terms as well as to the evaluation of the resulting Cauchy principal value integral. The main feature of the proposed formulation is its generality, which makes possible its direct extension to solve the problem of three‐dimensional heat conduction in anisotropic media and, foremost, to three‐dimensional orthotropic and anisotropic elasticity or elastoplasticity.

Elasto-static and elasto-plastic stress analysis of adhesive bonded tubular lap joints

The problem of an adhesive bonded lap joint between two dissimilar orthotropic circular cylindrical laminated shells is considered. The principal directions of orthotropy do not have to coincide with the principal directions of curvature, and the external loads are allowed to be of non-axisymmetric type. The adhesive layer is modelled in two ways. The first approach assumes the adhesive layer to behave as a linear elastic material. The second, more realistic approach takes into account the predominantly inelastic behaviour of many polymeric adhesives, and it is shown that the non-linear behaviour affects the adhesive stress distribution even at low levels of external loading. The developed numerical solution procedures have been used to conduct a parametric study, and a few general design recommendations are given.

On the adjoint constitutive law in nonlinear elastic optimal design

This work is concerned with a structural optimization problem, formulated in quite general terms, involving an elastic nonlinear isotropic three-dimensional continuum. The resolution is approached through a variational technique (Lagrange multiplier method); this technique yields, in addition to the optimality condition, a set of equations which can be interpreted as governing equations of another structural problem, ≪adjoint≫ to the given one. The constitutive law of the adjoint problem is studied in detail and the differences between the real and the adjoint constitutive laws are pointed out. In particular, it is shown that the material of the adjoint problem is orthotropic and its principal directions of orthotropy are determined. Finally, the results obtained are specialized to a ≪compliance≫ optimization problem for elastic nonlinear plates in bending; the difference between the present case and the already known case where the plate is linearly elastic is discussed.

A large orthotropic plate with misfit pin under arbitrarily oriented biaxial loading

The problem of misfit (interference or clearance) pin in a large orthotropic plate was solved earlier by the authors for biaxial loading in the principal directions of orthotropy. Here, a more general case of arbitrarily oriented loading is considered. The most important aspect of the problem studied is the partial contact at the pin-hole interface. The solution is obtained by extending the use of ‘inverse technique’ which was successfully applied earlier by the authors to problems of pins in isotropic and orthotropic domains. The loss of symmetry because of the arbitrary orientation of loading makes the problem more complex. Additional parameters are then involved in the inversion of the problem for the solution. Numerical results are presented primarily for a smooth interference fit pin in a typical orthotropic plate.