Dynamic computer simulation and energy absorption of foam-filled conical tubes under axial impact loading

This paper treats the dynamic response and energy absorption of aluminum foamfilled
conical tubes under axial impact loading using non-linear finite element
techniques. The influence of geometrical, material and loading parameters on the impact
response is investigated using validated numerical models. Results are quantified in
terms of important impact response parameters and indicate that the foam filler
stabilizes the crushing process and thus improves the energy absorption capacity. The
superior performance of foam-filled conical tubes as impact energy absorbers is evident
from the results. The research information generated will be useful in developing
guidance towards the design of these devices in impact applications.

Dynamic computer simulation and energy absorption offoam-filled conical tubes under axial impact loading

Foam-filled thin-wall structures exhibit significant advantages in light weight and high energy absorption. They have been widely applied in automotive, aerospace, transportation and defense industries. Quasi-static tests were done to investigate the crash behavior of the empty and polyurethane foam-filled end-capped conical tubes. Non-linear dynamic finite element analyses were carried out to simulate the quasi-static tests. The predicted numerical crushing force and fold pattern were found to be in good agreement with the experimental results. The energy absorption capacities of the filled tubes were compared with the empty end-capped conical tubes. The results showed that the energy absorption capability of foam-filled tube is somewhat higher than that of the combined effect of the empty tube and the foam alone. Finally, the crash performance of the empty and foam filled conical and cylindrical tubes were compared. Results from this study can assist aerospace industry to design sounding rocket carrier payload based on foam-filled conical tubes.

Experimental and numerical crashworthiness investigation of empty and foam-filled end-capped conical tubes

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.

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

When dealing with computationally expensive simulation codes or process measurement data, surrogate modeling methods are firmly established as facilitators for design space exploration, sensitivity analysis, visualization, prototyping and optimization. Typically the model parameter (=hyperparameter) optimization problem as part of global surrogate modeling is formulated in a single objective way. Models are generated according to a single objective (accuracy). However, this requires an engineer to determine a single accuracy target and measure upfront, which is hard to do if the behavior of the response is unknown. Likewise, the different outputs of a multi-output system are typically modeled separately by independent models. Again, a multiobjective approach would benefit the domain expert by giving information about output correlation and enabling automatic model type selection for each output dynamically. With this paper the authors attempt to increase awareness of the subtleties involved and discuss a number of solutions and applications. In particular, we present a multiobjective framework for global surrogate model generation to help tackle both problems and that is applicable in both the static and sequential design (adaptive sampling) case.

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Multiobjective global surrogate modeling, dealing with the 5-percent problem

Experimental and numerical investigations were carried out to optimize thin-walled conical shells for their use in design for energy absorption. Geometrical parameters, such as bottom diameter, height, and semi-apical angle were considered to obtain the design space. The numerical analysis and impact experiments were designed using design of experiments (DOE). A three-level, second-order Box–Bhenken technique was used to select the design points from the design space. Various set of numerical simulations were carried out using LS-DYNA. To investigate the influence of flow stress of the material on the energy absorption, numerical simulations were carried out using frusta made of aluminium, zinc, and mild steel. From the numerical results, mathematical models were created using response surface methodology (RSM). With the help of impact experiments carried out on specimens made of zinc on a drop mass test rig, a mathematical model has been developed using RSM. The mathematical models developed using experimental data and the numerical data were used as objective functions for optimization of the design. The non-dominated sorting genetic algorithm code NSGA II was used to optimize the design. The mathematical models were also used to predict the energy absorbed and deformation. The influence of various design parameters on energy absorption has been analysed and is discussed.

N. Shanmugapriyan

Papers

Optimization of thin conical frusta for impact energy absorption