Crashworthiness design of functionally graded foam-filled multi-cell thin-walled structures

Foam-filled thin-walled structure has recently gained attention due to its excellent crashworthiness. Based on the previous study, a new kind of foam-filled thin-walled structure called as functionally graded foam-filled thin-walled structure has more excellent crashworthiness than the traditional uniform foam-filled thin-walled structure. Moreover, as far as we know multi-cell thin-walled structure has more excellent crashworthiness than the traditional single-cell thin-walled structure. As an integrator of the above two kinds of excellent thin-walled structures, functionally graded foam-filled multi-cell thin-walled structure (FGFMTS) may has extremely excellent crashworthiness. Based on our study, the crashworthiness of the FGFMTSs is significantly affected by the design parameter of the graded functional parameter m. Thus, in order to obtain the optimal design parameters, the FGFMTSs with different cross sections and different wall materials are optimized using the multiobjective particle swarm optimization (MOPSO) algorithm to achieve maximum specific energy absorption (SEA) capacity and minimum peak crushing force (PCF). At the same time, the corresponding uniform foam-filled multi-cell thin-walled structures (UFMTS) which have the same weight as these FGFMTSs are also optimized in our study. In the multiobjective design optimization (MDO) process, polynomial functional metamodels of SEA and PCF of FGFMTSs are used to reduce the computational cost of crash simulations by finite element method. The MDO results show that the FGFMTS with PCF in the initial period of its crash not only has better crashworthiness than the traditional UFMTS with the same weight but also performs superior balance of crashing stability. Thus, the optimal design of the FGFMTS with PCF occurring in the initial crash is an extremely excellent energy absorber and can be used in the practical engineering.     

An analytical model for axial crushing of a thin-walled cylindrical shell with a hollow foam core

A thin-walled tube filled with light-weighted foam has wide engineering applications because of its excellent energy absorption capacity. When the structure is axially crushed, the interaction between the tube and foam core plays an important role in its energy absorption performance. Previous theoretical studies so far have largely been concerned with fully in-filled tubes. In this paper, a theoretical model is proposed to predict the axi-symmetric crushing behaviour of such structures but with a partial infill. Using a modified model for shell and considering the volume reduction for the foam core, the mean crushing force is predicted by the energy balance. The proposed formula agrees well with previous results reported in literature. A parametric study is carried out to examine the contribution of foam core plateau stress (σ_f), amount of filling and shell's radius-to-thickness ratio (R/h) on the axial crushing behaviour of the structure. This study can give valuable design guidelines in using thin-walled structures as an energy absorber.     

Crashworthiness optimization design for foam-filled multi-cell thin-walled structures

Foam-filled thin-walled structure and multi-cell thin-walled structure both have recently gained attentions for their excellent energy absorption capacity. As an integrator of the above two kinds of thin-walled structures, foam-filled multi-cell thin-walled structure (FMTS) may have extremely excellent energy absorption capacity. This paper firstly investigates the energy absorption characteristics of FMTSs by nonlinear finite element analysis through LS-DYNA. Based on the numerical results, it can be found that the FMTS with nine cells has the most excellent crashworthiness characteristics in our considered cases. Thus, the FMTSs with cell number n=9 are then optimized by adopting a multi-objective particle swarm optimization (MOPSO) algorithm to achieve maximum specific energy absorption (SEA) capacity and minimum peak crushing force (PCF). During the process of multi-objective optimization design (MOD), four kinds of commonly used metamodels, namely polynomial response surface (PRS), radial basis function (RBF), Kriging (KRG) and support vector regression (SVR) for SEA and PCF, are established to reduce the computational cost of crash simulations by the finite element method. In order to choose the best metamodel for optimization, the accuracies of these four kinds of metamodels are compared by employing the error evaluation indicators of the relative error (RE) and the root mean square error (RMSE). The optimal design of FMTSs with nine cells is an extremely excellent energy absorber and can be used in the future vehicle body.     

Quasi-static response and multi-objective crashworthiness optimization of oblong tube under lateral loading

This paper addresses the energy absorption responses and crashworthiness optimization of thin-walled oblong tubes under quasi-static lateral loading. The oblong tubes were experimentally compressed using three various forms of indenters named as the flat plate, cylindrical and a point load indenter. The oblong tubes were subjected to inclined and vertical constraints to increase the energy absorption capacity of these structures. The variation in responses due to these indenters and external constraints were demonstrated. Various indicators which describe the effectiveness of energy absorbing systems were used as a marker to compare the various systems. It was found that unconstrained oblong tube (FIU) exhibited an almost ideal response when a flat plate indenter was used. The design information for such oblong tubes as energy absorbers can be generated through performing parametric study. To this end, the response surface methodology (RSM) for the design of experiments (DOE) was employed along with finite element modeling (FEM) to explore the effects of geometrical parameters on the responses of oblong tubes and to construct models for the specific energy absorption capacity (SEA) and collapse load (F) as functions of geometrical parameters. The FE model of the oblong tube was constructed and experimentally calibrated. In addition, based on the developed models of the SEA and F, multi-objective optimization design (MOD) of the oblong tube system is carried out by adopting a desirability approach to achieve maximum SEA capacity and minimum F. It is found that the optimal design of FIU can be achieved if the tube diameter and tube width are set at their minimum limits and the maximum tube thickness is chosen.     

On the fracture possibility of thin-walled tubes under axial crushing

Thin-walled tubes are widely used as energy absorption components in vehicle crashworthiness design where axial crushing is one of the most typical loading conditions. Lightweight materials such as high-strength steel, aluminum and magnesium have been applied for thin-walled tubes for weight reduction. Meanwhile, most of these lightweight materials are more brittle and easily fractured than traditional steel. Distribution and history of stress triaxiality and equivalent strain in the thin-walled tubes under axial crushing have been analyzed in this article with finite element simulation, as these two parameters of stress and strain states are commonly used for constructing fracture locus of materials. It is observed that both stress triaxiality and equivalent strain are transferring along the tube length like waves. Analysis results show that fracture is more likely to take place on the edge than the other positions of square thin-walled tubes. For identical axial crushing stroke, there is little difference of stress and strain states inside the square thin-walled tubes with initial impact velocity varying from 6 m/s to 24 m/s. Influence of geometrical parameters on the stress and strain states have also been analyzed, including the shape of cross-section corner, the wall thickness and the shape of cross-section, respectively. Analysis results in this article may offer references for design of thin-walled tubes and the necessary experimental characterization of mechanical properties for lightweight materials.     

Multiobjective crashworthiness optimization of multi-cornered thin-walled sheet metal members

Plastic deformation of structures absorbs substantial kinetic energy when impact occurs. Therefore, energy-absorbing components have been extensively used in structural designs to intentionally absorb a large portion of crash energy. On the other hand, high peak crushing force, especially with regard to mean crushing force, may lead to a certain extent and indicate the risk of structural integrity. Thus, maximizing energy absorption and minimizing peak to mean force ratio by seeking for the optimal design of these components are of great significance. Along with this analysis, the collapse behavior of square, hexagonal, and octagonal cross-sections as the baseline for designing a newly introduced 12-edge section for stable collapse with high energy absorption capacity was characterized. Inherent dissipation of the energy from severe deformations at the corners of a section under axial collapse formed the basis of this study, in which multi-cornered thin-walled sections was focused on. Sampling designs of the sections using design of experiments (DOE) based on Taguchi method along with CAE simulations was performed to evaluate the responses over a range of steels grades starting from low end mild steels to high end strength. The optimization process with the target of maximizing both specific energy absorption (SEA) and crush force efficiency (CFE), as the ratio of mean crushing load to peak load, was carried out by nonlinear finite element analysis through LS-DYNA. Based on single-objective and multi-objective optimizations, it was found that octagonal and 12-edge sections had the best crashworthiness performance in terms of maximum SEA and CFE.     

Experimental behaviour of thin-walled hollow structural steel (HSS) columns filled with self-consolidating concrete (SCC)

In modern building construction, thin-walled hollow structural steel (HSS) sections are often filled with concrete to form a composite column. In recent years, the use of self-consolidating concrete (SCC), or self-compacting concrete, in such kinds of columns has been of interest to many structural engineers. Due to its rheological properties, the disadvantage of vibration can be eliminated while still obtaining good consolidation. Apart from reliability and constructability, advantages such as elimination of noise in processing plants, and the reduction of construction time and labor cost can be achieved. It is expected that SCC will be used in concrete-filled HSS columns in the future because of its good performance. However, the composite members are susceptible to the influence of concrete compaction. The lack of information on the behavior of HSS columns filled with SCC indicates a need for further research in this area.The present study is an attempt to study the possibility of using thin-walled HSS columns filled with SCC. New test data on 38 HSS columns filled with SCC to investigate the influence of concrete compaction methods on the member capacities of the composite columns are reported. The specimen tests allowed for the different conditions likely to arise in the manufacture of concrete: cured, well compacted with a poker vibrator, well compacted by hand, and self-consolidating without any vibration. The main parameters varied in the tests are: (1) column section type, circular and square; (2) tube diameter (or depth) to thickness ratio, from 33 to 67; and (3) load eccentricity ratio (e/r), from 0 to 0.3 mm. Comparisons are made with predicted column strengths using the existing codes such as AISC-LRFD-1999, AIJ-1997, BS5400-1979, EC4-1994, DL5085/T-1999 and GJB4142-2000.     

Square hollow section (SHS) T-joints with concrete-filled chords subjected to in-plane fatigue loading in the brace

In recent years, there has been an increased use of concrete-filled composite tubular joints in bridge construction. The reliability of these joints under fatigue therefore need to be investigated to avoid any catastrophic failures. In this paper, hollow section T-joints made up of square hollow section (SHS) chords and braces are investigated. The chords of the SHS–SHS T-joints were concrete-filled thereby forming welded composite tubular T-joints. The SHS–SHS T-joints with concrete-filled chords were strain gauged and tested under static loading to determine stress concentration factors (SCFs) at hot spot locations, where cracks are likely to propagate. Fatigue tests of the welded composite joints were also carried out under cyclic in-plane bending in the brace to obtain stress range vs. number of cycles (S–N) data. The maximum stress concentration factor (SCF) at hot spot locations in a welded composite tubular T-joint was found to be generally lower than the maximum SCF in an empty (or called unfilled) hollow section SHS–SHS T-joint. Fatigue failure in welded composite tubular T-joints occurred through the initiation and propagation of cracks at weld toes in either the chord or brace member, with the majority of tests exhibiting the first visual crack at weld toes in the chord. The welded composite tubular T-joints were found to have better fatigue strength compared to the empty hollow section SHS–SHS T-joints. Design rules are recommended for the SHS–SHS T-joints with concrete-filled chords through analysis of fatigue test data using the hot spot stress method.     

Structural resistance of longitudinal double plates-to-RHS connections

The purpose of the study reported herein is to investigate the behavior of longitudinal double plates-to-RHS connections in a T-configuration. A total of seven specimens (5 for double-plate type, 2 for single-plate type) were tested under compression. The main experimental parameters were the width ratio of the branch plate to the chord (β) and the type (or number) of branch plates. Test results showed that the value of β and thereby the strength of the double-plate type specimens increased due to the space between the plates. Furthermore, a combined failure of chord flange yielding and chord web buckling, which was not generally observed in longitudinal single plate-to-RHS connections, was observed in one of the double-plate specimens. A yield line analysis was also performed for different locations of plastic hinges, considering the corner radius of the HSS chord, as well as the welds for the plates. The strengths based on the proposed yield line model showed good agreement with the experimental results when the plastic hinges were assumed to be located at the web of the HSS chord adjacent to the corner radius, and at the toe of the welds.     

Tests and calculations for hollow structural steel (HSS) stub columns filled with self-consolidating concrete (SCC)

The behaviour of self-consolidating concrete (SCC) filled hollow structural steel (HSS) stub columns subjected to an axial load was investigated experimentally. A total of 50 specimens were tested. The main parameters varied in the tests are: (1) sectional types: circular and square; (2) steel yielding strength: from 282 to 404 MPa; and (3) tube diameter or width to wall thickness ratio (D/t or B/t): from 30 to 134.A mechanics model is developed in this paper for concrete-filled HSS stub columns. A unified theory is described whereby a confinement factor (ξ) is introduced to describe the composite action of the steel tube and the filled concrete. The predicted load versus deformation relationship was in good agreement with test results. The theoretical model was used to investigate the influence of important parameters that determine the ultimate strength of the composite columns. The parametric and experimental studies provide information for the development of formulae for the calculation of the ultimate strength and the axial load versus axial strain curves of the composite columns. Comparisons are made with predicted stub column strengths using the existing codes, such as ACI-1999, AISC-LRFD-1999, AIJ-1997, BS5400-1979 and EC4-1994.     

Effect of drying temperature on surface roughness of oak (Quercus petraea ssp. iberica (Steven ex Bieb) Krassiln) Veneer

This paper reports the effect of various drying temperatures on the surface roughness (SR) characteristics of veneer samples. Three SR parameters [average roughness (R_a), average maximum height of the profile (R_z), and root mean square roughness (R_q)] were measured on sliced veneer obtained from Oak logs (Quercus petraea ssp. iberica (Steven ex Bieb) Krassiln). The sliced veneers were dried at 100, 115 and 130 °C drying temperatures for 2 min. Roughness measurements were taken from the surface of the samples in across the grain orientation of the veneer. The results showed that the effect of drying temperatures used in practice is statistically significant on SR of the sliced veneers.     

Axial crushing of circular tubes with buckling initiators

This paper presents a study of the effectiveness of adding a buckling initiator which is used to reduce the initial peak force of a thin-walled circular tube under axial impact loadings. The buckling initiator is installed near the impact end of the circular tube and is composed of a pre-hit column along the axis of the tube and several pulling strips uniformly distributed around the top edge of the tube. This device functions just before the impact happens and does not affect the structural stiffness under its normal working conditions. By using two kinds of aluminum-alloy circular tubes, a series of quasi-static compression tests were conducted. The deformation mode, the initial peak force and the mean crushing force of the tubes with different number of pulling strips N, pre-hit height h and inclined angle of the pulling strips θ₀ were studied in the experiments. The results reveal that by using this buckling initiator, the large progressive deformation of the axially crushed circular tube switches from ring mode or mixed mode to diamond mode. Although specimens with N=2, 3 and 4 were tested, the stable deformation tended to diamond mode with lobe number N=3. With suitable selection of pre-hit height h, the initial peak force could be reduced by more than 30%. In addition, a simplified theoretical analysis is conducted to illustrate the reduction of the initial force as well as the energy dissipation mechanisms, leading to good agreements with the experimental results.     

Thin circular hollow section-to-plate T-joints: Stress concentration factors and fatigue failure under in-plane bending

Welded thin-walled (t<4 mm) tube-to-plate T-joints made up of cold-formed circular hollow sections welded onto a plate to form a moment resistant connection are used in the road transport and agricultural industry to manufacture equipment and other structural systems. Fatigue design of these joints is not available in current standards. An understanding of the stress concentrations and failure in these connections is therefore necessary as a step towards understanding the fatigue behaviour of these connections. Stress concentration factors (SCFs) of welded thin-walled (t<4 mm) circular hollow section (CHS)-to-plate T-joints are determined at different locations along the weld toes on the tubular brace. The distribution of SCFs along the weld toes shows that the highest SCF occurs at the weld toes in the circular brace at the 0° line. The ratio of the end of test fatigue life (N4) to the through-thickness fatigue life (N3) in the thin CHS-plate T-joints is found to fall within the range of N4/N3 found in previous research of both thick and thin-walled joints. Surface crack growth monitoring is used to obtain an approximation of the length of surface crack at the point of occurrence of a through-thickness crack. The relationship between surface crack length and the occurrence of a through-thickness crack is important in that it can be used as a measure of the criticality of a surface crack during structural health monitoring of equipment or structures.     

Effect of weld details on the ductility of steel column baseplate connections

Results from six two-thirds scale tests on moment-resisting steel column base plates are presented. The test specimens incorporate Complete Joint Penetration (CJP) and Partial Joint Penetration (PJP) weld details between the column and the base plate. The test data indicate that both details are resilient to fracture and sustain inelastic column hinging to story drift ratios of 6%-9%, which exceeds the typical acceptance criteria of 4% drift ratio for seismically detailed special moment frames. In five of the six tests, fractures initiated in the Heat Affected Zone (HAZ) at the fusion line between the weld and column flange. In the sixth test, fractures initiated at the inside face of the column flange at the upper edge of the weld access hole of the CJP weld detail. Contrary to the initial expectations, the specimens with the PJP welds exhibited higher displacement ductility than those with CJP welds. This is attributed to the fillet reinforcing that strengthens the PJP welds and enables them to sustain stresses and strains necessary to fully develop yielding in the column flanges. The test data further support the adequacy of the FEMA 350 provisions for determining the required strength of the welds based on the probable moment demand with the material overstrength factor of R_y=1.1 and strain hardening factor of C_pr=1.2.     

Axial crushing and optimal design of square tubes with graded thickness

Introducing thickness gradient in cross-section is a quite promising approach to increase the energy absorption efficiency and crashworthiness performance of thin-walled structures. This paper addresses the deformation mode and energy absorption of square tubes with graded thickness during axial loading. Experimental study is firstly carried out for square tubes with two types of thickness distributions and numerical analyses are then conducted to simulate the experiment. Both experimental and numerical results show that the introduction of graded thickness in cross-section can lead to up to 30–35% increase in energy absorption efficiency (specific energy absorption) without the increase of the initial peak force. In addition, structural optimization of the cross-section of a square tube with graded thickness is solved by response surface method and the optimization results validate that increasing the material in the corner regions can indeed increase the energy absorption efficiency of a square tube.     

Multiobjective crashworthiness optimization of hollow and conical tubes for multiple load cases

Much attention of current design analysis and optimization of crashworthy structures have been largely paid to the scenarios with single load case in literature. Nevertheless the designed structures may often have to be operated in other load conditions, thus raising a critical issue of optimality. This paper aims to understand and optimize the dynamic responses and energy absorption of foam-filled conical thin-walled tubes under oblique impact loading conditions by using multiobjective optimization method. The crashworthiness criteria, namely specific energy absorption (SEA) and crushing force efficiency (CFE), are related to loading parameters and design variables by using D-optimal design of experiments (DoE) and Kriging model. To obtain the optimal Pareto solutions of hollow and foam-filled conical tubes, design optimization is first performed under different loading case (DLC) using multiobjective particle swarm optimization (MOPSO) algorithm separately. The optimal designs indicate that hollow tube has better crashing performance than the foam-filled tube under relatively high impacting velocity and great loading angle. To combine multiple load cases (MLC) for multiobjective optimization, a double weight factor technique is then adopted. It is found that the optimal foam-filled tube has better crashing performance than empty conical tube under any of overall oblique loading cases concerned. The study gains insights in deriving multiobjective optimization for multiple load cases, providing a guideline for design of energy absorber under multiple oblique loading.     

CFRP Effect on the Buckling Behavior of Dented Cylindrical Shells

Considering that the use of thin-walled shells is expanding every day, it is important to examine the problem of instability in this form of structure. Many steel structures such as high-water tanks, water and oil reservoirs, marine structures, and pressure vessels, including shell elements, are under stress tension. In addition, shell elements are subject to instability owing to the loads applied. Ten thin-walled cylindrical shell specimens in two groups with different dent depths of t_c and 2t_c, and the different dent number subject to uniform external pressure were tested in the present research (t_c is the thickness of cylindrical shell). The samples were modified to include either one or two dent line with amplitudes of h/3 in height (h the height of cylinder shell). Moreover, CFRP Strips on the dent depth was used in one of the groups. The results of testing under different theories and codes are compared.

     

Transition of gap-graded soil fabric – shear wave measurements and dispersion relation

The dynamic response of gap-graded soils is complex; it requires massive experimental and theoretical investigation in order for a sound understanding to be developed. The complexity of the behaviour of such soils arises partially due to the presence of many influential parameters, such as the finer sand/silt content (F_s), size ratio (R_d), and void ratio (e). In this contribution, experiments are conducted on a series of gap-graded soil mixtures, where the coarser sand is mixed with four different finer sands or non-plastic silt with different sizes, namely various R_d, and one well-graded material is also tested. The S-wave velocity (V_s) and low-pass threshold frequency (f_lp) are measured in the isotropic stress state using a triaxial apparatus equipped with planar piezoelectric transducers. The experimental results reveal that, for a given e or relative density (D_r), both f_lp and V_s decrease at a low F_s, but increase at a high F_s. The slope of the linear regression between f_lp and V_s appears to capture this transitional behaviour, depending on F_s and R_d, which can then be used to correlate the physical state of the gap-graded soil fabric. The transitional behaviour is more noticeable at a larger R_d, which is in line with the existing literature. To understand the effect of the R_d on the shear wave propagation at a low F_s, the particle-scale dispersion relation for binary chains is newly introduced and correlated with accompanying experimental observations.     

Estimation of convergence of a high-speed railway tunnel in weak rocks using an adaptive neuro-fuzzy inference system(ANFIS) approach

Estimation of tunnel diameter convergence is a very important issue for tunneling construction,especially when the new Austrian tunneling method(NATM) is adopted.For this purpose,a systematic convergence measurement is usually implemented to adjust the design during the whole construction,and consequently deadly hazards can be prevented.In this study,a new fuzzy model capable of predicting the diameter convergences of a high-speed railway tunnel was developed on the basis of adaptive neuro-fuzzy inference system(ANFIS) approach.The proposed model used more than 1 000 datasets collected from two different tunnels,i.e.Daguan tunnel No.2 and Yaojia tunnel No.1,which are part of a tunnel located in Hunan Province,China.Six Takagi-Sugeno fuzzy inference systems were constructed by using subtractive clustering method.The data obtained from Daguan tunnel No.2 were used for model training,while the data from Yaojia tunnel No.1 were employed to evaluate the performance of the model.The input parameters include surrounding rock masses(SRM) rating index,ground engineering conditions(GEC) rating index,tunnel overburden(H),rock density(?),distance between monitoring station and working face(D),and elapsed time(T).The model’s performance was assessed by the variance account for(VAF),root mean square error(RMSE),mean absolute percentage error(MAPE) as well as the coefficient of determination(R2) between measured and predicted data as recommended by many researchers.The results showed excellent prediction accuracy and it was suggested that the proposed model can be used to estimate the tunnel convergence and convergence velocity.     

Measured and predicted performance of prefabricated vertical drains (PVDs) with and without vacuum preloading

This paper presents the effectiveness of vacuum preloading in accelerating the consolidation of PVD improved soft Bangkok clay by comparing with the corresponding results without vacuum preloading. Laboratory tests were conducted using a large scale consolidometer having diameter of 300 mm and height of 500 mm with reconstituted specimens installed with prefabricated vertical drains (PVD) with and without vacuum preloading. In addition, field data were collected from Second Bangkok International Airport (SBIA) site improved by PVD with and without vacuum pressures. Analyses were carried out to compare the compressibility parameters (C_h and k_h/k_s) by back-calculation of laboratory and field settlements using Hansbo (1979) method. From the laboratory tests, the horizontal coefficient of consolidation (C_h) values from reconstituted specimens were 1.08 and 1.87 m²/yr for PVD without and with vacuum pressure, respectively and the k_h/k_s values were 2.7 for PVD only and 2.5 for vacuum-PVD. After the improvement, the water contents of the soft clay were reduced, thereby, increasing its undrained shear strengths. Similarly, the field data analysis based on the back-calculated results showed that the k_h/k_s were 7.2 and 6.6 for PVD without and with vacuum, respectively. The C_h values increased slightly from 2.17 m²/yr for PVD only to 3.51 m²/yr for vacuum-PVD. The time to reach 90% degree of consolidation for soils with vacuum-PVD was one-third shorter than that for soils with PVD only because of higher C_h values. Thus, the addition of vacuum pressure leads to increase horizontal coefficient of consolidation which shortened the time of preloading. The PVDCON software was found to be useful to predict the settlements of the PVD improved ground with and without vacuum preloading.