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A new model depicting the full phase of tubular string buckling in vertical wellbores is proposed. The buckling modes of the tubular string are divided into: no buckling, 2D lateral buckling, 3D lateral buckling, continuous contact buckling and helical buckling. For the 2D lateral and 3D lateral buckling, the tubular string is respectively depicted by two and four suspended sections; for the continuous contact and helical buckling, the tubular string includes four suspended sections and one continuous contact section. With the suspended and continuous contact sections respectively depicted by beam-column model and buckling differential equation, the general buckling configurations of the entire tubular string are deduced. Substituting relevant continuity, boundary and stability conditions, the tubular string buckling problem is converted into a system of nonlinear equations. Solving these equations with iteration method, the critical buckling loads and the buckling configurations under different buckling modes for a weightless tubular string are obtained. Later, the weightless model is extended to the case for a tubular string with weight. On the basis of the new buckling model, the axial force and torque transfer along the tubular string under the coupling effect of friction force and buckling is discussed. The results show that the existence of tubular string weight increases the complexity of buckling mechanism and calculation. The continuous contact between the tubular string and wellbore reduces the axial force and torque transfer along the tubular string. To increase the axial force and torque transfer and inhibit buckling, the installation of stabilizers of low friction and buckling inhibition on the buckling-prone sections is wiser than unilaterally increasing the diameter and thickness of the tubular string. Compared with the previous results, the new model provides a more sophisticated description of tubular string buckling in vertical wellbores. [ABSTRACT FROM AUTHOR]

In this paper, isogeometric finite element method (IGA) based on Non-Uniform Rational B-splines (NURBS) basis function is applied for the buckling analysis of generally laminated composite beam with various boundary conditions. A beam element with four degrees of freedom per control point is investigated, which has considered the bending-torsion deformation. The model for the buckling analysis of laminated composite beam is detailed by the principle of virtual work. Several numerical examples of symmetric and anti-symmetric, cross-ply and angle-ply composite beam are performed. Numerical results of critical buckling loads and mode shapes are presented, and compared with other available results to show the efficiency and accuracy of the present IGA approach. In addition, the impacts of the modulus ratios, slenderness ratios, stacking sequence and the fiber angle, especially the Poisson effect on the critical buckling loads of composite beam are clearly demonstrated. It should be noted the results with the Poisson effect neglected are only suit for the cross-ply composite beams. And the benchmark solutions presented in this work can be used as a reference for the buckling analysis of laminated composite beams in future. [ABSTRACT FROM AUTHOR]

The current article analyses the buckling response of piezoelectric cylindrical composite panels reinforced with carbon nano-tubes subjected to axial load. Classical laminated plate theory (CLPT) is employed to reach stress and displacement correlations embracing mechanical and magnetic terms. Stress–strain equations for piezoelectric cylindrical panels reinforced with carbon nanotubes are then written by using Mori–Tanaka method. The coupled electro-mechanical governing equations, Donnell theory as well as minimum potential energy method are thereafter utilized to calculate buckling loads and modes. The effects of such parameters as volume fraction of nano-tube, geometrical characteristics as well as two loading types of axial and biaxial on buckling load of the composite panel are investigated. The results show that increasing the volume fraction of nano-tube eventuates in increasing the buckling load. The results were compared with those already available in the existed literature using different shell theories for isotropic and composite cylindrical panels and a very good agreement was observed. [ABSTRACT FROM AUTHOR]

To obtain accurate buckling load for rectangular plates under compressive point loads, one of the important factor is that the in-plane stress distributions within the plate prior to buckling should be accurate enough. Although the differential quadrature method (DQM) has been successfully used in a variety of fields including the buckling analysis of thin rectangular plates under non-uniformly distributed edge compressions, however, the DQM has some difficulty in dealing with singular functions such as the Dirac-delta function appeared in the stress boundary condition. In this paper, novel formulations are presented to overcome the difficulty encountered in dealing with the Dirac-delta functions by using the DQM. The normal stress boundary condition is numerically integrated before being discretized in terms of the differential quadrature. Detailed formulations are given. Buckling of rectangular plates under either uniaxial or biaxial compressive point loads is successfully analyzed. It is demonstrated that accurate buckling loads can be obtained by the DQM for rectangular plates with nine combinations of boundary conditions and various aspect ratios. The compactness and computational efficiency of the DQM are retained in solving the partial differential equations with boundary conditions involving Dirac-delta functions. The accuracy of the differential quadrature (DQ) results is verified by comparing them with existing analytical solutions and finite element data. New results are tabulated which can be a reference for other researchers to develop new numerical methods. [ABSTRACT FROM AUTHOR]

The lateral buckling problem for continuous welded rail tracks under thermal loading has been well researched and is known to involve a localisation buckling phenomenon where only a limited region of the track buckles. In this paper, a sandwich column model is formulated to model the rail track-tie structure as sandwich column. The constitutive relations for the thermally induced stresses and finite strain are based on a hyperelastic constitutive model. A hyperbolic function for the nonlinearity of the axial and lateral resistance between the tracks and ballast was used. A critical track length is proposed beyond which the localisation is unaffected. Increasing the track length or changing the boundary conditions does not influence the localised buckling behaviour for track lengths beyond the critical length. The use of fasteners with large rotational stiffness substantially increases the lateral stability of the track-tie structure. Nonlinear numerical solutions are compared with the results in the literature. The variation in the axial compressive force within the localisation zone in the rail is studied and discussed. Parametric studies are performed on examples to identify the influence of track imperfections on the localised lateral buckling and safe temperature change. [ABSTRACT FROM AUTHOR]

Abstract: Axial deformation is not involved in the formulation of linear buckling caused by axial force. Likewise, twisting is not present in linear buckling caused by axial torque. The dynamic axial–torsional buckling of structural frames in the presence of follower axial force will be solved by means of dynamic stiffness using power series. Variationally consistent natural boundary conditions are given so that the resulting dynamic stiffness is symmetrical for conservative loading. Some parts of the boundary forces disappeared for follower axial forces due to consistent tangency to the neutral axis. The deficiency of the power series method to deal with non-uniform sections is highlighted. New instability phenomena for a simple column are studied in detail. It is shown that columns can buckle under direct follower tension. Follower tension decreases the natural frequency initially and then increases it rapidly after a turning point. The first pair of modes about the major axis and that about the minor axis of a rectangular section column meet at one crossing point. A very small axial torque will change the crossing into flutter-like tongues. These tongues are common in compressive follower force. These tongues caused by axial torque are reported here for the first time. [Copyright &y& Elsevier]

Abstract: This paper presents a numerical investigation on the local and distortional buckling behaviour of cold-formed steel zed-section beams subjected to uniformly distributed transverse loads. The analysis is performed using a semi-analytical finite strip method. The beams investigated include both detached sections and restrained sections. The results obtained from the present study highlight the differences in the local and distortional buckling behaviours of the thin-walled sections between pure bending and the uniformly distributed loading. [Copyright &y& Elsevier]

Abstract: A mathematical model for a slip-buckling problem has been proposed and its exact solution has been found for the analysis of materially inelastic two-layer composite columns with non-linear interface compliance. The mathematical model has been carried out to evaluate exact critical buckling loads. It has been demonstrated mathematically exactly, that exact critical buckling loads are influenced by the initial stiffness, and hence on linear portion of the interface force-slip relationship. Besides, it has been shown that material inelasticity can reduce the critical buckling loads significantly and that the interlayer stiffness has an important effect on the transition between the elastic and inelastic buckling. [Copyright &y& Elsevier]

Abstract: Buckling analysis of symmetrically laminated rectangular plates with parabolic distributed in-plane compressive loadings along two opposite edges is performed using the Rayleigh–Ritz method. Classical laminated plate theory is adopted. Stress functions satisfying all stress boundary conditions are constructed based on the Chebyshev polynomials. Displacement functions for buckling analysis are constructed by Chebyshev polynomials multiplying with functions that satisfy either simply supported or clamped boundary condition along four edges. Methodology and procedures are worked out in detail. Buckling loads for symmetrically laminated plates with four combinations of boundary conditions are obtained. The proposed method is verified by comparing results to data obtained by the differential quadrature method (DQM) and the finite element method (FEM). Numerical example also shows that the double sine series displacement for simply supported symmetrically laminated plates having bending–twisting coupling may overestimate the stiffness, thus providing higher buckling loads. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, buckling loads of rectangular composite plates having nine sets of different boundary conditions and subjected to non-uniform inplane loading are presented considering higher order shear deformation theory (HSDT). As the applied inplane load is non-uniform, the buckling load is evaluated in two steps. In the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using the above stress distribution the plate buckling equations are derived from the principle of minimum total potential energy. Adopting Galerkin''s approximation, the governing partial differential equations are converted into a set of homogeneous linear algebraic equations. The critical buckling load is obtained from the solution of the associated linear eigenvalue problem. The present buckling loads are compared with the published results wherever available. The buckling loads obtained from the present method for plate with various boundary conditions and subjected to non-uniform inplane loading are found to be in excellent agreement with those obtained from commercial software ANSYS. Buckling mode shapes of plate for different boundary conditions with non-uniform inplane loadings are also presented. [Copyright &y& Elsevier]

Abstract: This paper presents the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of I-section struts. The so-called exact strip is developed based on the concept that it is effectively a plate. The presented method, which is designated by the name Full-analytical Finite Strip Method, provides an efficient and extremely accurate buckling solution. In the development process, the Von-Karman''s equilibrium equation is solved exactly to obtain the buckling loads and mode shapes for the I-section struts. The investigation of buckling behavior is then extended to an initial post-buckling study with the assumption that the deflected form immediately after the buckling is the same as that obtained for the buckling. The current post-buckling study is effectively a single-term analysis, which is attempted by utilizing the so-called semi-energy method. Through the solution of the Von-Karman''s compatibility equation, the in-plane displacement functions which are themselves related to the Airy stress function are developed in terms of the unknown coefficient in the assumed out-of-plane deflection function. All the displacement functions are then substituted in the total strain energy expressions. The theorem of minimum total potential energy is subsequently applied to solve for the unknown coefficient. Finally, the developed method is subsequently applied to analyze the initial post-buckling behavior of some representative I-sections for which the results were also obtained through the application of a Semi-energy Finite Strip Method [Ovesy HR. The development and application of a semi-energy post-local buckling finite strip. PhD dissertation, Cranfield University, UK, 1998]. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is significantly promoted. [Copyright &y& Elsevier]

Abstract: Thermal post-buckling analysis of columns with an axially immovable ends is studied using the Rayleigh–Ritz (R–R) method, where the admissible displacement functions are chosen based on the concept of coupled displacement field (CDF) criteria. Geometric non-linearity is considered using the von-Karman strain displacement relations of the beam. Furthermore, the displacement fields derived from CDF criteria are used in an intuitive formulation, where the thermal post-buckling behavior can be predicted by using two parameters namely tension developed in the column and linear buckling load. An exhaustive set of column boundary conditions are considered namely classical such as hinged–hinged, clamped–clamped, clamped–hinged and non-classical such as clamped–guided and hinged–guided. Post-buckling analysis results are presented in the form of closed form expressions, where the ratio of post-buckling load to linear buckling load parameter is expressed as a function of central amplitude of the column for all the boundary conditions considered. The amount of non-linearity predicted using the present formulations (R–R method and intuitive method) based on the concept of coupled displacement field (CDF) criteria shows an excellent agreement with the available literature results for both classical and non-classical boundary conditions. [Copyright &y& Elsevier]

Abstract: This paper proposes a new method for performing predefined simultaneous modification of natural frequencies and buckling loads of composite cylindrical panels. The method is based on the fact that both natural frequencies and buckling loads are eigenvalues of an algebraic system of simultaneous equations. First- and second-order derivatives of these eigenvalues are calculated and the first two terms in Taylor expansion are used for developing a modification procedure that is defined as an inverse eigenvalue problem. A four-layered composite cylindrical panel with an arbitrary angle-ply stacking sequence is considered as a case study and several simultaneous modifications for natural frequencies and buckling loads are carried out. It is shown that the proposed method can perform the predefined modification with an acceptable accuracy even for large perturbations in objective functions. [Copyright &y& Elsevier]

In the present study, the buckling behaviour of laminated composite skew plates with different boundary conditions subjected to linearly varying in-plane loads are presented. The skew plate is modelled based on higher order shear deformation theory, which accurately predicts the buckling behaviour for the thick plate. The in-plane stress distribution within the skew plate due to linearly varying in-plane load is equal to the applied in-plane edge load in the pre-buckling range. Using these in-plane stress distributions, the total potential energy functional is formulated. Total potential energy is a function of the total strain energy of skew plate and potential energy due to in-plane stress distributions. The total strain energy of skew plate contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total potential energy functionals mapped from physical domain to computational domain over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram–Schmidt orthogonalization process. Using a Rayleigh-Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials, the total potential energy functional is converted into sets of algebraic equations. Finally, these algebraic equations are rearranged as a linear eigenvalue problem, which is solved to obtain the critical buckling loads. The numerical results are presented for different skew angles, boundary conditions, length to thickness ratios, aspect ratios and in-plane loadings. It is observed that the critical buckling load increase with the increase of skew angle as well as change in the mode shape at a lower aspect ratio with the increase of skew angle. [ABSTRACT FROM AUTHOR]

Abstract: An arch under an in-plane central concentrated radial load is subjected to combined axial compressive and bending actions. When these combined axial compressive and bending actions reach a certain value, the arch may suddenly deflect laterally and twist out of its plane of loading and fail in a lateral–torsional buckling mode. This paper derives analytical solutions for the elastic lateral–torsional buckling load of pin-ended circular arches that are subjected to a central concentrated load, using the principle of stationary potential energy in conjunction with the Rayleigh–Ritz method. Analytical solutions of the buckling load for in-plane fixed and out-of-plane pin-ended arches and for the case of the load acting above or below the shear centre are also derived. The analytical solutions are compared with results of a commercial finite element package ANSYS and a finite element code developed by authors elsewhere for arches with different slendernesses, included angles, and cross-sections. The agreement between the analytical solutions and the finite element results is very good. [Copyright &y& Elsevier]

We study the stability of thin walled circular cylindrical shells subject to radial pressure loading. Towards this end, we first develop the equations of motion of these shells with predominant radial deflections. We identify additional terms in the shell equations of motion which have mostly been neglected in existing studies and ascertain their importance in predicting the correct static buckling pressure. For finite cylinders, incorporation of these terms results in the best prediction of the static buckling pressure. Furthermore, we also find that the assumed relationships between the in-plane displacements of a generic point and the in-plane displacements of the mid-surface, which change from one shell theory to the other, play a critical role in determining the correct onset of the buckling instability under radial loading. In particular, the Donnell shell theory which is very popular for the study of dynamic problems related to cylindrical shells does not predict the correct buckling pressure. We find that the Flügge–Luré–Byrne theory is best suited for this purpose. Accordingly, the shell equations with the additional terms and the in-plane displacements related as per the Flügge–Luré–Byrne shell theory have been used for the study of parametric instability of a cylinder subject to a uniform radially fluctuating pressure. Stability charts with respect to different combinations of the forcing parameters viz. the static component of the pressure, the amplitude and frequency of the fluctuating component of the pressure have been presented which can serve as design guideline for shells subject to fluctuating radial loads. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, instability of a thick through-the-thickness functionally graded material (FGM) rectangular plates under the practical cases of thermal and mechanical loading conditions is analyzed. Uniform shear, uniform uni-axial or biaxial compression/tension, uniform temperature rise, heat conduction across the thickness, and combined cases are considered. For thermal buckling and combined cases in thermal field, temperature dependency of the properties is also taken into account. The four-variable refined plate theory with parabolic distribution of shear strains through-the-thickness is implemented to establish the governing equilibrium and stability equations. Only the clamped type of boundary conditions is considered after the proof of bifurcation type buckling existence. The resulted equations are uncoupled in a reasonable manner. The multi-term Galerkin method is used to derive the critical buckling loads/temperatures and buckled shapes of the plate under various loading conditions. [Copyright &y& Elsevier]

Analytical solutions of natural frequencies and critical buckling loads for a set of homogenous plates in the complex plate system are determined in this paper. A different layerwise approach is found via interconnecting several plates into one kind of layered block. For this determination, the classical, first order and high order shear deformation theories are used to present rotary inertia and shear effects on systems with different numbers of elastically connected plates. Closed form solutions are determined in the form of explicit expressions of natural frequencies and critical buckling loads. General mode shapes are presented for systems of elastically connected plates. The stability of the complex system is determined and discussed for different stiffnesses of the support, layers and various geometric dimensions. These results are of considerable practical interest and have a wide application in the engineering practice of frameworks. The range of frequencies depending on number of elastically connected plates in the block is discovered. [ABSTRACT FROM AUTHOR]

In this paper, a novel actuator in the form of a Kagome truss composed of shape memory alloy (SMA) wires and common metallic wires is described. In the actuator, the SMA wires play dual roles as load supporters and actuating elements. The intersections between the SMA wires and between the SMA wires and the common metallic wires were joined by using shrinkable tubes, which induced the kinematically compatible buckling of the columns of SMA wires under compression, consequently enabling the large actuation displacement of up to 30% of the height with some sacrifice of the load capacity. An analytic solution was derived using the elementary mechanics of buckling and geometric relation of curved column, which gave fairly good estimation of the behavior of the Kagome actuator for the deformation and actuation stages, based on the behavior of a single SMA wire. The lightness and large actuation range of this actuator appear to be useful for practical applications. [ABSTRACT FROM AUTHOR]

In this work, the new type enhanced lattice (defined as hourglass) truss structures with the improved resistance of their core members and attached face sheets have been fabricated by an innovative interlocking method. The shear and bending properties of the produced sandwich structures characterized by three different relative densities have been investigated using various analytical methods and the obtained results were in good agreement with the experimental data. The truss failure under shear loading was dominated by the inelastic buckling of the truss members, while the four possible analytical models describing the bending properties and failure mechanism of the hourglass truss beams included elastic face sheet buckling, face sheet yielding, elastic core member buckling, and core member yielding were studied. The bending specimens, which were designed by constructing failure mechanism maps, were used to examine the yielding behavior of the truss core members as well as the elastic buckling and yielding of the face sheet members. The obtained results revealed that the specific shear strengths and bending failure loads of the studied hourglass truss structures were superior to those of pyramidal truss structures, and that the former could be considered promising candidates for manufacturing lightweight structures with high specific strength. [ABSTRACT FROM AUTHOR]

In this paper, we study the variation of natural frequencies for thin walled circular cylindrical shells subject to external radial load (uniform and hydrostatic pressure). The study has been performed for four different types of boundary conditions viz. pinned-pinned, pinned-free, clamped-free and one end is pinned and other end axially constrained. Towards this, we have used approximate shape functions and Galerkin projections of the PDEs governing the shell motion, linearized about a steady state solution due to the applied mean radial pressure. Our results have very good agreement with the experimental and theoretical results available in literature. They have also been verified against finite element analysis (FEA) using ABAQUS. We have found that with increasing magnitude of inward radial load, the natural frequency decreases, however, the circumferential wavenumber corresponding to the lowest natural frequency increases. For outward radial load the opposite happens. Furthermore, the circumferential wavenumbers corresponding to lowest natural frequency and first buckling mode are different for short cylinders with the difference decreasing with increasing length of the cylinder. We have also found an interesting result for the beam mode vibration of cylindrical shells. For short cylinders, the natural frequency of the beam mode increases (decreases) with internal (external) pressure, which is consistent with other circumferential modes. Subsequently, we obtain a critical length at which the applied radial pressure has no effect on the natural frequency. For cylinders longer than the critical length, the effect of the radial load is opposite of that observed for the short cylinders, and this is contrary to the behavior of the other circumferential modes. As a result, buckling of the beam mode happens for an outward radial (internal) pressure. [ABSTRACT FROM AUTHOR]

Sandwich panels with truss cores have been widely investigated due to their superior mechanical performances. When being used in the thermal protection system of a high-speed aircraft, sandwich panels are usually subjected to intense thermal loading and may fail due to various mechanisms. This paper presents a theoretical and numerical analysis on the failure mechanisms and optimal design of metallic sandwich panels with truss cores subjected to uniform thermal loading. Five failure modes are considered: global buckling, face sheet buckling, face sheet yielding, core member buckling and core member yielding. Failure maps of sandwich panels with several truss core topologies are developed based on these failure modes. Taking the five failure modes as constraint conditions, sandwich panels with truss cores are optimally designed for the minimum weight at given thermal loadings. It is found from the optimal analysis that sandwich panels with Kagome and X-type truss cores are more efficient than those with tetrahedral and pyramidal truss cores. Sandwich panels with fully-clamped boundary conditions have superior thermal loading resistance than those with simply-supported boundary conditions. [ABSTRACT FROM AUTHOR]

A functionally graded half-plane with shear modulus varying exponentially along the direction normal to the surface and surface effects accounted through Gurtin–Murdoch model, indented by long rigid smooth cylindrical indenter is solved to understand the effect of material inhomogeneity and surface effects on indentation response. The Green’s function relating surface load to surface displacement under plane strain condition is obtained semi-analytically through the combination of Airy stress function approach and Fourier transforms and utilized to solve the contact problem. The solution is used to study the effect of inhomogeneity through grading parameter and surface effects through residual surface tension based intrinsic length scale on the contact pressure, contact size and in-plane normal stress on the surface responsible for cracks during indentation. [ABSTRACT FROM AUTHOR]

Abstract: A simplified static procedure is proposed for analysing and designing composite beams with interlayer slip. The method is parallel to the Eurocode 5 method, but it is general in nature and can be applied to arbitrary boundary and loading conditions. In contrast with Eurocode 5, a general and correct way of choosing the effective beam length of the problem is given by the present procedure, which is that the effective beam length equals the buckling length that is found in the corresponding column buckling problem. The procedure predicts the deflections and internal actions and stresses, in principle by replacing the fully composite bending stiffness (EI ∞) with the effective (partially) composite bending stiffness (EI eff) in the expressions for these quantities in the corresponding fully composite beam. This effective bending stiffness depends on two non-dimensional parameters: the composite action parameter (shear connection stiffness) and the relative bending stiffness parameter. The method is applied to a number of simple practical cases and the results obtained have been compared with the exact values. The applicability of the simplified analysis procedure was found to be very good, except for interlayer shear stresses. The error in the Eurocode 5 procedure, as compared with the method proposed in this paper, can in some cases be up to almost 30% depending on the boundary conditions. [Copyright &y& Elsevier]

In this paper, the stress–strain behavior under load reversal of advanced high strength steel (AHSS) sheet samples was measured using a modified simple shear (SS) apparatus. The forward–reverse loading behavior was characterized for three different grades of AHSS; namely, DP, TRIP and TWIP steels. For comparison purpose, compression–tension (CT) tests were also carried out for the same materials. For all the cases, a typical complex anisotropic hardening behavior, including the Bauschinger effect, transient strain hardening with high rate and permanent softening, was observed during load reversal. No premature localization and sheet buckling occurred in these experiments, which have been major technical hurdles in CT tests. For example, an engineering shear strain of over 40%, which corresponds to an effective strain of roughly 0.2, at reversal was achieved for DP980 although the uniform elongation of this material in uniaxial tension is only 5%. A recently developed distortional hardening model (HAH) was employed to reproduce the SS stress–strain curves. Using the coefficients determined with these SS data, the CT behavior was predicted with the HAH model and compared with experimental results. This complementary study indicated that the constitutive model determined from the SS flow curves satisfactorily reproduced the CT hardening behavior. As an application, finite element simulations of springback were carried out for 2D draw-bending of a strip sheet. [ABSTRACT FROM AUTHOR]

The energy absorption characteristics of a type of conical tubes with graded thickness (CTGT) under oblique impact loads were investigated in this paper. The influences of load angle, structure layout, strain rate effect, inertia effect and forming effects on the responses of CTGT were analyzed numerically by using finite element model validated by experiments. The reverse layout of CTGTs showed very much better performance against oblique loads than the original straight circular tubes employed to fabricate it. The thickness variation and material hardening during fabrication delayed the switch from progressive to global buckling for reverse layout of CTGT and enabled it to preserve most of the axial crush resistance when subjected to oblique loads with load angle up to 20°. The increase in the extent of forming effects was not always found to be beneficial and moderate extent of forming was suggested in applications against oblique loads. The outcomes of this study will facilitate the crashworthiness design of CTGT structures with better performance when subjected to oblique loads. [ABSTRACT FROM AUTHOR]

Abstract: When rotary inertia is taken into account, free transverse vibration of a standing and hanging Rayleigh beam-column subjected to vertically orientated gravity load is investigated. The problem is reduced to an integral equation. By seeking a non-trivial solution of the integral equation, a characteristic equation of free bending vibration of a gravity-loaded cantilever is derived approximately. Natural frequencies and mode shapes are respectively calculated. An approximate expression for the fundamental frequencies is given in closed form for gravity-loaded cantilevers, and its accuracy reaches 99% for a standing gravity-loaded cantilever with gravity load less than the critical buckling load and 97% for a hanging gravity-loaded cantilever with an arbitrary gravity load. The effect of gravity load on the natural frequencies and mode shapes progressively becomes greater when the order number of free vibration is raised. A comparison of the natural frequencies is made for a hanging chain and a hanging cantilever with sufficiently small bending stiffness under own weight. Obtained results indicate that rotary inertia plays a dominant role in bending vibration with higher frequencies. [Copyright &y& Elsevier]

Abstract: A twin bridge cyclic shear test with in-plane torsion is proposed for the identification of kinematic hardening parameters for metallic sheets. Besides its simplicity, noteworthy advantages of the test are (a) reduced loads on the experimental device as compared to a one-sided shear test, (b) identical orientation of the principal stresses with respect to the rolling direction in both of the shear bridges, e.g. which cannot be realized by the classical Miyauchi shear test, and (c) no premature termination by instability mechanisms such as buckling or necking. Two main disadvantages appear to be (a) a preclusion of the use of analytically solved initial value problem in parameter identification due to a diffusivity of the plastic region around the shear bridges, (b) smeared out anisotropic material response proportional with the width of the shear bridge. As a remedy for the former, an inverse parameter identification methodology is used to determine the hardening parameters using an objective function devising the measured moment and rotation angle. For the latter, an optimum shear bridge width is selected which also minimizes the edge effect where a shear equilibrium is not possible. A combined non-linear isotropic and kinematic hardening model respectively based on Voce and Armstrong–Frederick is selected as the material model which is implemented as a VUMAT subroutine for ABAQUS/EXPLICIT. Strain-controlled tests are conducted using three different classes of steel sheet materials, namely a mild steel DC06, a dual phase steel DP600 and a Transformation Induced Plasticity steel TRIP700. These tests with one cycle including a forward shearing and a reverse shearing phase merely focus on the Bauschinger effect. Variations with different stress and strain based loading cycles for phenomena like shakedown, ratcheting, mean stress relaxation, cyclic hardening and softening are not explored and left beyond the scope of the current study. The results, besides showing the applicability of the test to the kinematic hardening parameter identification purposes, also show that the Armstrong–Frederick model falls short to capture the cyclic response of the selected materials, especially advanced high strength steels DP600 and TRIP700. [Copyright &y& Elsevier]

Stability issue has a significant role in the design of structures; especially it becomes even much more substantial when the design deals with the thin-walled structures under complex loading condition, which is a combination of two or more loading types at the same time. The present research paper aims to analyse the stability region of the thin-walled beams with doubly symmetric cross-sections under combined loads simultaneously: axial force, uniformly distributed transverse loads and bending moments at the ends. A novel approach was proposed by the authors and the energy method was used to solve the problem. The final results are able to be represented by mean of not only generalized algebraic equations among the critical loads, but also by three-dimensional graphs. Based on a particular thin-walled beam as an example, the analytical results obtained by using a novel approach were in agreement with the numerical results of analysis by finite element method in the feasible computational software. [ABSTRACT FROM AUTHOR]