Orthotropic Material Properties Research Articles

Transient Thermal Stress and Thermal Deformation of an Angle-Ply Laminated Rectangular Plate Due to Nonuniform Heat Supply Based on Higher-Order Shear Deformation Theory.

This paper is concerned with a theoretical treatment of thermal stress and thermal bending problems for a multi-layered anisotropic laminated plate due to partially distributed heat supply. As an analytical model, we consider a laminated rectangular plate consisting of a diagonal pile of layers having orthotropic material properties, i. e. an angle-ply laminate. We obtain the three-dimensional temperature in a transient state and thermal deformation of a simply supported plate using the higher-order shear deformation theory. As an example, numerical calculations are carried out for a 2-layered angle-ply laminate, and the numerical results are examined precisely.

Analysis of Thermal Stress and Deformation due to Nonuniform Heat Supply in an Angle-Ply Laminated Rectangular Plate.

This paper describes theoretical treatment of problems of thermal stress and thermal bending due to partially distributed heat supply for a multilayered anisotropic laminated plate. As an analytical model, we consider a laminated rectangular plate consisting of a diagonal stack of layers having orthotropic material properties, i. e. an angle-ply laminate. Introducing the Rayleigh-Ritz method based on the variational principle, a three-dimensional temperature solution for a transient state is given. Moreover, for the thermoelastic problems, the components of displacements are analyzed using the Rayleigh-Ritz method, and the characteristic behaviors of thermal stress and thermal deformation for a simply supported plate are determined. As an example, calculations are carried out for a 2-layered angle-ply laminate, and the results are examined precisely.

Stress and Displacement Analysis of Composite Laminated Plates

Multilayered composite plates are of interest for a variety of structural ap plications in such industries as automotive and aerospace, where high strength-to-weight ratios are desirable. In this investigation a series of plate elements is developed for such structures. These plate elements are formulated based on a variational principle, namely modified complementary energy. Mindlin thin plate theory is selected to govern the gen eral characteristics and behavior of these plates. Transverse shear deformation is included in the formulation. A series of in-plane strain functions is assumed from which the corre sponding in-plane stresses for each lamina are determined. By satisfying the equilibrium equations, the transverse stresses are calculated. The strain parameters can be determined by satisfying the interlaminar transverse stress continuity and the traction-free condition at the bottom surface. The top traction-free condition is ignored in this formulation. It will be demonstrated that the impact of ignoring the top traction-free condition on the results is negligible. Eight-node isoparametric elements with five degrees of freedom per node are utilized to describe the displacement field. These elements are invariant, fast converging, and insen sitive to the number of gauss points used in the numerical integrations. Moreover, it will be shown that these elements do not exhibit any shear locking in the thin plate limit. These elements are capable of handling the effects of transverse shear deformation, extension- bending, twisting-extension, and twisting-bending coupling that exist due to the different orthotropic material properties of each layer. It will also be demonstrated that these ele ments are capable of adequately predicting the displacements and the stresses for a variety of composite plate problems.

Application of Composite Plate Theory and the Finite Element Method to the Dynamics and Stress Analysis of Spatial Flexible Mechanical Systems

This investigation concerns itself with the dynamic and stress analysis of thin, laminated composite plates consisting of layers of orthotropic laminae. It is assumed that the bonds between the laminae are infinitesimally thin and shear nondeformable. The finite element formulation presented is sufficiently general to accept an arbitrary number of layers and an arbitrary number of orthotropic material property sets. In the dynamic formulation presented, the laminae is assumed to undergo large arbitrary rigid body displacements and small elastic deformations. The nodal shape functions of the laminae are assumed to have rigid body modes that need to describe only large rigid body translations. Using the expressions for the kinetic and strain energies, the lamina mass and stiffness matrices are identified. The nonlinear mass matrix of the lamina is expressed in terms of a set of invariants that depend on the assumed displacement field. By summing the laminae kinetic and strain energies, the body mass and stiffness matrices are identified. It is shown that the body invariants can be expressed explicitly in terms of the invariants of its laminae. Numerical examples of a spatial RSSR mechanism are presented in order to demonstrate the use of the present formulation.

Stability of variably thick orthotropic annular plates

The static and dynamic stability of variably thick orthotropic annular plates subjected to in-plane periodic forces with respect to time is studied. It is assumed that the periodic radial forces with the same period act along both the inner and outer edges of plate. The finite element method is used with a sector element based on the Mindlin plate theory. The wave propagation technique of cyclic symmetry is used in the formulation. The choice of the element enables the analyst to solve the axi-symmetric and asymmetric dynamic stability problem at the same time. Variations in the plate thickness in which it increases or decreases in the radial direction according to the equations h = h max ( r r o ) +λ or h = h max ( r r i ) −λ , respectively are considered. The instability regions for different boundary conditions are determined by Bolotin's method. It is found that the critical buckling load, buckling mode and instability regions are changed by variations in the polar orthotropic material properties.

Generalized plane strain analysis of solenoid magnets

A stress analysis assuming generalized plane strain conditions is presented for a solenoid magnet with orthotropic material properties. Analytic expressions are provided for the longitudinal, radial and axial stress and strain valid in a neighborhood of the mid-plane of a long solenoid. Calculations are made for an example magnet with multiple coil sections and external reinforcement. The results of generalized plane strain and finite element methods are compared with plane stress and plane strain analyses.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

IMPROVING DESIGN OF NATURAL DRAUGHT COOLING TOWERS AGAINST BUCKLING FAILURE

Abstract In this paper the buckling of hyperbolic cooling towers containing different forms of stiffening is presented. Stiffeners are sufficiently close in spacing that the stiffened shell may be modelled as a shell having homogeneous and orthotropic material properties. Analysis is completed by means of a finite element numerical method. The numerical results for critical loads and modes of the cooling towers with different stiffening types are described and compared with those of an equivalent weight smooth tower. A systematic examination of the contribution to strain energy is shown to elucidate the physical behaviour and demonstrate how the various stiffness components of shell and stiffeners affect the critical load spectra and the associated modes. Not only does this analysis provide a clear explanation of how the addition of different stiffening types affect the critical load spectra, but also suggests an effective design procedure for optimizing material efficiency.

Stresses and strains in hemispherical GRP pressure vessels with radial cylindrical branch connections

Experimental strain distributions are presented for two 1 m diameter chopped strand mat glass-fibre-reinforced polyester hemispherical pressure vessels with 200 mm diameter radial branch connections. One vessel had local reinforcement around the branch. The results are compared with theoretical predictions from computer programs based on thin-shell theory (BOSOR4) and axisymmetric solid finite element analysis (PAFEC, ASAS). The finite element approach is shown to give good agreement with experimental results when detailed information of the shape of the branch hemisphere junction is provided. In-plane and through-thickness stresses and strains are examined in detail for internal pressure and a radially outward load applied to the end of the branch. Fine finite element meshes are necessary for accurate prediction of through-thickness stresses at the junction. Orthotropic material properties are considered. Delamination occurred at the junction due to through-thickness tensile stresses, but for internal pressure loading the final fracture was due to in-plane stresses.

Delamination toughness computation for curved thermoplastic composites

The curved double cantilever beam (CDCB) test is a method used to characterize mode I delamination toughness of curved composite materials, fabricated by filament winding technology. A finite element model for this geometry is presented, that takes into consideration nonlinear deformational effects, orthotropic material properties and local mixed mode load at crack-tip. It can be used as the theoretical basis for analysis of experimental results. Especially for long cracks, compliant materials and thin samples large deflection should not become neclected in the modelling. In spite of its highly unsymmetrical geometry the crack tip loading state proved to be nearly pure mode I.

A New Probe for Characterizing Elliptically Polarized Microwave Fields

Recent research advances into applying microwave technology to characterize the physical properties of various orthotropic materials have created the need to identify elliptically polarized electromagnetic fields rapidly and efficiently. This paper presents a new microwave probe design consisting of multiple dipoles. The new probe has the capability to measure field information along different directions. Thus, the direction of the major and minor axes of the electric field ellipse can be determined together with the ratio of the two principalfield amplitudes without mechanical movement. This paper presents the theoretical basis for a new probe, and illustrates its use through an application example involving wood property measurement.

Effective Flange Width for Stress‐Laminated T‐System Timber Bridges

Stress-laminated T-system timber bridges consist of laminated deck sections combined with glued-laminated timber beams compressed transversely with high-strength steel bars. In the design of these structures, a deck-and-beam T-section is isolated and analysed as a T-beam. This paper presents a regression equation for the computation of effective flange width for stress-laminated T-system timber bridges; a width over which the normal stress can be assumed constant. Using actual dimensions, orthotropic material properties, and AASHTO truck loads, 125 bridge models were analyzed by a special finite element program for general anisotropic shell-and-beam-type structures. The results of the analysis were used to conduct a parametric study followed by a regression analysis to develop a prediction equation for the computation of effective flange width. Simplified equations for the computation of the effective width, which are within current upper and lower bound elasticity solutions, are proposed for use in design.

Finite-rotation theories for composite laminates

For the finite-element analysis of arbitrary composite laminates various finite-rotation theories are presented in a single formulation. First a refined theory is derived which allows a quadratic shear deformation distribution across the thickness. The so-called difference vector appearing in the kinematic relations is expressed in terms of rotational degrees of freedom permitting a clear determination of the deformed normal vector in every nonlinear range. The constitutive relations derived are applicable to orthotropic material properties varying arbitrarily across the thickness and to curvilinear laminate coordinates as well. This refined theory is then transformed into simplified theories of Kirchhoff-Love and Mindlin-Reissner types. Finally, the last formulation is used to formulate a layer-wise theory able to grasp the shear deformations very accurately. Kinematic relations and the corresponding constraints are presented in two alternative forms suitable for the application of isoparametric and classical finite-element formulations.

THE ANALYSIS OF FREE VIBRATION OF STIFFENED COOLING TOWERS

Abstract The present paper studies the dynamic characteristics of hyperbolic cooling towers with various types of stiffening. Stiffeners in both the meridional and circumferential directions are assumed to be sufficiently close that analysis may be simplified to that of a shell with orthotropic material properties. Analysis is completed by means of finite element numerical methods. Numerical results for vibration frequencies and modes of the cooling towers with various stiffening types are given, and compared to those of an unstiffened tower and an equivalent weight smooth tower. For each case a systematic examination of the contribution to strain energy, arising from the various components of the stiffeners and the shell, allows insights into the physical significance of the various stiffener types and predictions of how they influence the frequency spectra of cooling towers.

Post-buckling behaviour of circular plates resting on an axi-symmetric elastic partial foundation under uniform compressive loads

Finite element results for the post-buckling behaviour of circular plates resting on an axi-symmetric elastic partial foundation are presented. Orthotropic material properties and different configurations of foundations are considered to evaluate the linear critical loads and nonlinear loads.

Refined shear-deformation models for composite laminates with finite rotations

For arbitrary multilayered shell structures made particularly of composite material layers a refined finite-rotation theory with seven independent displacement variables is developed, approximating the displacement field by a cubic series expansion of thickness coordinates. This model allows a quadratic shear deformation distribution across the thickness. Procedures are given permitting a unique determination of the first order displacement term in the case of finite rotations. Kinematic relations are formulated in two alternative forms suitable for both classical and isoparametric finite element formulations. The constitutive relations presented model orthotropic material properties varying arbitrarily across the thickness. This third order single-layer theory is then transformed, by introducing further constraints, into three simplified models : a third order theory with five independent displacement variables, a Mindlin-Reissner type theory and a Kirchhoff-Love type theory. These four models differ, however, from each other essentially in the constraints imposed on the first and third order displacement variables : a significant advantage for a unified finite element development. Finally, the Mindlin-Reissner type theory is generalized to a layer-wise model being the most predictive one in dealing with local interlaminar effects. The theoretical models are transformed into adequate finite shell elements and then compared by means of appropriate examples concerning their prediction capability. Also examples are given demonstrating their applicability to finite-rotation phenomena.

Thermal Stress and Deformation of a Cross-Ply Laminated Rectangular Plate due to Partial Heating.

This paper is concerned with a theoretical treatment of thermal stress and thermal bending problems involving a multilayered anisotropic laminated plate due to partially distributed heat supply in a transient state. As an analytical model, we consider a laminated rectangular plate consisting of an orthogonal pile of layers having orthotropic material properties, i. e. a cross-ply laminate. By introducing the methods of finite consine transform and Laplace transform for the temperature field, we obtain the three-dimensional temperature solution with the aid of the residue theorem and evaluate the characteristic behavior of thermal stress and thermal deformation of a simply supported plate in a transient state using the classical plate theory based on Kirchhoff-Love's hypothesis. As an example, we carry out numerical calculations for a 5-layered cross-ply laminate and closely examine the numerical results.

Analysis of Microfabricated Textured Multicrystalline Beams: II. Probabilistic Approach

ABSTRACTThis paper reports on detailed approaches to the probabilistic modelling and analysis of multicrystalline microfabricated beams in the context of micro-electromechanical systems (mems) using simulation techniques. Random, textured multicrystalline beam structures are simulated and analyzed using the finite element method, employing randomly oriented orthotropic material properties to model each individual crystal grain.The simulation studies are used to assess the influence of size effects and texture on overall beam characteristics, such as stiffness. Results of these studies are then compared with the current approaches based on deterministic analysis and employing simplifying assumptions such as homogeneous, isotropic material properties, and with results obtained from the homogenization approach of Part I.

P-Version axisymmetric solid element for heat conduction

A nine-node two-dimensional axisymmetric solid element is presented for linear steady state axisymmetric heat conduction where the temperature field in the ξ and η directions of the element can be of arbitrary polynomial orders p ξ and p η . This is accomplished by first constructing the one-dimensional hierarchical approximation functions and the corresponding nodal variable operators in the ξ and η directions using Lagrange interpolating polynomials and then taking the product (sometimes also called tensor product) of these hierarchical one-dimensional approximation functions and the corresponding nodal variable operators. The resulting approximation functions and the nodal variables are hierarchical, i.e. the element approximation functions and the nodal variables corresponding to the polynomial orders p ξ and p η are a subset of those corresponding to the polynomial orders p ξ + 1 and p η + 1 and as a consequence the element matrices and the equivalent nodal heat vectors are hierarchical also. The formulation ensures C 0 continuity, i.e. the continuity of the temperature across the interelement boundaries is guaranteed. The weak formulation of the Fourier heat conduction equation in the cylindrical coordinate system r, z is constructed and the element properties are derived using the weak formulation (or the associated quadratic functional) and the hierarchical temperature approximation for the element. The element formulation permits isotropic as well as generally orthotropic material properties. The formulation allows distributed heat flux, convective boundaries and internal heat generation. Numerical examples are presented to demonstrate the accuracy, simplicity of modeling, faster convergence rate and overall superiority of the present formulation over existing isoparametric axisymmetric solid elements. For each example the results obtained from the present formulation are compared with available analytical solutions and h-models employing isoparametric elements. Convergence graphs showing the rates at which the errors are decreasing are presented for both h and p-models. The results obtained from the present formulation exhibit excellent accuracy, faster convergence rate and require extremely simple models.

Determination of directional dependence of orthotropic material properties in a mandible

Determination of directional dependence of orthotropic material properties in a mandible

Symmetric and Asymmetric Dynamic Buckling of Laminated Thin Shells with the Effect of Imperfection and Damping

The emphasis of this paper is to use a thin shell finite element to study the dynamic buckling behavior of a class of thin shell problems due to the effects of three parameters with design significance: (1) axisymmetric and asymmetric imperfections; (2) orthotropic and anisotropic material properties; and (3) Rayleigh viscous damping. Five types of thin shells were considered: (1) an orthotropic annular spherical cap; (2) an ortho tropic, axisymmetrically imperfect, whole spherical shell; (3) an axially compressed, laminated, asymmetrically imperfect, cylindrical shell; (4) an orthotropic, axisym metrically imperfect, spherical cap; and (5) an orthotropic, asymmetrically imperfect, spherical cap. While some basic results are compared with available solutions, extensive new results are also presented. The results quantify the effect of amplitude of imperfec tions, which can significantly reduce the dynamic buckling load. The results also quantify the effects of orthotropic material parameter and viscous damping.