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Background: Accurate predictions of thin sheet material springback during forming processes are of great interest in the forming industry. However, thin sheets are susceptible to buckling under shear loading. Objective: The present research aims at improving the so-called Arcan setup for testing thin (1-5 mm) sheet samples with large gauge areas (i.e., width about 21 mm) by introducing anti-buckling devices to mitigate sample buckling. Method: Three monotonic and one cyclic shear tests were carried out on 1 mm thick C60 high carbon steel. Results: The use of the proposed anti-buckling device resulted in the suppression of sample buckling. Numerical analyses of the experiment where buckling was eliminated revealed predominant shear stress states in the gauge area (i.e., stress triaxiality = 0), which highlights minor influences of the anti-buckling device on the sample stress state. Conclusion: To suppress buckling, the use of anti-buckling devices was essential. Moreover, the friction coefficient between the sample and the proposed devices was calibrated ( μ = 0.33 ) in addition to kinematic hardening parameters. [ABSTRACT FROM AUTHOR]

Mechanical properties are investigated for a class of microstructured materials with promising applications. Specifically, we consider a composite material with orthogonal, mutually interconnected fibers building a pantographic substructure. In order to predict the behavior of such a system in three-dimensional continuum, a reduced-order model is introduced by means of a bi-dimensional elastic surface accurately describing large deformations. The properties of this reduced-order model are characterized by an elastic energy density that involves second space derivatives of the displacement for capturing the resistance of twisted and bent fibers in plane as well as out of plane. For determining the coefficients in the elastic energy of the reduced-order model, we utilize a numerical inverse analysis and make use of ad hoc computational experiments performed by a direct numerical simulation on the microscale with detailed modeling of the pantographic substructure. This reduced-order model represents a homogenized material on macro-scale with its substructure on microscale. The homogenized model is capable of describing materials response at a significantly less computational cost than the direct numerical simulations. [ABSTRACT FROM AUTHOR]

A quadrilateral and a triangular element based on the strain approach are developed for static, free vibration and buckling analyses of Reissner–Mindlin plates. The four-node triangular element SBTP4 has the three essential external degrees of freedom at each of the three corner nodes and at a mid-side node; whereas the quadrilateral element SBQP has the same degrees of freedom at each of the four corner nodes. Both elements use the same assumed strain functions which are in the linear variation where bending and transverse shear strains are independent and satisfy the compatibility equations. The use of the strain approach allows obtaining elements with higher-order terms for the displacements field. The formulated elements have been proposed to improve the strain-based rectangular plate element SBRP previously published. Several numerical examples demonstrate that the present elements are free of shear locking and provide high-accuracy results compared to the available published numerical and analytical solutions. [ABSTRACT FROM AUTHOR]

GPa-grade steels which possess the ultimate tensile strength over 1000 MPa and higher elongation have been thoroughly researched to replace conventional high-strength steels in automobile industry to enhance fuel efficiency without sacrificing crashworthiness. However, high strength of GPa-grade steel does not only induce punching pin buckling due to high contact pressure, but also abrasive wear on the mold surface due to the unstable contact that results from the large amount of springback, which tend to impede widespread usage of GPa-grade steels. In this research, design criteria for an optimal aspect ratio of the punching pin preventing buckling failure has been proposed by linking with experimental and numerical analyses, which is validated with the analytic solutions. Furthermore, in order to prevent stripping failure, it is highly recommended that one of the main factors, a blank holder force (BHF), over 1.5 MPa has to be maintained during the withdrawal process to minimize the effect of springback in stamped panels applying GPa-grade steel, which is able to extend the tool life of the side punching pin about 100,000 cycles. [ABSTRACT FROM AUTHOR]

A composite material system comprised of a monostable negative stiffness (NS) structure within a polymer matrix was designed, fabricated, and experimentally evaluated. The monostable negative stiffness (NS) structure was designed using a combination of analytical and numerical models and manufactured in stainless steel. The NS structure was arranged in parallel with different polymer matrices to experimentally evaluate the effects of the matrix properties on the overall stiffness and energy dissipation of the composite NS-matrix system when loaded in uniaxial compression. A strong influence of the matrix properties on the stiffness and energy absorption capacity of the composite system was observed. Unlike conventional composites for which there is a natural tradeoff between stiffness and energy absorption capacity, the composite NS-matrix system enhanced stiffness while simultaneously improving energy absorption relative to a neat matrix, but only when the stiffness of the matrix was carefully matched to the stiffness of the NS structure. [ABSTRACT FROM AUTHOR]

A dynamic model for a rotating sandwich annular plate with a viscoelastic core layer is developed. All fundamental equations and boundary conditions are established based on Hamilton's principle, and the rotation effect and viscoelastic properties of the sandwich structure are taken into account. The aerodynamics force acting on the plate is described by a rotating damping model, and the constitutive behavior of the viscoelastic core layer is formulated by the frequency-dependent complex modulus. The effects of geometrical and material parameters on frequencies and damping of forward and backward traveling waves and the dynamic stability for the rotating sandwich plate are numerically analyzed by means of Galerkin's method. The results show that the critical and flutter speeds of the rotating plate can be increased at some certain parameters of the viscoelastic core layer. [ABSTRACT FROM AUTHOR]

Scale effects are studied on the buckling behavior of bilayer composite plates under non-uniform uniaxial compression via the nonlocal theory. Each isotropic plate is composed of a material that is different from others, and the adhesive between the plates is modeled as the Winkler elastic medium. According to the symmetry, effects of the Winkler non-dimensional parameter, the thickness ratio, the ratio of Young's moduli, and the aspect ratio are also considered on the buckling problem of bilayer plates, where only the top plate is under the uniaxial compression. Numerical examples show that the Winkler elastic coefficient, the thickness ratio, and the ratio of Young's moduli play decisive roles in the buckling behavior. Nonlocal effect is significant when the high-order buckling mode occurs or the aspect ratio is small. [ABSTRACT FROM AUTHOR]

The in-plane buckling behavior of funicular arches is investigated numerically in this paper. A finite strain Timoshenko beam-type formulation that incorporates shear deformations is developed for generic funicular arches. The elastic constitutive relationships for the internal beam actions are based on a hyperelastic constitutive model, and the funicular arch equilibrium equations are derived. The problems of a submerged arch under hydrostatic pressure, a parabolic arch under gravity load and a catenary arch loaded by overburden are investigated. Buckling solutions are derived for the parabolic and catenary arch. Subsequent investigation addresses the effects of axial deformation prior to buckling and shear deformation during buckling. An approximate buckling solution is then obtained based on the maximum axial force in the arch. The obtained buckling solutions are compared with the numerical solutions of Dinnik (Stability of arches, 1946) [] and the finite element package ANSYS. The effects of shear deformation are also evaluated. [ABSTRACT FROM AUTHOR]

Thin-walled members that have one dimension relatively large in comparison to the cross-sectional dimensions are usually modelled by using beam-type one-dimensional finite elements. Beam-type elements, however, are based on the assumption of rigid cross-section, thus they only allow considerations associated with the beam axis behaviour such as flexural-, torsional- or lateral-buckling and cannot consider the effects of local deformations such as flange local buckling or distortional buckling. In order to capture the local effects of this type shell-type finite element models can be used. Based on the Bridging multi-scale approach, this study proposes a numerical technique that is able to split the global analysis, which is performed by using simple beam-type elements, from the local analysis which is based on more sophisticated shell-type elements. As a result, the proposed multi-scale method allows the usage of shell elements in a local region to incorporate the local deformation effects on the overall behaviour of thin-walled members without necessitating a shell-type model for the whole member. Comparisons with full shell-type analysis are provided in order to illustrate the efficiency of the method developed herein. [ABSTRACT FROM AUTHOR]

In most cases, the research on the buckling of a helical spring is based on the column, the spring is equivalent to the column, and the torsion around the axial line is ignored. A three-dimensional (3D) helical spring model is considered in this paper. The equilibrium equations are established by introducing two coordinate systems, the Frenet and the principal axis coordinate systems, to describe the spatial deformation of the center line and the torsion of the cross section of the spring, respectively. By using a small deformation assumption, the variables of the deflection can be expanded into Taylor's series, and the terms of high orders are ignored. Hence, the equations can be simplified to the functions of the twist angle and the arc length, which can be solved by a numerical method. The reaction loads of the spring caused by the axial load subjected to the center point are also discussed, giving the boundary conditions for the solution to the equilibrium equations. The present work is useful to the research on the behavior of the post-buckling of the compressed helical spring. [ABSTRACT FROM AUTHOR]

This paper reports the results of numerical analysis of the bifurcation solutions of nonlinear boundary-value problems of plane bending of elastic arches and panels. Problems are formulated for a system of six nonlinear ordinary differential equations of the first order with independent fields of finite displacements and rotations. Two loading versions (by follower and conservative pressures) and two versions of boundary conditions (rigid clamping and pinning) are considered. In the case of clamped arches and panels, the set of solutions consists of symmetric and asymmetric bending modes which exist only for positive values of the load parameter. In the case of pinning, the set of solutions includes symmetric and asymmetrical modes which correspond to positive, negative, and zero values of the parameter. In both problems, the phase relations between the state parameter and the load parameter are bifurcated, ambiguous, have isolated branches, and admit a catastrophe — a finite jump from the fundamental equilibrium mode to a buckled mode. [ABSTRACT FROM AUTHOR]

The governing equations of elasticity theory for natural vibration and buckling of anisotropic plate are derived from Hellinger-Reissner’s variational principle with nonlinear strain-displacement relations. Simply supported rectangular hybrid plates are studied with a precise integration method. This method, in contrast to the traditional finite difference approximation, gives highly precise numerical results that approach the full computer precision. So the results for natural vibration and stability of hybrid plates presented in the paper can be riewed as approximate analytical solutions. Furthermore, several types of coupling effects such as coupling between bending and twisting, and coupling between extension and bending, when the layer stacking sequence is asymmetric, are considered by only one set of governing equations. [ABSTRACT FROM AUTHOR]

A mathematical formulation is given of nonlinear axisymmetric buckling problems for plates and shells in the two-phase zones of austenite-to-martensite transformation. Numerical solutions of the direct-and inverse-transformation problems are used to construct hysteresis loops for thermomechanically cycled, pressure-loaded circular plates and shallow spherical domes of titanium nickelide (NiTi) alloy. It is shown that dynamic instability of the dome deformation process can occur during transformation under loads notably lower than the upper critical values for the isothermal states of the material outside the transformation zone. A theoretical analysis gives external loads below which the dome remains stable in the thermally cycled material with phase transformations. [ABSTRACT FROM AUTHOR]

The factors responsible for the errors often encountered in the stability analysis of elastic systems are found by testing the Bubnov-Galerkin method for the buckling problem of a single-layer flexible elastic bar. Refined formulas are obtained for the maximum deflection of a longitudinally compressed hinged three-layer bar. [ABSTRACT FROM AUTHOR]

The axisymmetric strain problem for a shell in the direct phase transformation interval is formulated approximately as a nonlinear boundary-value thermoelastic problem with an implicit temperature dependence (through a phase parameter simulating the volume fraction of the new-phase crystals). The buckling problems for a circular plate and a shallow spherical dome of TiNi alloy loaded by normal pressure in the direct phase transformation interval are solved numerically. The branches of buckled equilibrium states are obtained for various values of the loading and phase parameters. It is found that the deflections increase abruptly with an increase in the phase parameter for a fixed value of the loading parameter. The evolution of the buckling modes and the phase-strain distribution along the meridian are studied. [ABSTRACT FROM AUTHOR]

The problem of a rod and a plate subjected to plane strain in the interval of the direct phase transformation is formulated as a nonlinear boundary-value thermoelastic problem with an implicit dependence on temperature (through a phase parameter simulating the volume fraction of new-phase crystals). An analytical solution of the problem of a rod bent into a ring and a plate bent into a tube as a result of phase strains under the action of a small end bending moment is given. A numerical analysis of the buckling problem of a titanium nickelide (alloy) rod (plate) under longitudinal compression in the interval of the direct phase transformation shows that buckling becomes possible if the compressive load is much lower than the Euler critical load calculated before the transformation. Branches of buckled equilibrium states corresponding to loads lower than the Euler load are plotted as functions of the phase parameter. In all cases considered, the deflections increase abruptly in the neighborhood of the critical points. The evolution of buckling modes is studied, and the phase-strain distributions along the rod (plate) are shown. [ABSTRACT FROM AUTHOR]

The nonlinear boundary-value problem of the axisymmetric buckling of a simply supported conical shell (dome) under a radial compressive load applied to the supported edge is formulated for a system of six first-order ordinary differential equations for independent fields of finite displacements and rotations. Multivalued solutions are obtained using the shooting method with specified accuracy. For various values of the loading parameter, bifurcation of the solutions of the problem is studied and a parametric branching diagram is constructed. The buckling modes are obtained for three branches of the solution. Curves of the buckling modes corresponding to three isolated branches of the solution are given. [ABSTRACT FROM AUTHOR]

The buckling of a fabric sheet subjected to a uniaxial tension in a direction making arbitrary angle, θ (0°<θ<90°) say, with respect to that of warp is investigated. The equation to determine the buckling direction angle, β say, was obtained and, as illustration, the solution curves of the equation for θ=45° and θ=30° were plotted. It is shown that when the fabric sheet is subjected to tension in non-warp/non-weft direction the out-of-plane buckling of fabric is possible, two buckling modes (flexural and extensional modes) and the both corresponding buckling conditions are obtained. The results given by ZHANG and FU (2001) are the special cases of this paper. [ABSTRACT FROM AUTHOR]

Based on small-deflection buckling equation, a weighted solution for critical load is presented. Usually, it is very difficult to solve the equation for general problems, especially those with complicated boundary conditions. Axisymmetric problem was studied as an example. Influencing factors were found from the equation and averaged as the buckling load by introducing weights. To determine those weights, some special known results were applied. This method solves general complicated problems by using the solutions of special simple problems, simplifies the solving procedure and expands the scope of solvable problem. Compared with numerical solution, it also has fine precision. [ABSTRACT FROM AUTHOR]

Based on small-deflection buckling equation, a weighted solution for critical load is presented. Usually, it is very difficult to solve the equation for general problems, especially those with complicated boundary conditions. Axisymmetric problem was studied as an example. Influencing factors were found from the equation and averaged as the buckling load by introducing weights. To determine those weights, some special known results were applied. This method solves general complicated problems by using the solutions of special simple problems, simplifies the solving procedure and expands the scope of solvable problem. Compared with numerical solution, it also has fine precision. [ABSTRACT FROM AUTHOR]

The purpose of the present study is to develop a new finite element method for analyzing buckling of delaminated composite plates and shells. This is achieved by establishing a new finite element called the reference-surface element. By use of the compatibility condition under Mindlin assumptions, the formulation of the reference-surface element was derived from whichever plate-element or shell-element being capable of analyzing composite plates and shells. This method assures a reasonable description of displacement field and the satisfaction of compatibility conditions for delamination problem. Numerical results for linear delamination buckling of axially compressed shells are presented to validate the method. [ABSTRACT FROM AUTHOR]