Topology optimization for nonlinear dynamic problems: Considerations for automotive crashworthiness

Crashworthiness of automotive structures is most often engineered after an optimal topology has been arrived at using other design considerations. This study is an attempt to incorporate crashworthiness requirements upfront in the topology synthesis process using a mathematically consistent framework. It proposes the use of equivalent linear systems from the nonlinear dynamic simulation in conjunction with a discrete-material topology optimizer. Velocity and acceleration constraints are consistently incorporated in the optimization set-up. Issues specific to crash problems due to the explicit solution methodology employed, nature of the boundary conditions imposed on the structure, etc. are discussed and possible resolutions are proposed. A demonstration of the methodology on two-dimensional problems that address some of the structural requirements and the types of loading typical of frontal and side impact is provided in order to show that this methodology has the potential for topology synthesis incorporating crashworthiness requirements.     

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 of continuum structures for natural frequencies considering casting constraints

A method for the topology optimization on the natural frequency of continuum structures with casting constraints is proposed. The objective is to maximize the natural frequency of vibrating continuum structures subject to casting constraints. When the natural frequencies of the considered structures are maximized using the solid isotropic material with penalization (SIMP) model, artificial localized modes may occur in areas where elements are assigned with lower density values. In this article, the topology optimization is performed by the bi-directional evolutionary structural optimization (BESO) method. The effects of different locations of concentrated lump mass, different volume fractions and meshing sizes on the final topologies are compared. Both two and four parting directions are investigated. Several two- and three-dimensional numerical examples show that the proposed BESO method is effective in achieving convergent solid–void optimal solutions for a variety of frequency optimization problems of continuum structures.     

Topology optimization of geometrically nonlinear structures using an evolutionary optimization method

The topology optimization using isolines/isosurfaces and extended finite element method (Iso-XFEM) is an evolutionary optimization method developed in previous studies to enable the generation of high-resolution topology optimized designs suitable for additive manufacture. Conventional approaches for topology optimization require additional post-processing after optimization to generate a manufacturable topology with clearly defined smooth boundaries. Iso-XFEM aims to eliminate this time-consuming post-processing stage by defining the boundaries using isovalues of a structural performance criterion and an extended finite element method (XFEM) scheme. In this article, the Iso-XFEM method is further developed to enable the topology optimization of geometrically nonlinear structures undergoing large deformations. This is achieved by implementing a total Lagrangian finite element formulation and defining a structural performance criterion appropriate for the objective function of the optimization problem. The Iso-XFEM solutions for geometrically nonlinear test cases implementing linear and nonlinear modelling are compared, and the suitability of nonlinear modelling for the topology optimization of geometrically nonlinear structures is investigated.     

汽车前纵梁吸能盒结构耐撞性多目标优化

吸能盒上诱导槽的分布形式对汽车碰撞性能有很大影响.以汽车前纵梁吸能盒结构为对象,建立整车正面碰撞仿真模型,对吸能盒结构的耐撞性进行了多目标优化设计.以吸能盒上诱导槽之间的间距为设计变量,使用Hammersley方法采集样本点后,以车辆吸能盒的最大吸能量E、最大刚性墙反力F以及车身最大加速度a为目标函数,通过krigin...     

Bidirectional evolutionary structural optimization for nonlinear structures under dynamic loads

This study aims to develop efficient numerical optimization methods for finding the optimal topology of nonlinear structures under dynamic loads. The numerical models are developed using the bidirectional evolutionary structural optimization method for stiffness maximization problems with mass constraints. The mathematical formulation of topology optimization approach is developed based on the element virtual strain energy as the design variable and minimization of compliance as the objective function. The suitability of the proposed method for topology optimization of nonlinear structures is demonstrated through a series of two- and three-dimensional benchmark designs. Several issues relating to the nonlinear structures subjected to dynamic loads such as material, geometric, and contact nonlinearities are addressed in the examples. It is shown that the proposed approach generates more reliable designs for nonlinear structures.     

Al/CFRP混合薄壁结构耐撞性能可靠性优化设计

轻量化是实现汽车产业向安全、节能、环保发展的一个重要途径。Al/CFRP（carbon fiber reinforced plastic,碳纤维增强复合材料）混合材料能够在提升轻量化效果的同时兼顾材料成本和结构耐撞性能。为探索方形截面Al/CFRP混合薄壁结构的最佳组合方式,首先,制备了Al方管、CFRP方管和Al/CFRP混合方管,并开展准静态压溃实验。然后,建立能够精确模拟Al/CFRP混合方管压溃响应的有限元模型。最后,将试验设计方法、代理模型技术、多目标优化算法和蒙特卡罗模拟技术相结合,对Al/CFRP混合方管分别进行多目标确定性与可靠性优化设计,并对效果较好的可靠性优化解进行仿真验证。准静态压溃实验结果表明,Al/CFRP混合方管具有优异的耐撞性能;优化结果表明,可靠性优化解的约束可靠度相比于确定性优化解提高了10.96%,大大降低了失效概率,具有更强的实用性。研究结果有望对Al/CFRP混合薄壁吸能构件的优化设计提供参考。     

Topology optimization of structures under multiple load cases using a fiber-reinforced composite material model

This paper presents a method to optimize the topology of structures under multiple load cases with stress constraints. Fiber-reinforced orthotropic composite is employed as the material model to simulate the constitutive relation of truss-like continua. The fiber densities and orientations at the nodes are taken as design variables. First, for each load case, the fiber orientations are aligned with the orientations of principal stress and the fiber densities are adjusted according to the strains along the fiber orientations. Then, to optimize the structure, the fiber densities and orientations under multiple load cases are determined by constraining its elastic matrix to approach the elastic matrix of the optimum structures defined for each single load case. Finally the member distribution in the optimal structure is suggested by the continuous lines formed according to the fiber densities and orientations. Several examples are presented to demonstrate the effectiveness of the proposed approach.     

复合材料薄壁管冲击断裂分析与吸能特性优化

为实现不同冲击载荷下的吸能管结构逆向设计, 应用复合材料强度和刚度理论, 计算得到树脂基纤维增强复合材料正交各向异性的力学参数, 同时应用非线性显式有限元算法模拟了轴向冲击载荷作用下管件的动态断裂过程。根据正交设计原理, 得到了管件比吸能与其几何参数之间的非线性映射关系, 并构造出了相应的响应表面。按照汽车正面碰撞对冲击加速度的要求, 应用序列二次规划算法对吸能管进行了优化设计, 得到了具有较优吸能效率和较小冲击力峰值的吸能管结构参数。结果显示: 方管的变形模式、吸能量、冲击载荷-位移曲线变化趋势、冲击载荷峰值等与试验结果吻合很好; 当管件的壁厚、截面长度、管长分别选取2.1、44、200 mm时, 可得到设计域内的最大比吸能29.23 J/g。      

Mixed nonlinear localization strategy for the buckling and post-buckling analyses of structures: parameter optimization and path following implementation

In previous work, the nonlinear localization was first presented and studied in the case of large displacements but only for globally stable structural responses. In this paper, the influence of the local error criterion on the performance of the strategy is investigated in structures exhibiting more complex behaviour, such as snap-through and snap-back. Second, a path following method is implemented in the domain decomposition framework of the strategy in order to track the solution around a critical point (snap-through and snap-back).     

Numerical analysis of low cycle fatigue for welded joints considering welding residual stress and plastic damage under combined bending and local compressive loads

The numerical analysis of low cycle fatigue of HTS‐A steel welded joints under combined bending and local compressive loads are implemented using the damage mechanics approach. First, a finite element numerical simulation of the welding process is employed to extract the welding residual stresses, which are then imported as initial stresses in the subsequent fatigue analysis. Second, a multiaxial fatigue damage model including damage coupled elasto‐plastic constitutive equations and plastic damage evolution formulation is applied to evaluate the mechanical degradation of the material under biaxial fatigue loads. Further, the fatigue lives of the HTS‐A steel welded joints are computed and compared with the experimental results from literature. A series of predicted load‐life curves clearly illustrates the variation of fatigue lives along with the combined loadings. Finally, the effects of local compression on accumulated plastic strain and fatigue damage are studied in detail. It is revealed that the local compression induces a damage competition between two critical zones.     

A topological optimization approach for structural design of a high‐speed low‐load mechanism using the equivalent static loads method

In high‐speed low‐load mechanisms, the principal loads are the inertial forces caused by the high accelerations and velocities. Hence, mechanical design should consider lightweight structures to minimize such loads. In this paper, a topological optimization method is presented on the basis of the equivalent static loads method. Finite element (FE) models of the mechanism in different positions are constructed, and the equivalent loads are obtained using flexible multibody dynamics simulation. Kinetic DOFs are used to simulate the motion joints, and a quasi‐static analysis is performed to obtain the structural responses. The element sensitivity is calculated according to the static‐load‐equivalent equilibrium, in such a way that the influence on the inertial force is considered. A dimensionless component sensitivity factor (strain energy caused by unit load divided by kinetic energy from unit velocity) is used, which quantifies the significance of each element. Finally, the topological optimization approach is presented on the basis of the evolutionary structural optimization method, where the objective is to find the maximum ratio of strain energy to kinetic energy. In order to show the efficiency of the presented method, we presented two numerical cases. The results of these analyses show that the presented method is more efficient and can be easily implemented in commercial FE analysis software. Copyright © 2011 John Wiley & Sons, Ltd.