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We study experimentally the axial crushing behavior and crashworthiness characteristics of thin-walled steel tubes containing annular grooves. The grooves determine the positions of the folds and control the buckling mode of deformation. In the present work we aim to improve the uniformity of the load-displacement behavior and to predict the energy absorption capacity of the tubes. Grooves are cut circumferentially and alternately inside and outside the tubes at predetermined intervals. Quasi-static axial crushing tests are performed with different groove distances. Photographs are taken during axial buckling and the specimens after crushing are sectioned axially to carry out the... 

In the present study, crashworthiness characteristics of thin-walled steel tubes containing annular grooves are studied. For this purpose, the grooves are introduced in the tube to force the plastic deformation to occur at predetermined intervals along the tube. The aims are controlling the buckling mode and predicting energy absorption capacity of the tubes. To do so, circumferential grooves are cut alternately inside and outside of the tubes at predetermined intervals. Quasi-static axial crushing tests are performed and the load-displacement curves are studied. Theoretical formulations are presented for predicting the energy absorption and mean crushing load. It is found a good agreement... 

The initial buckling load of a tube corresponds to the peak load in the first buckling cycle. In practice, this load is very important for crashworthiness design that gives an indication of the force required to initiate collapse and hence begin the energy absorption process. In this paper, the effects of grooves on the initial buckling load of thin-walled tubes under axial compression are investigated. The grooves are introduced in the tube to force the plastic deformation to occur at predetermined intervals along the tube. The aims are improve the uniformity of the load-displacement behaviour of axially crushed tubes, predict and control the collapse load of the tube. An analytical study... 

In this paper, the nonlinear cylindrical bending of a functionally graded plate is studied. The material properties of the plate are assumed to be graded continuously in the direction of thickness. The variation of the material properties follows a simple power-law distribution in terms of the volume fractions of constituents. The von Karman strains are used to construct the nonlinear equilibrium equations of the plates subjected to in-plane and transverse loadings. The governing equations are reduced to linear differential equation with nonlinear boundary conditions yielding a simple solution procedure. The results show that the functionally graded plates exhibit different behavior from... 

This article investigates the free vibration of the rotating, tapered, thin-walled, composite box beam. The structural model incorporates a number of non-classical effects, such as transverse shear, warping inhibition, non-uniformtorsional model, and rotary inertia.The results obtained in this article seek to clarify the effect of flap-twist coupling, taper ratio, slenderness ratio, angular velocity, fibre orientation, and hub ratio on natural frequencies and mode shapes of the rotating thin-walled composite beams. The results are expected to offer better predictions of the vibrational behaviour of these kinds of structures in general, and in the design of rotor blades of turbo machinery, in... 

An investigation of the possible performance improvements of thin walled composite beams through the use of the variable stiffness concept with curvilinear fiber is presented. The beams are constructed from a single-cell closed cross section and a number of non-classical effects such as material anisotropy, transverse shear, warping inhibition and nonuniform torsional model are considered in the beam model. The governing equations were derived by means of the extended Hamilton's principle. Also the extended Galerkin's method is used to solve governing equations. Composite beams subjected to different loading with given geometry and material properties are optimized for maximum failure load.... 

The equilibrium governing equations of nonlocal anisotropic thin-walled circular cylindrical shell under combined axial compressive force, torsional load, and external pressure are explicitly derived. This is accomplished by appropriately combining the equilibrium equations and the strain-displacement relations according to Flügge's shell theory and the stress-stain equations of Eringen's nonlocal elasticity theory. An analytical solution for the buckling of the shells is presented by using the complex method. This model is validated by a good agreement between the results given by the present model and available data in the literature. Furthermore, the model is utilized to elucidate the... 

A finite element analysis of a double layered shell with a circular hole is carried out with the computer aided engineering software Abaqus (Dassault Systèmes, FR). The model proposed has been used to perform a stress analysis on three pipes with different sized hole. Moreover, thermal expansion has been implemented in the testing. For the purpose of the research, the elastic properties of the materials have been considered and the results compared with the ones previously published in literature. The outcome of the investigation will benefit towards the design of optimal and sustainable pipes with circular cut outs  

In this paper, a method has been presented to study the free vibration of a rotating shell consisting of p coupled conical shells. This method considers the Coriolis and centrifugal forces as well as the initial hoop tension resulting from rotation of the shell. Matrix transform and power series methods were employed to solve the equations. The advantage of using the matrix transform approach is that the dimension of the coefficient matrix, which is finally constructed to obtain the natural frequencies of a shell made of p cones, remains 8×8. The obtained results were validated with the help of existing special cases of the studied problem reported in the literature, and by means of FEM... 

The buckling of generally laminated conical shells having thickness variations under axial compression is investigated. This problem usually arises in the filament wound conical shells where the thickness changes through the length of the cone. The thickness may be assumed to change linearly through the length of the cone. The fundamental relations for a conical shell with variable thickness applying thin-walled shallow shell theory of Donnell-type and theorem of minimum potential energy have been derived. Nonlinear terms of Donnell equations are linearized by the use of adjacent-equilibrium criterion. Governing equations are solved using power series method. This procedure enables us to... 

The buckling of generally laminated conical shells having thickness variations under axial compression is investigated. This problem usually arises in the filament wound conical shells where the thickness changes through the length of the cone. The thickness may be assumed to change linearly through the length of the cone. The fundamental relations for a conical shell with variable thickness applying thin-walled shallow shell theory of Donnell-type and theorem of minimum potential energy have been derived. Nonlinear terms of Donnell equations are linearized by the use of adjacent-equilibrium criterion. Governing equations are solved using power series method. This procedure enables us to... 

The aeroelastic stability of an aircraft wing modeled as an anisotropic composite thin-walled beam in an incompressible flow is investigated. The wing is built-up as a single-cell box beam whose central point is noncoincident with the mid-chord of the profile. The effects of material anisotropy, transverse shear, warping inhibition, nonuniform torsional model and rotary inertia are considered in the structural model. The unsteady incompressible aerodynamics based on Wagner's function is used to determine the aerodynamic loads. The effects of the offset between reference axis and the mid-chord ("a" parameter), fiber orientation and sweep angle on stability boundary are considered, their... 

Axial-torsional vibrations of rotating pretwisted thin-walled composite box beams exhibiting primary and secondary warping are investigated. Considering the nonlinear strain-displacement relations, the coupled nonlinear axial-torsional equations of motion are derived using Hamilton's principle. Ignoring the axial inertia term leads to differential equation of motion in terms of elastic torsion in the case of axially immovable beams. Centrifugal load in the presence of material anisotropy and pretwist angle leads to an induced static torque. The nonlinear equation should be linearized about the corresponding equilibrium state to obtain the linear differential equation of motion. Extended... 

Today, structural Health monitoring is a major concern in the engineering community. Multisite fatigue damage, hidden cracks and corrosion in hard-to-reach locations are among the major flaws encountered in today's extensive diagnosis and/or prognosis of aircraft structures. Ultrasonic waves, lamb waves are particularly advantageous because of their propagation at large distances with little damp in thin-wall structures. In this paper a new rectangular shape array of embedded piezoelectric sensors is developed to detect some damages in large planar structures. An artificial neural network is trained to identify the damage state and its location. Output signals of each sensor due to various... 

Nonlinear torsional vibrations of thin-walled beams exhibiting primary and secondary warpings are investigated. The coupled nonlinear torsional-axial equations of motion are considered. Ignoring the axial inertia term leads to a differential equation of motion in terms of angle of twist. Two sets of torsional boundary conditions, that is, clamped-clamped and clamped-free boundary conditions are considered. The governing partial differential equation of motion is discretized and transformed into a set of ordinary differential equations of motion using Galerkin's method. Then, the method of multiple scales is used to solve the time domain equations and derive the equations governing the... 

The aeroelastic design of composite wings modeled as thin-walled beams is investigated through the use of curvilinear fiber. The structural model considers non-classical effects such as transverse shear, warping restraint, rotary inertia, nonuniform torsional model and also aerodynamic loads based on Wagner's function. In this paper, a linear spanwise variation of the fiber orientation resulting in a variable-stiffness structure is used to optimize the wing for maximum aeroelastic instability speed purpose, while manufacturing constraints are incorporated. Numerical results indicate improvements of aeroelastic stability of variable-stiffness wings over conventional, constant-stiffness ones  

The aim of this study is to carry out the numerical computation of nonlinear normal modes for rotating pretwisted composite thin-walled beam in axial-torsional vibrations. The structural model considered here, incorporates a number of non-classical effects such as primary and secondary warping, non-uniform torsional model, rotary inertia and pretwist angle. Ignoring the axial inertia term leads to differential equation of motion in terms of angle of twist in the case of axially immovable beam ends. The governing differential equations of motion are derived using Hamilton's principle and the reduced model around the static equilibrium position is obtained using 2-mode Galerkin discretization... 

The effect of heat treatment on the axial crushing behavior of thin-walled aluminum 6061 alloy tubes is studied in this work. For this purpose, thin-walled grooved specimens were subjected to different aging heat treatments to obtain different work hardening behaviors. Afterward, quasi-static axial compression tests were achieved to evaluate the crushing behavior. Additionally, a finite element method simulation was employed to determine the distributions of stress, strain, and imposed damage during axial compression. Results show that the optimum energy absorption characteristics can be obtained using moderated strain hardening exponent, ''n''. Low strain hardening exponent results in the... 

Thin-walled cylindrical steel silos are susceptible to instability under wind pressure when they are empty or only partially filled. This paper investigates numerically the wind buckling behavior of a real steel corrugated silo with 8.02 m diameter and 17.62 m height, strengthened by open-section vertical stiffeners. Accordingly, comprehensive 3D finite element models were used and detailed linear and non-linear buckling analyses were conducted. The effects of sinusoidal corrugated sheet profile dimensions on this issue were specially explored. Wind load vertical and circumferential distributions were adopted from Eurocode. Two proposed circumferential pressure distributions for an isolated... 

Thin-walled cylindrical steel silos are one of the key structures for storage of materials in many industries and agricultural sectors. They are susceptible to instability under wind pressure when they are empty or partially filled. This paper investigates numerically the wind buckling behavior of three sample steel silos with stepped walls composed of isotropic rolled shells. Wind load vertical and circumferential distributions were adopted from Eurocodes. Two proposed circumferential pressure distributions for an isolated silo and a silo in a group with a closed roof were taken into consideration. Moreover, the effect of additional inward pressure, proposed by Eurocode, on buckling...