Theoretical analysis for axial crushing behaviour of aluminium foam-filled hat sections

A theoretical analysis was performed to predict the crushing behaviour of aluminium foam-filled single hat and double hat sections subjected to axial compression. The experimental results and superfolding element theory were used to create deformation models for the aluminium foam contained in the hat sections, and several assumptions were made for the theoretical analysis. According to the energy method and superfolding elements theory, the mean crushing force and the interactive effect were theoretically predicted for the axial compression of the aluminium foam-filled hat sections. The final formula specified the relationship between the mechanical characteristics of the aluminum foam and the height of the superfolding element. The mean crush forces and the interactive effect predicted by the theoretical analysis were in good agreement with the experimental results. The theoretical prediction results showed that the interactive effect was mainly from the aluminium foam.     

Static crushing of square aluminium extrusions with aluminium foam filler

An experimental investigation was carried out to study the behaviour of square aluminium extrusions filled with aluminium foam under quasi-static loading conditions. Based on the experimental work, simple relations between dimensionless numbers governing the influence of the foam on the characteristics of the crush problem were identified. Furthermore, a simplified set of equations applicable for design of foam-filled components was proposed.     

铝泡沫填充薄壁结构耐撞可靠性优化设计

泡沫填充薄壁结构能有效地改善汽车薄壁吸能部件的耐撞性。为设计更轻与更有效的吸能结构,并满足汽车安全性设计要求,提出一种新颖的轻质铝泡沫填充双管薄壁结构,并对其耐撞性展开确定性最优化设计。但是,由于薄壁结构的厚度、屈服强度以及铝泡沫的密度等设计参数易受到仿真以及制造误差等不确定性因素的影响,导致确定性最优解收敛于约束边界,从而丢失了应有的使用可靠性要求。因此,提出基于Kriging近似模型与一阶可靠性分析方法的铝泡沫填充结构可靠性最优设计方法,并进一步开展基于参数不确定性的铝泡沫填充结构的耐撞性可靠性优化设计研究。优化结果显示,可靠性最优解不仅远离约束边界,而且较好地满足了铝泡沫填充结构的安全性与可靠性设计要求。     

Effect of an ultralight metal filler on the bending collapse behavior of thin-walled prismatic columns

The effect of low-density metal filler, such as aluminum foam or honeycomb, is studied on the bending collapse resistance of thin–walled prismatic columns. A combination of analytical and numerical results is used to predict the initial and post collapse response of empty and filled columns. Closed-formed solutions for the bending-rotation characteristics are constructed in terms of the geometrical parameters and the filler strength. The low-density metal core retards sectional collapse of the thin-wall column, and increases bending resistance for the same rotation angle. Numerical simulations show that, in terms of achieving the highest energy absorption to weight ratio, columns with aluminum honeycomb or foam core are preferable to thickening the column wall. Moreover, the presence of adhesive improved the specific energy absorption significantly.     

Energy absorption of pressurized thin-walled circular tubes under axial crushing

By pressurizing cellular materials, honeycombs, or thin-walled structures, their energy absorption can be greatly enhanced, and this enhancement can be controlled by the applied pressure. This concept shines light on the possibility of achieving adaptive energy absorption. To investigate the effect of internal pressure on energy absorption of thin-walled structures, this paper presents a study of axial crushing of pressurized thin-walled circular tubes. In the experiments, three groups of circular tubes with radius/thickness ratio R/t=120-200 were axially compressed under different pressurizing conditions. The results show that with an increase of internal pressure, the deformation mode switches from diamond mode with sharp corners to that with round corners, and eventually to ring mode. In diamond mode, the mean force of the tubes increases linearly with internal pressure. The enhancement comes from two mechanisms: direct effect of pressure and indirect effect due to interaction between pressure and tube wall. After the deformation switches to ring mode, the enhancement resulting from the second mechanism becomes weaker. Based on experimental observations, the deformation mode, energy dissipation mechanisms as well as interaction between internal pressure and tube wall are analyzed theoretically and the theoretical results are in good agreement with the experimental ones.     

Influence of spot-weld failure on crushing of thin-walled structural sections

Structural effectiveness differences have been observed in a recent study on the progressive axial collapse of thin-walled structural sections when made from different classes of steels (mild steel, interstitial-free rephosphorized high-strength steel and high-strength low-alloyed steel). A higher effectiveness was observed for spot-welded top-hat sections made from a mild steel than for similar sections made from a high-strength steel. For square sections, the structural effectiveness was not affected by the steel classes. It is anticipated that this observation applies not only for spot-welded top-hat and square sections, but for other joined and unjoined thin-walled structures as well.

The part and full failure of spot-welds, during the axial collapse of the thin-walled structural sections, is one possible explanation for the above inconsistency. This is investigated experimentally in this article using peel tests on spot-weld samples under quasi-static and dynamic conditions. Despite having a lower material strength, the mild steel spot-weld samples exhibited a higher peak force and similar energy absorption during failure when compared with a high-strength steel, both under quasi-static and dynamic loadings.

The potential contribution to the mean crushing force during progressive axial collapse is estimated from the experimental results and comparisons are made with deformed thin-walled structural sections from a recent experimental study. Possible implications for the determination of the mean crushing force from analytical and numerical models are identified and discussed.     

Quasi-static axial compression of thin-walled circular aluminium tubes

This paper presents further experimental investigations into axial compression of thin-walled circular tubes, a classical problem studied for several decades. A total of 70 quasi-static tests were conducted on circular 6060 aluminium tubes in the T5, as-received condition. The range of D/t considered was expanded over previous studies to D/t=10–450. Collapse modes were observed for L/D10 and a mode classification chart developed. The average crush force, F_AV, was non-dimensionalised and an empirical formula established as F_AV/M_P=72.3(D/t)^0.32. It was found that test results for both axi-symmetric and non-symmetric modes lie on a single curve. Comprehensive comparisons have been made between existing theories and our test results for F_AV. This has revealed some shortcomings, suggesting that further theoretical work may be required. It was found that the ratio of F_MAX/F_AV increased substantially with an increase in the D/t ratio. The effect of filling aluminium tubes with different density polyurethane foam was also briefly examined.     

Buckling of elastic—plastic square tubes under bending

This paper addresses the response, buckling and collapse of long, thin-walled, seamless steel square tubes under pure bending using a combined experimental and analytical approach. All tubes tested had nominal cross-sections with height equal to 1 in. (25.4 mm) and ranged in height-to-thickness ratios (h/t) from 15.4 to 28.6. The experiments were conducted under curvature control. It was found that the deformation of the cross-section that accompanied bending was uniform along the tubes for low values of curvature. At higher values, periodic ripples with wavelengths approximately equal to the width of the cross-section appeared on the compression flange. These ripples increased in amplitude with further bending. For tubes with higher h∼ the increase was more pronounced. Tubes with lower h/t showed more moderate increases in ripple amplitude but developed regions spanning several ripples in which the cross-section deformation was more pronounced. In all cases, collapse occurred when a kink formed on the compression flange of the tube.Rayleigh—Ritz type formulations based on the principle of virtual work were developed to predict the response and buckling of the tubes. Results include predictions of the response considering the effect of uniform cross-section deformation and predictions of the critical curvature at which the ripples appear. The numerical results are in good agreement with experimental observations.     

Experimental quasi-static axial crushing of top-hat and double-hat thin-walled sections

Quasi-static axial crushing tests have been carried out on thin-walled top-hat and double-hat mild steel spot-welded sections. Several post-test collapse modes were identified for the structures and the associated energy-absorbing characteristics have been examined and compared with previous tests. A new empirical equation is suggested for relating the structural effectiveness to the structural density of top-hat and double-hat sections.     

Comparative study of thermal post-buckling analysis of uniform slender & shear flexible columns using rigorous finite element and intuitive formulations

Thermal post-buckling analysis of uniform, isotropic, slender and shear flexible columns is presented using a rigorous finite element formulation and a much simpler intuitive formulation. The ends of the columns are axially restrained to move and consequently any temperature rise above the stress free condition of the column produces an equivalent constant compressive mechanical load that causes the column to buckle at a critical temperature. Further increase in temperature beyond critical temperature results in the thermal post-buckling phenomenon. As a result of constraints imposed on the axial displacement at the ends of the column, the post-buckling phenomenon is governed by the von-Karman strain displacement relation applicable to one dimensional problems. Empirical formula for ratio of nonlinear axial load to critical load (equivalent constant mechanical load for a given temperature rise) as a function of the central deflection are obtained using both the rigorous finite element and intuitive formulations for various boundary conditions. The boundary conditions considered are the classical such as hinged-hinged, clamped-clamped and clamped-hinged conditions and nonclassical boundary conditions like the hinged-guided or the clamped-guided conditions. Post-buckling analysis results pertaining to nonclassical boundary conditions are meagre in the literature. It is observed that results obtained from both the formulations are in excellent agreement for all boundary conditions considered. Also the accuracy and simplicity of the intuitive formulation is aptly demonstrated to slender and shear flexible columns.     

轴盘系统扭振固有频率的精确计算

把带有圆盘的轴分为若干段,对圆盘厚度范围段,可视为一特殊的段,在这一段内,不考虑圆盘的变形,截面极惯性矩就等于轴的截面极惯性矩,转动惯量为轴和盘转动惯量之和。每一段的扭振方程可精确求出,然后,根据边界条件和连续条件可将扭振固有频率计算出来。     

General approach to residual stresses determination in thin-walled structures by combining the hole drilling method and reflection hologram interferometry

Main questions, which are connected with a determination of residual stresses by combining the hole-drilling method and whole-field displacement measurements, are considered in detail. The relations, which are needed for converting initial experimental data into stress values of interest, are presented for thin-walled plane structures. Required input data are obtained by simultaneous measurements of probe hole distortions in two principal strain directions on opposite sides of thin plane specimen. Emphasis is made on a careful quantitative formulation of the inverse problem, a solution of which is capable of deriving both membrane and bending residual stress components with the highest possible accuracy. It is shown that an availability of two-side initial data is both an essential and a necessary condition of such formulation. Detailed analysis of accuracy of the results obtained is performed proceeding from three different criteria. All presented considerations are supported with a set of high-quality actual interferograms and analogous reference fringe patterns related to weld-induced residual stress fields.     

Finite-element simulation of the lateral compression of aluminium tube between rigid plates

The lateral compression of aluminium and clad tubes owing to a large deformation is examined by an incremental elasto-plastic finite-element method based on an updated Lagrangian formulation in which a sliding-sticking friction mode is specially considered. It is mainly expected to predict the buckling process and load–deflection curves for energy dissipation capacity during the design stage, before trials. The high non-linearity of the process due to geometric changes, the inelastic constitutive behavior, and the deformation-dependent boundary conditions are taken into account in an incremental manner. A static explicit approach to the solution is applied, tangent stiffness matrix equation is solved without iteration and the r_min technique is employed to limit the step size to linear relation. The simulated load–deflection curve agrees with a published experimental result. The predicted geometries of the compressed tube clearly demonstrate the processes of the formation of buckling until unloading. The effects of various parameters of the process, such as elastic modulus, strain hardening exponent, tube thickness, friction coefficient and configurations of the clad tube, on the occurrence of buckling of tube are discussed and interpreted in simulation. The present work may be expected to improve the understanding of the buckling mechanism of lateral compression.