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In this study, a 2D axisymmetric numerical model is developed for simulating buckling of suspension droplets for processes with a high evaporation rate. This model not only demonstrates droplet distortion during buckling but also predicts and visualizes solid particles' behavior inside the droplet. The core element of the simulation method is the so-called D3-law predicting the droplet size and shape during different stages of the process. For improving the accuracy in the droplet shape and forces exerted on the solid particles, the effect of solid particles' concentration on buckling process has been considered. In this method, the solid particles are modeled in Lagrangian manner and possible collision of particles during the buckling has been considered. It is shown that the role of capillary forces in the shape of agglomerated particles is significant. The numerical results also reveal that the size of agglomerated particle depends on the initial solid particle fraction and the suspension droplet size. For all cases considered, the results are in good agreement with experiment measurements reported in the literature. [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]

The study investigates the effect of eccentric load on the stability and post-critical states of thin-walled composite top-hat cross-section columns made of CFRP under compression. The specimens were subjected to compressive load on the universal testing machine Zwick Z100 with regard to both axial and eccentric compressive loads. On the basis of the experimental studies, numerical models of thin-walled composite profiles were designed and verified by numerical analysis based on the FEM. The first stage of the conducted studies was performing a linear buckling analysis of stability of composite structures. The second stage of the analysis involved performing a nonlinear analysis of the thin-walled structures with geometric imperfections reflecting the lowest buckling modes. The obtained test results showed various effects of non-axial compressive load on the critical load values and stiffness of the construction in the post-critical state. In the case of eccentric loading in the direction parallel to the web of the top-hat profiles, the critical load values practically did not change – a drop in the force did not exceed 1.5%, as well as there was no change in the stiffness of the structure in the post-critical state. The realization of the eccentricity in the direction perpendicular to the profile web caused a drop in the critical force equal 43% and a significant decrease in the stiffness of the structure. On the other hand, implementation of the eccentricity load toward the web caused an increase in the critical force by more than 20%, despite very small eccentricity values of only 4 mm were applied. This proved high sensitivity of the tested structures to the non-axial load in the direction perpendicular to the web of the profile. The FEM results and the experimental findings showed satisfactory agreement. [ABSTRACT FROM AUTHOR]

This paper studies the buckling behavior of simply-simply supported Single-walled Carbon nanotubes (SWCNTs) with and without defects. The buckling of carbon nanotubes without defects was investigated using the Finite element method (FEM) and analytical treatment and that of carbon nanotubes with defects was studied only by FEM. The carbon nanotubes were modeled as beams and shells. Computations showed that beam elements in the given form provided varying results as shells in their numerical or analytical manner for a small aspect ratio. The defects resulted from the removal of randomly determined carbon atoms and beam elements connected to the nodes. The increasing number of defects decreased the critical buckling force of SWCNTs. The decrease in the critical buckling force was almost the same for SWCNTs with the same diameter but with different chirality. [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]

A low-order mimetic finite difference method for Reissner-Mindlin plate problems is considered. Together with the source problem, the free vibration and the buckling problems are investigated. Details about the scheme implementation are provided, and the numerical results on several different types of meshes are reported. [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]

The delamination buckling problem for a rectangular plate made of an orthotropic composite material is studied. The plate contains a band crack whose faces have an initial infinitesimal imperfection. The subsequent development of this imperfection due to an external compressive load acting along the crack is studied through the use of the three-dimensional geometrically nonlinear field equations of elasticity theory for anisotropic bodies. A criterion of initial imperfection is used in determining the critical forces. The corresponding boundary-value problems are solved by employing the boundary-form perturbation technique and the FEM. Numerical results for the critical force are presented. [ABSTRACT FROM AUTHOR]

The buckling of imperfect composite cylinders under concentric and eccentric compression is investigated experimentally and numerically, with particular attention given to the imperfection sensitivity of the shells. A series of glass-fiber-reinforced plastic cylinders have been tested under different load eccentricities to validate the corresponding nonlinear numerical analyses performed in this study. A good agreement between the experimental and numerical results was achieved through use of the ABAQUS/Explicit finite-element code and the introduction of initial imperfections. Both the experimental and the numerical results show that the knockdown factor increases as the loading eccentricity grows. [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]

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 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]