Abstract:In this work, a new high-order displacement-based method is proposed to investigate stresses and strains in thick arbitrary laminated orthotropic cantilever straight tubes under transverse loading. The most general displacement field of elasticity for an arbitrary thick laminated orthotropic straight tube is developed. A layer-wise method is employed to analytically determine the local displacement functions and stresses under transverse loading. The accuracy of the proposed method is subsequently verified by … Show more
“…The experimental results correlate to the analytic bending stiffness by Jolicoeur and Cardou (1994), but with only two specimens the experiment does not provide an adequate statistical coverage. Sarvestani et al (2016) presented a new high-order displacement-based method for thick cantilever tubes under transverse loading, which has a good match with the experimental data, which are generated with a three-point bending test, FEM and the Lekhnitskii (1963) solution with a [0°] composite tube, because Lekhnitskii only examines single layer cylinders with monolithic homogeneous orthotropic cylindrical shells. The method was also based on the equation of Lekhnitskii (1963), but they used a layer-wise theory with Lagrangian linear interpolation functions, because of the thick composite tubes, and using the principle of minimum total potential energy to get the equilibrium equations of a laminated orthotropic straight tube.…”
Fiber-reinforced plastic (FRP) tubes are used in many different industries, such as electrical engineering and pipeline construction. The tubes are frequently subjected to bending loads, depending on the application. In order that the dimensioning of the tubes can be ensured, analytical bending models are used to calculate the resulting stresses, strains and displacements in the individual layers of the laminate. This enables the making of a statement about the failure of the fiber-reinforced tube by choosing an appropriate failure criterion. For the use of these bending models, it is necessary to understand the respective underlying theory. The theory provides the basis for the mathematical description of the mechanical properties for a single-layered tube and using the relationships between the stresses and strains that occur in the Cylindrical coordinate system for this calculation step. For this reason, a redefinition of the compliance matrix from the transformation about the winding angle to the Cylindrical coordinate system and a modification of the stress and strain vectors is necessary, because the defined Cartesian coordinate system of the model cannot be used for wounded FRP tubes. The transformation causes an exchange of entries in the compliance matrix, which remain in the correct relationship between the particular stress and strains. This step is not specified and may lead to incorrect results due to the incorrect entry of compliances. The present publication refers to sketch on this issue and represent a simplification of the changeover to the level required by the bending models notation of vectors in the form of a permutation. In addition, a new name for the pre-acquisition of the redefined compliances is given to prevent confusion when entering the material law of a bending model. Finally, the permuted and redefined compliances are proved in an example to determine their accuracy.
“…The experimental results correlate to the analytic bending stiffness by Jolicoeur and Cardou (1994), but with only two specimens the experiment does not provide an adequate statistical coverage. Sarvestani et al (2016) presented a new high-order displacement-based method for thick cantilever tubes under transverse loading, which has a good match with the experimental data, which are generated with a three-point bending test, FEM and the Lekhnitskii (1963) solution with a [0°] composite tube, because Lekhnitskii only examines single layer cylinders with monolithic homogeneous orthotropic cylindrical shells. The method was also based on the equation of Lekhnitskii (1963), but they used a layer-wise theory with Lagrangian linear interpolation functions, because of the thick composite tubes, and using the principle of minimum total potential energy to get the equilibrium equations of a laminated orthotropic straight tube.…”
Fiber-reinforced plastic (FRP) tubes are used in many different industries, such as electrical engineering and pipeline construction. The tubes are frequently subjected to bending loads, depending on the application. In order that the dimensioning of the tubes can be ensured, analytical bending models are used to calculate the resulting stresses, strains and displacements in the individual layers of the laminate. This enables the making of a statement about the failure of the fiber-reinforced tube by choosing an appropriate failure criterion. For the use of these bending models, it is necessary to understand the respective underlying theory. The theory provides the basis for the mathematical description of the mechanical properties for a single-layered tube and using the relationships between the stresses and strains that occur in the Cylindrical coordinate system for this calculation step. For this reason, a redefinition of the compliance matrix from the transformation about the winding angle to the Cylindrical coordinate system and a modification of the stress and strain vectors is necessary, because the defined Cartesian coordinate system of the model cannot be used for wounded FRP tubes. The transformation causes an exchange of entries in the compliance matrix, which remain in the correct relationship between the particular stress and strains. This step is not specified and may lead to incorrect results due to the incorrect entry of compliances. The present publication refers to sketch on this issue and represent a simplification of the changeover to the level required by the bending models notation of vectors in the form of a permutation. In addition, a new name for the pre-acquisition of the redefined compliances is given to prevent confusion when entering the material law of a bending model. Finally, the permuted and redefined compliances are proved in an example to determine their accuracy.
“…Derisi (2008) designed and manufactured composite straight tubes and performed four-point bending tests to determine the strains to failure of different laminates. Recently, a method for the stress analysis of thick composite straight tubes subjected to cantilever loading was developed (Yazdani Sarvestani et al, 2016a, 2016b. Now, in order to provide some insight into the mechanical behavior of the curved part of the helicopter landing gear, a simple-input displacementbased method is developed to examine stresses in a composite curved tube.…”
“…The cylindrical coordinates ( x , θ , r ) are placed at the middle surface of the composite tube where x and r are the axial and radial coordinate, respectively. The appropriate integration of the linear strain–displacement relations of elasticity, within cylindrical coordinate system yields the most general form of the displacement field for the k th layer of thick-laminated composite straight tubes as 18,19 where u1(k)(x,θ,r), u2(k)(x,θ,r) and u3(k)(x,θ,r) represent the displacement components in the x , θ and r directions, respectively, of a material point located at ( x , θ , r ) in the k th ply of the laminated composite tube in Figure 2. Figure 2.The geometry of a composite straight tube and the coordinate system.…”
Section: Theoretical Formulationmentioning
confidence: 99%
“…17 A method to obtain stress distributions of the composite cantilever straight tube was developed. 18,19…”
Analysis and design of composite helicopter landing gears are challenges. Cross tubes of helicopter landing gears consist of straight tubes at the middle and curved tubes at the sides. In this work, to simulate ground handling, thick laminated composite straight tubes subjected to pure bending moments are studied using a new high-order simple-input analytical method. The accuracy of the proposed method is subsequently verified by comparing the numerical results obtained using the proposed method with finite element method and experimental data. The results show good agreement. High efficiency in terms of computational time is achieved when the proposed method is used as compared with finite element method. In addition, a simple non-dimensional coefficient is proposed to predict interlaminar radial stresses of thick composite straight tubes.
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