Crashworthiness design optimization using successive response surface approximations

 Finite Element (FE) method is among the most powerful tools for crash analysis and simulation. Crashworthiness design of structural members requires repetitive and iterative application of FE simulation. This paper presents a crashworthiness design optimization methodology based on efficient and effective integration of optimization methods, FE simulations, and approximation methods. Optimization methods, although effective in general in solving structural design problems, loose their power in crashworthiness design. Objective and constraint functions in crashworthiness optimization problems are often non-smooth and highly non-linear in terms of design variables and follow from a computationally costly (FE) simulation. In this paper, a sequential approximate optimization method is utilized to deal with both the high computational cost and the non-smooth character. Crashworthiness optimization problem is divided into a series of simpler sub-problems, which are generated using approximations of objective and constraint functions. Approximations are constructed by using statistical model building technique, Response Surface Methodology (RSM) and a Genetic algorithm. The approximate optimization method is applied to solve crashworthiness design problems. These include a cylinder, a simplified vehicle and New Jersey concrete barrier optimization. The results demonstrate that the method is efficient and effective in solving crashworthiness design optimization problems. Received: 30 January 2002 / Accepted: 12 July 2002 Sponsorship for this research by the Federal Highway Administration of US Department of Transportation is gratefully acknowledged. Dr. Nielen Stander at Livermore Software Technology Corporation is also gratefully acknowledged for providing subroutines to create D-optimal experimental designs and the simplified vehicle model.     

A system methodology for optimization design of the structural crashworthiness of a vehicle subjected to a high-speed frontal crash

The structural crashworthiness design of vehicles has become an important research direction to ensure the safety of the occupants. To effectively improve the structural safety of a vehicle in a frontal crash, a system methodology is presented in this study. The surrogate model of Online support vector regression (Online-SVR) is adopted to approximate crashworthiness criteria and different kernel functions are selected to enhance the accuracy of the model. The Online-SVR model is demonstrated to have the advantages of solving highly nonlinear problems and saving training costs, and can effectively be applied for vehicle structural crashworthiness design. By combining the non-dominated sorting genetic algorithm II and Monte Carlo simulation, both deterministic optimization and reliability-based design optimization (RBDO) are conducted. The optimization solutions are further validated by finite element analysis, which shows the effectiveness of the RBDO solution in the structural crashworthiness design process. The results demonstrate the advantages of using RBDO, resulting in not only increased energy absorption and decreased structural weight from a baseline design, but also a significant improvement in the reliability of the design.     

Topology optimization for crashworthiness of thin-walled structures under axial crash considering nonlinear plastic buckling and locations of plastic hinges

Although topology optimization is established for linear static problems, more effort is required for solving nonlinear plastic problems. A new topology optimization approach with equivalent static loads (ESLs) is suggested to find the optimum topologies and locations of plastic hinges of thin-walled crash boxes by considering crash-induced deformation, the main crash energy-absorbing mechanism. Together with finite element method crashworthiness analyses, considering all nonlinearities with rate-dependent plasticity, the method was developed using an appropriate time-incremental scheme of ESLs without removing any high values of loads. Analyses show that the crash boxes with optimum topologies have energy-absorbing capabilities equivalent to the original structure. The proposed method is evaluated for two crashes: a crash box at low speed and a double cell subjected to high-speed collision. The results indicate that this method captures nonlinear crushing behaviours and accurate locations of plastic hinges where, if proper reinforcements are made, energy absorption can be enhanced.     

A bidirectional evolutionary structural optimization algorithm for mass minimization with multiple structural constraints

A bidirectional evolutionary structural optimization algorithm is presented, which employs integer linear programming to compute optimal solutions to topology optimization problems with the objective of mass minimization. The objective and constraint functions are linearized using Taylor's first-order approximation, thereby allowing the method to handle all types of constraints without using Lagrange multipliers or sensitivity thresholds. A relaxation of the constraint targets is performed such that only small changes in topology are allowed during a single update, thus ensuring the existence of feasible solutions. A variety of problems are solved, demonstrating the ability of the method to easily handle a number of structural constraints, including compliance, stress, buckling, frequency, and displacement. This is followed by an example with multiple structural constraints and, finally, the method is demonstrated on a wing-box, showing that topology optimization for mass minimization of real-world structures can be considered using the proposed methodology.     

Adaptive crashworthiness concept

A design methodology for adaptive structures (structures equipped with controllable dissipaters) with high crashworthiness performance is proposed. A numerical package capable of solving particular problems, i.e. (i) crashworthiness analysis of structure with fixed properties of dissipaters, (ii) optimal remodelling of adaptive structure and (iii) optimal design of yield stress levels triggering plastic-like distortions in dissipaters, is presented and verified using test examples.Some general, quantitative conclusions and suggestions for further applications of the adaptive crashworthiness concept are formulated.     

Evaluation of response surface methodologies used in crashworthiness optimization

Optimization of car structures is of great interest to the automotive industry. This work is concerned with structural optimization of a car body with the intent to increase the crashworthiness properties of the vehicle or decrease weight with the crashworthiness properties unaffected. In this work two different methodologies of constructing an intermediate approximation to the optimization problem are investigated, i.e. classical response surface methodology and Kriging. The major difference between the two methodologies is how the residuals between the true function value and the polynomial surface approximation value at a design point are treated.Several different optimization problems have been investigated, both analytical problems as well as finite element impact problems.The major conclusion is that even if the same kind of updating scheme is used both for Kriging and linear classic response surface methodology, Kriging improves the sequential behaviour of the optimization algorithm in the beginning of the optimization process. Problems may occur if a constraint is violated after several iterations and then classic response surface methodology seems to more easily be able to find a design point which satisfies the constraint.     

Topological derivative for multi‐scale linear elasticity models applied to the synthesis of microstructures

This paper proposes an algorithm for the synthesis/optimization of microstructures based on an exact formula for the topological derivative of the macroscopic elasticity tensor and a level set domain representation. The macroscopic elasticity tensor is estimated by a standard multi‐scale constitutive theory where the strain and stress tensors are volume averages of their microscopic counterparts over a representative volume element. The algorithm is of simple computational implementation. In particular, it does not require artificial algorithmic parameters or strategies. This is in sharp contrast with existing microstructural optimization procedures and follows as a natural consequence of the use of the topological derivative concept. This concept provides the correct mathematical framework to treat topology changes such as those characterizing microstuctural optimization problems. The effectiveness of the proposed methodology is illustrated in a set of finite element‐based numerical examples.Copyright © 2010 John Wiley & Sons, Ltd.     

A multiobjective topology optimization approach for cost and time minimization in additive manufacturing

The ever-present drive for increasingly high-performance designs realized on shorter timelines has fostered the need for computational design generation tools such as topology optimization. However, topology optimization has always posed the challenge of generating difficult, if not impossible to manufacture designs. The recent proliferation of additive manufacturing technologies provides a solution to this challenge. The integration of these technologies undoubtedly has the potential for significant impact in the world of mechanical design and engineering. This work presents a new methodology which mathematically considers additive manufacturing cost and build time alongside the structural performance of a component during the topology optimization procedure. Two geometric factors, namely, the surface area and support volume required for the design, are found to correlate to cost and build time and are controlled through the topology optimization procedure. A novel methodology to consider each of these factors dynamically during the topology optimization procedure is presented. The methodology, based largely on the use of the spatial gradient of the density field, is developed in such a way that it does not leverage the finite element discretization scheme. This work investigates a problem that has not yet been explored in the literature: direct minimization of support material volume in density-based topology optimization. The entire methodology is formulated in a smooth and differentiable manner, and the sensitivity expressions required by gradient based optimization solvers are presented. A series of example problems are provided to demonstrate the efficacy of the proposed methodology.     

Multimaterial multijoint topology optimization

In this paper, a methodology that solves multimaterial topology optimization problems while also optimizing the quantity and type of joints between dissimilar materials is proposed. Multimaterial topology optimization has become a popular design optimization technique since the enhanced design freedom typically leads to superior solutions; however, the conventional assumption that all elements are perfectly fused together as a single piece limits the usefulness of the approach since the mutual dependency between optimal multimaterial geometry and optimal joint design is not properly accounted for. The proposed methodology uses an effective decomposition approach to both determine the optimal topology of a structure using multiple materials and the optimal joint design using multiple joint types. By decomposing the problem into two smaller subproblems, gradient‐based optimization techniques can be used and large models that cannot be solved with nongradient approaches can be solved. Moreover, since the joining interfaces are interpreted directly from multimaterial topology optimization results, the shape of the joining interfaces and the quantity of joints connecting dissimilar materials do not need to be defined a priori. Three numerical examples, which demonstrate how the methodology optimizes the geometry of a multimaterial structure for both compliance and cost of joining, are presented.     

An adaptive response surface method for crashworthiness optimization

Response surface-based design optimization has been commonly used for optimizing large-scale design problems in the automotive industry. However, most response surface models are built by a limited number of design points without considering data uncertainty. In addition, the selection of a response surface in the literature is often arbitrary. This article uses a Bayesian metric to systematically select the best available response surface among several candidates in a library while considering data uncertainty. An adaptive, efficient response surface strategy, which minimizes the number of computationally intensive simulations, was developed for design optimization of large-scale complex problems. This methodology was demonstrated by a crashworthiness optimization example.     

On a cellular division method for topology optimization

This paper concerns a comparative analysis of a novel biologically inspired method for topology optimization. The proposed methodology develops each individual topology according to a set of rules that regulate a ‘cellular division’ process. These rules are then evolved using a genetic algorithm to minimize objective functions while satisfying a set of constraints. The results reported in this work show that the methodology suits engineering design and represents an improvement over existing topology optimization methods based on evolutionary algorithms. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimization of foam-filled bitubal structures for crashworthiness criteria

Thin-walled structures have been widely used as key components in automobile and aerospace industry to improve the crashworthiness and safety of vehicles while maintaining overall light-weight. This paper aims to explore the design issue of thin-walled bitubal column structures filled with aluminum foam. As a relatively new filler material, aluminum foam can increase crashworthiness without sacrificing too much weight. To optimize crashworthiness of the foam-filled bitubal square column, the Kriging meta-modeling technique is adopted herein to formulate the objective and constraint functions. The genetic algorithm (GA) and Non-dominated Sorting Genetic Algorithm II (NSGA II) are used to seek the optimal solutions to the single and multiobjective optimization problems, respectively. To compare with other thin-walled configurations, the design optimization is also conducted for empty bitubal column and foam-filled monotubal column. The results demonstrate that the foam-filled bitubal configuration has more room to enhance the crashworthiness and can be an efficient energy absorber.     

CRASHWORTHINESS ANALYSIS AND DESIGN USING RIGID–FLEXIBLE MULTIBODY DYNAMICS WITH APPLICATION TO TRAIN VEHICLES

Different formulations based on multibody dynamics are shown to be suitable for the development of a methodology for the impact simulation and crashworthiness design of railway vehicles. The proposed design methodology comprises different computer-aided tools of increasing complexity and accuracy which can be used with greater advantage and efficiency in the different design stages of railway stock. In general, the crashworthiness design methods and associated multibody dynamic tools which are presented in this paper require information to be obtained from numerical or experimental crush tests of specific structural components, subassemblies and critical energy absorption devices normally located in car extremities. This hybrid feature lends to the present design process various efficiency gains as a result of a better understanding of the crash and different collapse mechanisms and ease of use. To access the merits of the present methodologies some new designs are discussed and the application of the proposed numerical tools is illustrated for different structural configurations of car extremities. A formulation for the sensitivity analysis and optimization of planar constrained mechanical systems is also presented. An example of crashworthiness design of an end underframe model of a railway car is solved to demonstrate the use of the methodology. © 1997 by John Wiley & Sons, Ltd.     

响应表面法在薄壁构件耐撞性优化设计中的应用研究

汽车结构的耐撞性及碰撞吸能优化是现代汽车工业重要的研究内容。耐撞性的优化涉及材料与结构的众多参数。传统的设计、碰撞仿真及试验往往只能在一定程度上改善结构的碰撞性能而无法达到限定条件下的最优状态。利用国际上近年来新发展起来的一种优化理论方法--响应表面法,结合传统的优化手段以及非线性有限元程序对薄壁构件的耐撞性问题进行了优化研究。耐撞性优化的结果表明,该方法具有较高的精确性和有效性。     

飞行器机身结构耐撞性分析与设计

耐撞性不仅是飞行器设计中的重要问题,而且还是其取得适航证的必要条件。该文对美国、欧盟和日本等在耐撞性研究方面的研究进行了总结,阐述了耐撞性设计中采用的数值模拟和试验研究方法及其主要问题。主要针对各种飞行器结构耐撞性设计方法进行介绍,对比了轻型固定翼飞机、直升机和大中型民用飞机的耐撞性设计特点。能量吸收结构是耐撞性设计的关键问题之一,对提高飞行器机身能量吸收能力的机身底部结构、机身加强框和客舱地板撑杆结构等设计方法进行详细介绍,总结了飞行器耐撞性可靠性分析和优化设计方法。最后对飞行器结构耐撞性设计的发展作了展望。     

Simulation modelling and analysis of scheduling in robotic flexible assembly cells using Taguchi method

Due to increasing competition in the developing global economy, today’s companies are facing greater challenges than ever to employ flexible manufacturing systems (FMS) capable of dealing with unexpected events and meeting customers’ requirements. One such system is robotic flexible assembly cells (RFACs). There has been relatively little work on the scheduling of RFACs, even though overall scheduling problems of FMS have attracted significant attention. This paper presents Taguchi optimisation method in conjunction with simulation modelling in a new application for dynamic scheduling problems in RFACs, in order to minimise total tardiness and number of tardy jobs (N_T). This is the first study to address these particular problems. In this study, Taguchi method has been used to reduce the minimum number of experiments required for scheduling RFACs. These experiments are based on an L9 orthogonal array with each trial implemented under different levels of scheduling factors. Four factors are considered simultaneously: sequencing rule, dispatching rule, cell utilisation and due date tightness. The experimental results are analysed using an analysis of mean to find the best combination of scheduling factors and an analysis of variance to determine the most significant factors that influence the system’s performance. The resulting analysis shows that this proposed methodology enhances the system’s scheduling policy.     

A Research Methodology for Studying Complex Service Systems

This article describes a research methodology for studying problems of analysis, and control in complex service systems. The proposed methodology is based upon the total systems point of view in the sense that the physical and decision-making aspects of the service system are considered and are related to environmental factors. An example is included to illustrate the methodology as a way to approaching real problems. While field studies may be expected to present challenges because of the identification, modeling, and data requirements which will arise in actual situations, the methodological plan presented here focuses attention on these requirements as an integral part of systems analysis.     

Two-level parallelization for finite-element based design optimization via case studies

Computing clusters created with commodity chips are gaining popularity owing to relative ease of assembly and maintenance compared to a supercomputer. Such clusters are able to solve much larger problems owing to increased memory and reduced compute time. The challenge, however, is to develop new algorithms and software that can exploit multiple processors. In this paper we discuss the parallel processing options and their implementations in a gradient-based design optimization software system. The main objectives are as follows—(a) implement a design optimization methodology for sizing, shape and topology optimization using two-level parallelism and (b) provide a benchmark in the area of FEA-based design optimization for studying speedups with increasing number of processors to speed development of effective parallel algorithms. The two-level parallelism is implemented using nested parallel gradient calculations in conjunction with parallel FEA, and parallel line search with parallel FEA. Two case studies involving topology and shape optimization are studied in detail and they include three-dimensional finite element meshes with about 160 000 hexahedral elements and about 175 000 nodes. Furthermore, the case studies have been implemented using a workbench where the topology and shape optimization have an interface with a commercial CAD package, permitting a solid model representation of both the initial and the final optimized part.     

Swarm algorithms with chaotic jumps for optimization of multimodal functions

In this article, the use of some well-known versions of particle swarm optimization (PSO) namely the canonical PSO, the bare bones PSO (BBPSO) and the fully informed particle swarm (FIPS) is investigated on multimodal optimization problems. A hybrid approach which consists of swarm algorithms combined with a jump strategy in order to escape from local optima is developed and tested. The jump strategy is based on the chaotic logistic map. The hybrid algorithm was tested for all three versions of PSO and simulation results show that the addition of the jump strategy improves the performance of swarm algorithms for most of the investigated optimization problems. Comparison with the off-the-shelf PSO with local topology (l _best model) has also been performed and indicates the superior performance of the standard PSO with chaotic jump over the standard both using local topology (l _best model).