Shear Extension Coupling Research Articles

Experimental investigation of shear-extension coupling effect in anisotropic reinforced concrete membrane elements

Performance based analysis under seismic loads using the finite element method for wall-type reinforced concrete (RC) members in buildings and in important structures like liquid retaining structures, nuclear containment structures, offshore concrete gravity structures etc., necessitates the understanding of the non-linear behaviour of the constituent membrane elements. The current orthotropic formulation of the softened membrane model (SMM) can be strictly used only when the reinforcement is symmetric to the principal axes of applied stresses. When the reinforcement is asymmetric, shear strain is generated due to the normal stresses in the principal axes of applied stresses, which is referred to as shear-extension coupling. An anisotropic formulation is required to capture the generated shear strain. The current study quantifies the shear strain due to asymmetry in reinforcement, by testing panels under biaxial tension-compression using a large-scale panel testing facility. A model for the shear strain is proposed based on the tests data. The paper presents the experimental programme, important test results and the modelling of shear strain. Expression developed for the shear strain can be incorporated in the solution algorithm of the SMM for improved prediction of the shear behaviour of a membrane element. This further aids in accurate prediction of the seismic performance of the important structures mentioned earlier.

Analytical model for stress and deformation of multiple-winding-angle filament-wound composite pipes/vessels under multiple combined loads

An multi-angle filament wound(FW) model is proposed under pressure, torsion and axial loads (multiple combined loads), which can calculate stresses and displacements of arbitrary multi-layers and bring more uniform strength though FW wall thickness. Based on orthotropic constitutive relation and axisymmetric thick-walled cylinder theory, a three-dimensional (3D) analytical solution for deformations and stresses of multi-angle FW pipes/vessels is presented. First, the stresses of fiber layer in cylindrical coordinate are obtained. Then, the deformations and stresses of each orthotropic winding layers, including longitudinal stresses σ1, transverse stresses σ2, σ3 and shear stresses τ12 are obtained, respectively. Moreover, the effect of shear extension coupling is taken into consideration because it is impossible for the ±ϕ winding angles to exist in the same radius. Subsequently, the proposed formulae are verified by numerical and experimental examples with finite element method (FEM). Results show that our new method calculates accurate stresses of FW pipes/vessels under multiple combined loads, which provides a theoretical foundation for damage analysis and optimization for FW structures.

Emergence of tangential stiffness through the use of inclined orthotropic material

A flexible bearing support structure is effective for stabilizing the self-excited vibration of a bearing, such as oil whirl. The stabilization effect is increased if the structure has static tangential stiffness, where the reaction force is perpendicular to the displacement. In this study, it is shown that a support component made of inclined orthotropic material, which exhibits shear–extension coupling, can have tangential stiffness. The circumferential average of the tangential stiffness was found to vanish with a rotationally symmetric configuration of these components because the tangential forces of each component cancel out. However, the tangential force was recovered by allowing separation on the contact surface. A circular formation of an inclined orthotropic sheet that shows an axisymmetric stiffness matrix is proposed. Theoretical and numerical analyses clarified the effects of the friction coefficient, fitting interference, and degree of anisotropy of the material. Zero interference was found to be the best condition to maximize tangential stiffness.

Mechanical behavior of pressurized composite pipes made of various materials

Abstract In this study, multi-layered composite pipes with varied orientation angles and subjected to internal pressure were investigated by using the 3-D finite element method (FEM) and through experimental tests. The composite pipes were made of E-glass and T300/934 carbon fiber. The studies were carried out experimentally, analytically and numerically. The T300/934 carbon fiber reinforced composite pipes and E-glass reinforced composite pipes were given numerical model codes via ANSYS 14.5 software. These models were then compared with analytical results in the literature and with the experimental results. Finite element analyses (FEA) were carried out to predict failure loads. Each layer of the composite pipes was numerically examined from various orientation angles. Hoop and shear stress wereobtained numerically for each layer. Radial strain and radial stress were achieved in the radial direction of the composite pipes. Shear extension coupling was considered because the layup angles with + θ and - θ layers were in varied radii. Subsequently, the effects of the orientation angles were examined for all models. Moreover, it was found that an embedded adhesive joint is important for industrial applications.

Mechanical behavior of pressurized composite pipes made of various materials

Abstract In this study, multi-layered composite pipes with varied orientation angles and subjected to internal pressure were investigated by using the 3-D finite element method (FEM) and through experimental tests. The composite pipes were made of E-glass and T300/934 carbon fiber. The studies were carried out experimentally, analytically and numerically. The T300/934 carbon fiber reinforced composite pipes and E-glass reinforced composite pipes were given numerical model codes via ANSYS 14.5 software. These models were then compared with analytical results in the literature and with the experimental results. Finite element analyses (FEA) were carried out to predict failure loads. Each layer of the composite pipes was numerically examined from various orientation angles. Hoop and shear stress wereobtained numerically for each layer. Radial strain and radial stress were achieved in the radial direction of the composite pipes. Shear extension coupling was considered because the layup angles with + θ and - θ layers were in varied radii. Subsequently, the effects of the orientation angles were examined for all models. Moreover, it was found that an embedded adhesive joint is important for industrial applications.

Active control of adaptive thin-walled beams incorporating bending-extension elastic coupling via piezoelectrically induced transverse shear

Abstract Problems related to mathematical modeling and active control of adaptive composite thin-walled beams incorporating lateral bending-extension elastic coupling and piezoelectrically induced transverse shear-extension actuation coupling are considered. The adaptive capabilities are provided by anisotropic piezo-actuators embedded into the host structure. Based on classical negative velocity feedback control and linear-quadratic regulator optimal control, the control authority played by the directionality property of piezo-actuators on vibration suppression is discussed, considering in conjunction with that of the structural tailoring. The results show that the control strategy based on the piezoelectrically induced transverse shear-extension coupling can be more efficient than that based on the piezoelectrically induced bending. In addition, the control effectiveness based on the piezoelectrically induced transverse shear is sensitive to the bending-extension elastic coupling.

Mechanical behavior of internal pressurized composite pipes jointed with embedded tubular sleeves

Abstract In this paper, composite pipes bonded with embedded tubular sleeve subjected to internal pressure were analyzed by using the three dimensional finite element method (FEM). In the analysis, the composite pipes and sleeves are made of carbon/epoxy (AS4/3501-6) with different fiber orientation angles and DP 410 is the adhesive. The shear extension coupling of composite pipe and patch was considered because the lay-up angles with +θ and –θ layers were in different radii. The models for the numerical analyses were generated by using the ANSYS software package. The finite element analyses (FEA) were carried out to predict the failure loads. Radial, tangential, axial and shear stress values were obtained via numerical analyses on composite pipes and adhesive layers. In addition, the von Mises stress distributions on the adhesive were obtained. Consequently, the effects of orientation angles, overlap widths and adhesive layer were examined. The most effective parameters were determined for composite pipes adhesively bonded with embedded tubular sleeve.

Stress analysis of multi-layered hybrid composite pipes subjected to internal pressure

The stress analysis of multi-layered hybrid composite pipes with symmetrical orientation angles, under internal pressure, was investigated. The codes of numerical models were created in ANSYS software for numerical analyses. Two inner surfaces of first model are E-glass fiber/epoxy and two outer surfaces of its are carbon/epoxy (AS4/3501-6). Inner surfaces of second model are carbon/epoxy (AS4/3501-6) and outer surfaces of its are E-glass fiber/epoxy. The problem was studied using a computational tool based on the Finite Element Method (FEM). Each layer of the composite pipes was examined with different orientation angles. T he hoop and shear stresses were obtained numerically for each layer. Also, radial, tangential, axial and shear stresses were determined in the thickness direction of the composite pipes. The shear extension coupling was considered because the lay-up angles with [+ θ, – θ] s layers were in the different radii.

Standardized Compliance Matrices for General Anisotropic Materials and a Simple Measure of Anisotropy Degree Based on Shear-Extension Coupling Coefficient

The compliance matrix for a general anisotropic material is usually expressed in an arbitrarily chosen coordinate system, which brings some confusion or inconvenience in identifying independent elastic material constants and comparing elastic properties between different materials. In this paper, a unique stiffest orientation-based standardized compliance matrix is established, and 18 independent elastic material constants are clearly shown. During the searching process for the stiffest orientation, it is interesting to find from our theoretical analysis and an example that a material with isotropic tensile stiffness does not definitely possess isotropic elasticity. Therefore, the ratio between the maximum and minimum tensile stiffnesses, although widely used, is not a correct measure of anisotropy degree. Alternatively, a simple and correct measure of anisotropy degree based on the maximum shear-extension coupling coefficient in all orientations is proposed. However, for a two-dimensional constitutive relation, both the stiffness ratio and the shear-extension coupling coefficient can be adopted as proper measures of anisotropy degree.

Experimental failure testing and repair of internal pressurized composite pipes using different fracture models

Abstract The failure testing and repair of composite pipes using different fracture models and different orientation angles under internal pressure was experimentally investigated. Patches with different dimensions were made from composite material for repair. Fracture models on composite pipes were created for three different angles. These are horizontal crack, vertical crack and inclined crack. Adhesive layers created by using DP 410 for repair and failure testing of the composite pipes with different fractures were carried out. Failure loads were obtained from experimental tests. The shear extension coupling of composite pipe and patch was considered because the lay-up angles with + θ and – θ layers were in different radii. Effects of orientation angles and types of fracture models were investigated regarding interaction between the pipe, the adhesive and the patch. The most effective patch width and orientation angles were determined.

Determination of in-plane elastic constants of angle ply laminates from tensile measurements

This paper presents a new method to completely characterise the in-plane elastic properties of an important type of angle ply laminates using only unidirectional tests. The angle ply laminates having the same number of identical plies are considered. Some new results for orthotropic laminates are found using this technique, namely, the conditions of existence of a particular direction in which there is no shear extension coupling. The laminates are subjected to three tensile tests: two in the orthotropic axes and the third one in a particular direction. The results allow a complete semiexperimental characterisation of the angle ply laminate, which do not need a priori knowledge of the elastic properties of the constitutive layer. Comparisons are made between numerical predictions and experimental results. Finally, the computational results were compared to the experimental results, verifying the capability of the method in order to predict the in-plane elastic properties of composite laminates.

Indentation Analysis of In-Plane Prestressed Composite Sandwich Plates: An Improved Contact Law

In this article a closed form solution is derived for the deformation response of a composite sandwich plate subjected to static indentation of a flat-ended cylindrical indenter. The facesheet deflection is several times the laminate thickness so that bending moments may be neglected and only membrane forces are considered in the facesheet. In contrast to the existing analytical model for the indentation of composite sandwich plates, in the present model, the stacking sequence of the facesheets can be completely arbitrary, so that the shear-extension coupling terms, i.e. and , can also be included in the analysis. Furthermore, in the present model the effects of the initial in-plane normal and shear stresses on the edges of the sandwich plate are also considered. An improved contact law is derived based on the minimum total potential energy principle. The elastic strain energy, the plastic work dissipated in crushing the core and the external work are calculated using an appropriate shape function for the facesheet deflection. The relations between the indentation load and the deflection and length of deformation are obtained by minimization of the total potential energy. Analytical predictions of the load-indentation response compare well with experimental results. The effects of stacking sequence, ply thickness, number of layers and initial in-plane forces on the load-indentation response are studied and discussed.

Dynamic analysis of multi-layered filament-wound composite pipes subjected to cyclic internal pressure and cyclic temperature

Based on the three-dimensional anisotropic elasticity, the stress analysis of multi-layered filament-wound composite pipes subjected to cyclic internal pressure and temperature loading is conducted in this article. The time-dependent stress, strain and deformation distributions are numerically obtained by the use of the finite difference technique. The pressure and temperature are considered to be symmetrical about the axis of the cylinder and independent of the axial coordinate. Each layer of the pipes is made of a homogeneous, anisotropic and linearly elastic material and it is assumed that the material properties do not change with increasing the temperature. The shear extension coupling is also considered because of lay-up angles. Numerical results obtained from the present model are compared with other published results and good agreement has been achieved.

Analysis of multi-layered filament-wound composite pipes under combined internal pressure and thermomechanical loading with thermal variations

The composite pipes manufactured by filament winding technology have anisotropic behavior owing to different reinforced ply angles. Composite pipes can be exposed to the thermomechanical loading due to hot fluid that flows into them. In this paper, based on the three-dimensional anisotropic elasticity, an exact elastic solution for thermal stresses and deformations of the pipes under internal pressure and a temperature gradient has been studied. Giving heat convection conditions the variation of temperature field within the pipe is obtained by solving the conduction equation at the wall. The influence of temperature field in the governing equations of thermoelasticity has been considered via a constitutive law. The shear extension coupling is also considered because of lay-up angles. Stress, strain and deformation distributions for different angle-ply pipe designs are investigated using the present theory.

Complete In-plane Elastic Characterisation under Tensile Tests of Angle-Ply Laminates Composed of Polymer-Matrix Layers

In this paper we present a new strategy to completely characterise the in-plane elastic properties of a large range of angle-ply laminates using only unidirectional tests. We consider laminates having the same number of identical plies in the α and – α directions. This new method uses some preceding results found by Verchery for orthotropic laminates, namely the conditions of existence of a specific direction ω, in which the shear-extension coupling is null. The characterisation of the laminate is then made using the results of three tensile tests: two in the orthotropy axes, and the third one in the ω direction, in order to have always a pure one-dimensional state of stress. We show that for the most common unidirectional fibre-reinforced materials, the angle ω is, in most cases, close to the α direction of the fibres. This result permits a complete experimental characterisation of the laminate, which then does not need any a priori knowledge of the elastic properties of the elementary layer. In addition, it provides a simple method to verify the predictions of the laminate behaviour obtained by the Classical Laminated Plate Theory (CLPT) when the elementary layer is completely known. The paper ends with numerical examples and with the results of some experimental tests.

Analysis of multi-layered filament-wound composite pipes under internal pressure

Composite pipes in this study are composed of multi-layered filament-wound (FW) structures. Each layer of the pipes is assumed to be anisotropy. Based on the three-dimensional (3-D) anisotropic elasticity, an exact elastic solution for stresses and deformations of the pipes under internal pressure is presented. Moreover, detailed stress and strain distributions for three given angle-ply pipe designs are investigated by using the present theory. The shear extension coupling is also considered because the lay-up angles with + φ and − φ layers cannot exist in the same radius. For cylindrical-pressure vessels with different angle-ply pipe, the ratio of applied hoop-to-axial stress in each layer is different. Even if quite a thin-walled pipe, the ratio of hoop-to-axial stress is no longer a constant of 2:1.

Determination of the Mechanical Properties of Composite Materials by Tensile Tests. Part I: Elastic Properties

Elastic constants as measured by means of tensile tests at different angles, are interrelated by the transformation rules. Based on these rules, a new data evaluation scheme is proposed to make tensile test data consistent. It also offers a way to measure the shear modulus and the shear-extension coupling constants by simple tensile tests. The method is applicable for all types of anisotropic materials. For strong anisotropy, the end-constraint effect can be accounted for in an iterative way. As an example, results are shown for a glass/epoxy woven fabric composite and for knitted fabric composites with monoclinic and triclinic symmetry. Next, the optimal test design is looked for: which tensile tests have to be performed to get the best estimate of the elastic constants? This problem is addressed both theoretically and by means of simulations for the case of woven and knitted fabric composites.

Effect of Loading Parameters on Damage-Induced Shear-Extension Coupling in Laminate

The shear extension coupling due to damage in an initially balanced laminate was studied using a damage evolution model developed by the authors. The effects of complex loading application and loading rate and deviation were investigated. It was shown that the combination of shear loading with uniaxial or biaxial tension and compression reduces shear extension coupling when the longitudinal to shear loading ratio is sufficiently high

Effect of loading parameters on damage-induced shear-extension coupling in laminate

Effect of loading parameters on damage-induced shear-extension coupling in laminate

The Influence of Layer Waviness on the Stress State in Hydrostatically Loaded Cylinders: Failure Predictions

This paper extends the work of two previous papers by using the stress analysis techniques described in those papers to predict the failure pressure of imperfect thick multilayer composite cylinders, the imperfection being due to layer waviness. The past work is briefly reviewed and then the discussion focuses on failure predictions. The maximum stress failure criterion is used. Waves of varying length and amplitude are con sidered. Failure pressures in the presence of waviness are compared with failure pressures for perfect cylinders. Failure mode and location are predicted. Residual thermal stresses due to curing are included in the analysis. The results indicate that the primary modes of failure are fiber compression or interlaminar shear. Fiber compression stresses are aggravated due to the eccentricities associated with waviness. Interlaminar shear stresses occur due both to the geometry of the wave, and to the shear-extension coupling associated with local anisotropy of the material. A third failure mode, interlaminar normal tension, is also possible. Residual thermal stresses influence failure to some degree. Finally, it is shown that because of the higher stresses at the inner radial location of a thick cylinder, mild levels of waviness occurring away from the inner radial location have no influence on failure.