Buckling Of Struts Research Articles

Analytical and numerical analysis on local and global buckling of sandwich panels with strut-based lattice cores

Additive manufacturing (AM) offers new possibilities to fabricate and design lightweight lattice materials. Due to the superior mechanical properties of these lattice structures, they have the potential to replace honeycombs as cores in sandwich panels. In addition to the advantage of the integral fabrication thanks to AM, additively manufactured lattice core sandwich panels may be also used as heat exchangers, enabling a multifunctional use of the core. To ensure a reliable and safe structure, the mechanical response of lattice core sandwich panels under given load conditions must be predictable. In conventional sandwich panels subjected to compressive loads, the sandwich’s global buckling and the face sheets’ local buckling are the dominant failure modes. In constrast, core strut buckling may be the critical failure mode in lattice core sandwich panels. Therefore, an analytical 2D model to predict the local buckling of lattice core struts is considered in this study. Furthermore, the critical load for global buckling is obtained based on the first-order shear deformation theory. Thus, the transition from local buckling to global buckling depending on the length-to-thickness ratio is captured by the presented model. The comparison with finite element modeling of the sandwich model with truss cores has proved the accuracy of the derived model.

A novel method for optimizing energy absorption of tensegrities with multi- self-stress modes

To explore the factors that affect the energy absorption performance of tensegrities with multi-self-stress modes, the Beetle Antennae Genetic Algorithm (BAGA) is carried out in developing reasonable energy absorption optimization strategies. In the first stage, based on the form-finding theory, the initial self-stress (including prestress level and distribution) that meets unilateral property of components was found. Then, the maximum energy that the structure can absorb under vertical loads is taken as the objective function, and constraint conditions regarding cable relaxation, elastic failure, global volume, strut buckling and component collision are considered in obtaining the satisfactory optimal initial self-stress. Finally, three tensegrities with multi-self-stress modes are taken as illustrative examples, the impact of optimal prestress level and the corresponding distribution on the structural energy absorption performance are explored. The results indicate that, for a 18-rod tensegrity and two types of assembled complicated tensegrity, the energy absorption can be respectively increased by about 156.88 %, 50.75 % and 131.09 % with simultaneously optimizing the pre-stress level and its distribution, verifying the effectiveness of the proposed algorithm. Additionally, for the assembled complicated tensegrity constructed using two different assembling ways (corresponding to different assembled prestress distributions), the optimal structural energy absorption ratio can be as high as 1.88 times.

Uniaxial compression test of cement-solidified dredged slurry columns encased with geogrid

This study investigated the performance of unreinforced and geogrid-encased cement-stabilized dredged slurry columns by uniaxial compression tests to simulate the extreme case where the surrounding soil offers no confinement. The objective was to understand the strength characteristics and visualize the deformation damage patterns of the columns with respect to the water content, cement content, length-to-diameter ratio, and geogrid strength. The results show that the unreinforced specimens exhibited strain-softening behavior, whereas geogrid encasement induced strain-hardening, with high-strength geogrids showing superior strain-hardening capacity. Notably, regardless of geogrid strength, encasement enhanced the resistance to deformation and ductility of the columns. Increasing the cement content, reducing the water content, and decreasing the length-to-diameter ratio all contributed to higher peak strength in both unreinforced and geogrid-encased specimens. Geogrid encasement provides confinement that enhances peak strength. The influence of geogrid encasement on peak strength becomes more pronounced at lower cement contents, higher water contents, and higher length-to-diameter ratios. Geogrid encasement also affects failure modes, altering the predominant inclined shear failure observed at the top of unreinforced specimens. Specimens encased with geogrids of higher tensile strength exhibit enhanced integrity and deformation resembling compression strut buckling, with a symmetrically inclined failure trend at the top and bottom.

Compression and energy absorption characteristics of short fiber‐reinforced 2D composite lattices made by material extrusion

AbstractWith the advent of additive manufacturing, lattice structures have been of increasing interest for engineering applications involving light‐weighting and energy absorption. Several studies have investigated mechanical properties of various lattices made up of mostly unreinforced polymers and lack numerical analysis for reinforced lattice structures. In this paper, mechanical response of short fiber reinforced lattice structures under compression is investigated through experiments and numerical simulations. Three different 2D lattices namely, square grid, honeycomb, and isogrid along with their rotated counterparts were fabricated using 15% wt carbon fiber‐acrylonitrile butadiene styrene and experimentally evaluated through uniaxial compression testing up to 30% strain. As simulations on fiber‐reinforced lattices under large compressive strains are rarely performed and published, finite element models accounting for fiber orientation induced anisotropic mechanical properties and geometrical imperfections were developed to predict the stress–strain characteristics up to 30% compressive strains. The stress–strain curves predicted from the numerical simulations matches well with the experimental responses for various lattice geometries. Various failure mechanisms such as thin strut buckling, contact within the lattice, and fracture of struts under large deformation were investigated. Analyzing energy absorption characteristics of these lattices revealed that the honeycomb structures in horizontal configuration exhibits superior energy absorption capability.

Design and mechanical behaviours of a novel tantalum lattice structure fabricated by SLM

ABSTRACT Tantalum (Ta) has excellent prospects in the bone-implant field due to its satisfactory biocompatibility. Two novel Ta lattice structures were designed and printed by selective laser melting (SLM), including the imitation saddle surface (ISS) and the imitation arch bridge telescopic (IABT) structures. Quasi-static compression tests and finite element analysis were adopted to investigate the effects of design parameters on the mechanical properties, deformation modes, and energy absorption of lattice structures. Compared with the typical lattice structure body-centred cubic (BCC) structure, the ISS lattice structure had a higher yield-stress-to-elastic-modulus ratio, and the IABT lattice structure had higher energy absorption. The failure mode of the BCC and ISS lattice structures was shear band formation. The IABT lattice structure showed hierarchical deformation during compression and collapsed with vertical strut buckling. The results indicated that the ISS lattice is the most potential candidate for bone implant applications.

Analysis of Microstructure Evolution and Mechanical Properties during Compression of Open-Cell Ni-Foams with Hollow Struts Using Micro-CT and FEM.

Based on electron backscatter diffraction (EBSD), hollow structures of Ni foam struts fabricated by electroplating on a chemically removable template were observed. Three-dimensional (3D) pore structures of Ni foams were also obtained using X-ray computed tomography (CT), and microstructural features such as porosity, pore size and strut thickness were statistically quantified. Evolution of microstructure and mechanical properties during ex situ compression of open-cell Ni-foams was investigated based on X-ray CT, and experimental results were compared with predictions by the finite element method (FEM). 3D microstructures obtained by X-ray CT revealed that the stress drop started with the buckling of struts at the center of the Ni-foams. The flow stress increased after the buckling of the struts spreads to most of the regions. For effective simulation of the compressive deformation and determination of the microstructural evolution, small domains of interest were selected from the entire set of observed 3D microstructures based on X-ray CT, and struts of Ni foams with a hollow structure were simplified with relevant thin-solid struts. Numerical 3D modeling comprehensively disclosed that compression caused the transverse buckling of the struts, with the bending and buckling of struts thus reducing the stress. Thickness variation of the struts causes a change in the porosity of Ni-foams without a change in pore shape or connectivity. The overall range of strut thickness was from 59 to 133 m, and the range of porosity values was from 80% to 93.7%. A stress drop was predicted with a decrease in the strut thickness or an increase in the porosity, as measured experimentally. It was also found that the stress drop contributed to an increase in the calculated energy absorption efficiency.

Minimal mass design of active tensegrity structures

Tensegrity structures have been widely utilized as lightweight structures due to their high stiffness-to-mass and strength-to-mass ratios. Minimal mass design of tensegrity structures subject to external loads and specific constraints (e.g., member yielding and buckling) has been intensively studied. However, all the existing studies focus on passive tensegrity structures, i.e., the structural members cannot change their lengths actively and the structure has to passively resist external loads. An active tensegrity structure equipped with actuators can actively adapt its internal forces and nodal positions and thus can actively resist external loads. Therefore, it is expected that active tensegrity structures use less material compared to passive tensegrity structures thus leading to a smaller mass. Due to the integration of the active control system, the design of active tensegrity structures is different from passive tensegrity structures. This study proposes a general approach for the design of minimal mass active tensegrity structures based on a mixed integer programming scheme, in which the member cross-sectional areas, prestress, actuator layout and control strategies (i.e., actuator length changes) are designed simultaneously. The member cross-sectional areas, prestress level, and actuator control strategies are treated as continuous variables and the actuator layout is treated as a binary variable. The equilibrium condition, member yielding, cable slackness, strut buckling, and the limitations on the nodal displacements as well as other practical requirements are formulated as constraints. Three typical active tensegrity structures are designed through the proposed approach and the results are benchmarked with the equivalent minimal mass passive designs. It is illustrated that the active designs can significantly decrease the material consumption compared with the equivalent passive designs thus leading to more lightweight tensegrity structures.

Tensegrity Metamaterials: Toward Failure-Resistant Engineering Systems through Delocalized Deformation.

Failure of materials and structures is inherently linked to localized mechanisms, from shear banding in metals, to crack propagation in ceramics and collapse of space-trusses after buckling of individual struts. In lightweight structures, localized deformation causes catastrophic failure, limiting their application to small strain regimes. To ensure robustness under real-world nonlinear loading scenarios, overdesigned linear-elastic constructions are adopted. Here, the concept of delocalized deformation as a pathway to failure-resistant structures and materials is introduced. Space-tileable tensegrity metamaterials achieving delocalized deformation via the discontinuity of their compression members are presented. Unprecedented failure resistance is shown, with up to 25-fold enhancement in deformability and orders of magnitude increased energy absorption capability without failure over same-strength state-of-the-art lattice architectures. This study provides important groundwork for design of superior engineering systems, from reusable impact protection systems to adaptive load-bearing structures.

Dynamic compressive behaviour of sandwich panels with lattice truss core filled by shear thickening fluid

The compressive behaviour of sandwich panels with lattice truss core filled by shear thickening fluid (SPLTC-STF) at high strain-rates is performed analytically and numerically. Firstly, a hydrodynamic constitutive model for the shear thickening fluid (STF) involving shear thinning, shear thickening, and hydrostatic compressibility is undertaken to describe the dynamic behaviour of the STF. Then an analytical model based on the squeezing flow of viscous fluids is proposed. The squeezing resistance of the STF between the two panels of the SPLTC under various loading velocities is analysed using a fluid-structure interaction (FSI) simulation, by which the constitutive parameters of the STF are obtained. Finally, the dynamic response of the SPLTC-STF involving buckling and post-buckling of core struts in the STF is investigated using the FSI method. The enhanced energy absorption capacity of the SPLTC-STF observed in Ref [1] is numerically interpreted. The effects of shear thickening behaviour of STF on the dynamic response of SPLTC-STF are predicted, providing a method of optimal design for STF filled sandwich panels over a wide range of impulse loadings for dynamic energy absorption.

Experimental Study of Cold-Formed Steel Built-Up Beams

This paper describes a comprehensive experimental program on cold-formed steel built-up beams with two different cross-sectional geometries. The work aimed to experimentally investigate the interaction between the individual components under increasing loading and to quantify the effect of the connector spacing on the cross-sectional moment capacity and the behavior of the beams. In total, 12 specimens were tested in a four-point bending configuration, with lateral restraints provided at the loading points in order to avoid global instabilities. The built-up specimens were composed of three or four plain channels with nominal thicknesses of 1.2 and 1.5 mm, which were joined together using M6 bolts. Each built-up geometry was tested with three different connector spacings. The specimens were designed to fail by local buckling of their components. Additionally, strut buckling of the channel comprising the top flange in between connector points was observed. The local buckling deformations and the beam deflections were recorded during the tests. The material properties of the test specimens were determined by means of coupon tests and the geometric imperfections were measured prior to testing. The experimental results showed clear evidence of interaction between the local buckling patterns of the components, with the interaction being affected by the connector spacing and the type of geometry. However, the connector spacing showed a less significant effect on the ultimate capacity when failure was governed by local instabilities of the components.

Dynamic failure of ceramic particle reinforced foam-filled composite lattice core

The ceramic particle reinforced foam-filled carbon fiber reinforced composites sandwich unit cell subjected to quasi-static and dynamic compressions are studied experimentally. The weight fraction of the ceramic particle is discussed to analyze its effect on the failure and energy absorption of the composite cells. The results show that the failure modes and energy absorption mechanisms of the cell are influenced significantly by the strain rate and ceramic particle reinforcement effects. The cluster of the particle makes the strut experience node failure under impulsive loadings, not the strut buckling and fracture shown at other cells. The mechanical property, especially the plateau stress, is enhanced noticeably as the foam is reinforced with the higher weight fraction of ceramic particles. The filling foams improve the impact resistance of the cells by transmitting less impulses and absorbing more energy. With a higher energy absorption efficiency, the foam-filled cell with higher weight fraction of ceramic particle has the highest energy absorption capacity under the quasi-static compression. Under the impulsive loading, the increasing ceramic particles can reduce the transmitted impulse, but cannot absorb additional energy.

Dynamic collapse of metal self-similar hierarchical corrugated sandwich plates subject to shear and compression coupled loading

Analysis of dynamic collapse response of metal self-similar hierarchical triangular corrugated sandwich plates subject to the shear loading and the shear coupled with compression is conducted. The initial collapse modes of the triangular corrugated sandwich cores are identified, in which different shear or shear-compression coupled impact velocities and various slenderness ratios of the large and small struts are considered, i.e. Euler buckling of large struts, Euler buckling of small struts, the wrinkling of large struts, the mode of combined Euler buckling of small struts with the wrinkling of large struts, and the mode of combined Euler buckling of large struts with the wrinkling of large struts. The collapse mechanism maps are then figured out with the axes representing the slenderness ratios of the large and small struts for hierarchical corrugated sandwich cores under single shear loading and combined shear and compression. In particular, the theoretically predicted collapse mechanism maps are in good agreement with the numerical results at applied velocity V0 = 1 m/s under the single shear loading and the shear coupled with compression. It is demonstrated that the velocity has insignificant influence on the dominant deformation mode of self-similar hierarchical corrugated sandwich plates for the cases of velocities V0 = 1 m/s and 10 m/s under the single shear loading and the shear coupled with compression. The designed self-similar hierarchical corrugated sandwich core has better energy absorption than traditional corrugated sandwich core subject to the single shear loading.

Structural design and behavior of prestressed cable domes

A cable dome system is a spatial network of cables and struts that are pin-jointed, and whose forces are eventually brought to balance by a perimeter ring beam and supporting walls or columns. This paper provides insights about the structural design and behavior of prestressed radial-type cable domes. Through a study of parametric effects, the paper emphasizes careful selection of geometric parameters and cable prestressing forces. A simplified planar model equivalent to that of a three-dimensional model is derived for efficient analysis and design under symmetric loading conditions. The equivalent planar parameters are obtained using the geometrical and nodal force equilibrium relationships, and the Principle of Virtual Work. Results from planar analysis are compared and validated with the three-dimensional analysis results. The calculation of initial member sizes and initial cable prestressing forces is explained. This is followed by a discussion of the structural behavior of cable domes under asymmetric snow loads and wind uplift and the ensuing stability issues. The analysis results revealed that either strut buckling or overall system stiffness were the dominant limit states, the former being the governing limit state in domes with fewer hoops. A design enhancement in the form of cable-stayed struts is as such recommended to not only increase the strut buckling strength, but also to substantially increase a dome’s load bearing capacity.

Mechanical analysis and modeling of metallic lattice sandwich additively fabricated by selective laser melting

Abstract In order to balance the strength and weight, 3D lightweight metallic kagome lattice sandwiches were fabricated by selective laser melting with 304 stainless steel (SS) and Co-Cr-Mo (CCM) alloy. Systematical experiments, numerical modeling and theoretical prediction for compression and bending behaviors were conducted. The experimentally measured strengths are very close to the theoretical predictions, demonstrating the excellent mechanical properties. The numerical modeling can capture the stress-strain, load-deflection curves, and the failure mode is the strut buckling initiated from the plastic hinges with high stress level. The CCM alloy kagome lattice sandwich presents non-synchronous deformation. The buckling of the struts near bottom facesheets always arises first, and is followed by the subsequent buckling of the struts near up facesheets. The strength and modulus of CCM alloy are higher than those of 304 SS, resulting in relative high values of strength and load capacity for CCM alloy kagome lattice sandwich. In contrast, the superior plasticity of 304 SS enables relative high plastic deformation ability of 304 SS kagome lattice sandwich. The kagome lattice sandwiches provide a solution to effectively balance the strength and weight, as they present lower density than engineering alloys and higher strength than honeycombs, foams and pyramid lattice sandwich.

Dynamic collapse of metal self-similar hierarchical corrugated sandwich plates

The dynamic collapse response of metal self-similar hierarchical corrugated sandwich plates is analyzed. The analytical model is derived for the reaction forces of the top and bottom face sheets. Finite element analysis is conducted to investigate the dynamic collapse of the self-similar hierarchical corrugated sandwich cores. Collapse modes of cores are found compressed at different impact velocities. The analytical model captures the average reaction forces reasonably. The collapse mechanism maps are constructed with axes representing the slenderness ratio of the big and small struts for hierarchical corrugated sandwich cores and are in good agreement with numerical results. The results reveal that the increase in the velocity changes the dominant deformation modes of the collapse mechanism maps. The region of Euler buckling of small struts increases with increasing velocity.

Response of anisotropic polyurethane foam to compression at different loading angles and strain rates

Polyurethane (PU) foam can display mechanical anisotropy because of elongation of cells in the vertical direction when component liquid chemicals are mixed to generate PU foam. Existing studies on the anisotropic mechanical response of PU foam appear limited, particularly for high strain-rate loading. In this investigation, a PU foam with an apparent density of 36.5 kg/m3 was fabricated, and 40 mm cubic specimens were cut at 0°, 30°, 45°, 60° and 90° to the foam-rise direction, and subjected to quasi-static (0.0042–0.42 s−1 global strain rate) and dynamic (∼190 s−1 global strain rate) compression, to identify the effects of loading direction and strain rate on the resulting mechanical response. Dynamic compression tests were performed using a modified Hopkinson bar device, with force equilibrium in the foam specimens examined and validated via finite element modelling. The overall stress–strain response, as well as the deformation modes, varies significantly with loading direction. For compression along the foam-rise direction (0°), deformation of foam cells is dominated by unstable buckling of cell struts; this leads to deformation localization and subsequent layer-by-layer crushing. The corresponding overall stress–strain response displays a brief post-yield strain softening phase, generated by the initiation and development of localized deformation in the first cell layer to collapse. This is followed by a protracted stress plateau, whereby localized crushing propagates layer-by-layer through the specimen. For compression along the transverse direction (90°), deformation of foam cells is characterized by stable bending of cell struts, leading to uniform deformation within the foam specimen, accompanied by gradual post-yield hardening in the overall stress–strain response. For compression at various inclinations (e.g. 30°, 45°, 60°) to the foam-rise direction, foam cells deform via a combination of buckling and bending of cell struts, and the overall stress–strain response lies between that corresponding to compression along the foam-rise and the transverse directions. With respect to the influence of strain rate, a higher deformation rate generates a stiffer and stronger overall stress–strain response. Several material parameters — i.e. overall elastic stiffness, yield stress, densification strain and effective energy absorption capacity — were examined to characterize the mechanical properties of PU foam. The elastic stiffness, yield stress and effective energy absorption capacity all decrease with an increase in loading angle to the foam-rise direction, but they increase with strain rate. However, the densification strain varies little with loading angle or strain rate.

Defect Sensitivity of Truss Strength

Periodic trusses with missing or defective struts may exhibit reduced strength relative to those of otherwise pristine trusses. The principal goal of the present study is to determine the extent to which individual strut defects and free surfaces, both separately and together, elevate strains in neighboring struts and, in turn, the effects of strain elevations on truss strength, especially in trusses made from elastic-brittle materials. The goals are pursued through finite element analyses of three stretch-dominated truss structures with low relative density under uniaxial compressive loading. In all cases considered, strain elevations due to bulk defects (distant from free surfaces) are comparable to or lower than those associated with the surfaces themselves. Although defects located at truss corners and truss edges cause the highest elevations in strut strains, their effects on truss strength are small (5–25%). Guidelines are presented for the minimal tensile fracture strain of the constituent material required to achieve the full strength potential of the truss, dictated by large-scale strut buckling.

Stability Study of the Accident of a General Aviation Aircraft

In April 2014 an aircraft accident occurred at Jämijärvi aerodrome when a Comp Air 8 aircraft crashed into the woods. According to the scenario of the investigation report, the pilot reduced the engine power in such a way that the thrust became negative. Simultaneously the prop-washed kinetic pressure of the tail was reduced, which rapidly evoked a nose-down moment and a corresponding angular velocity. This led to a negative angle of attack and a large negative wing load and finally resulted in a wing strut buckling and the wing folding toward the aircraft’s body. In this study, six degree-of-freedom (6-dof) simulations are carried out for the aircraft to assess the supposed accident scenario. The simulations show that the proposed mechanism is possible, but there existed other potential courses of events after the thrust adjustment.

Compression and shear response of carbon fiber composite sandwich panels with pyramidal truss cores after thermal exposure

ABSTRACTThe composite pyramidal truss core sandwich panels with reinforced joints are manufactured by the water jet cutting and interlocking assembly method. The effect of thermal exposure on the out-of-plane compression and shear performances of composite sandwich panels is investigated experimentally. In particular, the out-of-plane compression and shear moduli and strengths of the structures after thermal exposure are predicted theoretically. Experimental results show that the out-of-plane compression and shear performances of composite pyramidal truss core sandwich panels first increase and then decrease with thermal exposure temperature at the thermal exposure of 6 h. The failure modes depend on the particular temperature and time of the applied thermal exposure. As well, the compression and shear performances first increase and then decease with thermal exposure time at 150°C. However, their compression and shear performances have a decreasing tendency with time for a given 230°C exposure temperature. In addition, the destruction responses of composite sandwich panels are also investigated and their possible failure modes (including the crushing, delamination and local buckling of struts) are complemented with the analytic results.

Effect of vacuum thermal cycling on the compression and shear performance of composite sandwich structures containing pyramidal truss cores

Composite pyramidal-truss core sandwich panels, in which the lattice core is strengthened by reinforced frames between dispersive nodes, were manufactured via water-jet cutting and interlocking assembly. The coefficients of thermal expansion and outgassing (mass loss) ratios of the composite laminates were determined. Subsequently, the effect of vacuum thermal cycling on the compression and shear performance of the composite sandwich panels with pyramidal-truss cores was studied using theoretical and experimental methods. In particular, the out-of-plane compression stiffness and strength, as well as the shear stiffness and strength of the structures subjected to vacuum thermal cycling, were predicted using theoretical equations. The compression and shear performance improved initially and then deteriorated with an increase in the vacuum thermal cycling-time. The observed failure modes depended on the number of vacuum thermal cycles. In addition, the catastrophic response of the composite sandwich panels with pyramidal-truss cores was investigated, and their possible failure modes (including the crushing and localized buckling of composite struts) were complemented with results of analytical modeling. The truss cores collapsed mainly due to crushing and localized-buckling processes, caused by matrix outgassing and debonding of the interface between the carbon fibers and epoxy resin, after prolonged thermal cycling.