Beam element modelling of vehicle body-in-white applying artificial neural network

In this study a large knowledge base is first established through numerous designs of experiments on beam elements, based on a validated finite element model of a reference vehicle body-in-white. Then a recurrent artificial neural network is applied to extract the input/output relationship between the crash dynamic characteristics and beam element features. With such established relationship, beam element features are predicted according to expected crash dynamic characteristics. Our analyses show that the predicted beam element model enables generating essential crash dynamic characteristics for concept BIW design evaluation at a reasonable level of accuracy. Last, a data assurance criterion is developed to quantitatively validate the beam element modelling.     

A time-space Kriging-based sequential metamodeling approach for multi-objective crashworthiness optimization

A time-space Kriging-based sequential metamodeling approach is proposed for multi-objective crashworthiness optimization (MOCO) in this paper. By defining the novel time-space design criteria, the constructed metamodels for the optimization objectives include the characteristic mechanical responses with respect to both the structural space domain and crash time domain, compared to standard metrics with the extremum of the time history of the entire structure. The adaptive addition of new samples is performed to gradually improve the approximation accuracy during the optimization with the guidance of an adaptive weighted sum method. The effectiveness of the proposed method is demonstrated by investigating a multi-cell thin-walled crashworthiness design problem. Finally, its effectiveness in practical engineering is validated by the crashworthiness design for a vehicle under full-overlap frontal crash loadcase.     

Application of the frontal algorithm in the collocation method

The author reports on a numerical experimentation with the collocation finite element procedure using Hermite basis functions and the frontal elimination technique to solve some large-scale problems where up to 1000 linear equations are involved. Several test cases, including some applications to engineering problems, are presented. The implementation of the frontal technique applied to collocation is discussed to some extent.     

Development of a new frame finite element for crash analysis, using a mixed variational principle and rotations as independent variables

This paper deals with the development and application of a new space curved frame finite element to be used for crash analysis (non-linear). The frame finite element has been developed using a mixed variational principle (complementary form) and using rotations as independent variables. The formulation has been validated for problems of large deflection and rotation, and for problems involving initially curved members. Based on the validation performed, it is expected that crash problems may be modelled using a single element per member thus retaining computational efficiency while performing an accurate analysis. An illustrative example (modelling of an S-leg seat) is presented here to illustrate the benefits of the proposed approach to a designer.     

An approximate numerical model for radiation problems

A variety of engineering problems can be successfully solved by coupling finite element and boundary element procedures. Approximate boundary elements, which can be used when dealing with radiation problems in unlimited domains are presented. They are simple to implement and can be easily inserted in existing frontal solution packages. Numerical examples are also reported.     

一种高精度的裂纹奇异单元

基于广义伽辽金法的多变量有限元算法,增加了连续体力学有限元模型建立的灵活性.本文利用它,通过数值试验的对比建立了一种高精度的含奇异性的裂纹单元,并对多变量奇异元的构成进行了探讨.     

A Holistic Simulation Approach from a Measured Load to Element Stress Using Combined Multi-body Simulation and Finite Element Modelling

The design of vehicle bodies requires the knowledge of the vehicle's structural response to external loads and disturbances. In rigid multi-body simulation the dynamic behaviour of complex systems is calculated with rigid bodies and neglect of body elasticity. On the other hand, in finite element models large degree of freedom numbers are used to represent the elastic properties of a single body. Both simulation methods can be combined, if the finite element model size is reduced to a degree of freedom number feasible to multi-body simulation. The application to practical purposes requires the use and interconnection of several different software tools. In this contribution a holistic method is presented, which starts with the measurement or synthesis of loads and excitations, continues with the integration of a reduced finite element model into a multi-body system, the dynamic response calculation of this combined model, and concludes with the result expansion to the full finite element model for calculating strain and stress values at any point of the finite element mesh. The applied software tools are Simpack, Nastran, and Matlab. An example is given with a railway vehicle simulated on measured track geometry. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional vehicle-ballasted track-subgrade interaction: Model construction and numerical analysis

In this work a three-dimensional vehicle-ballasted track-subgrade interaction model is developed, where the vehicle is modeled as a multi-rigid-body system, the track-subgrade interaction is modelled by finite element method (FEM) with the rail modelled as beam elements, the sleeper and the subgrade layers modelled as solid elements, and the vehicle and the track-subgrade system are coupled by unified matrix formulations and solved simultaneously and time-dependently. As the modelling advancement, the versatility for FEM construction of track-subgrade systems has been promoted, where the elemental scale can be arbitrarily chosen without consideration of the node-to-node matching principle as the conventional methods; besides the vehicle and the track-subgrade systems have been coupled effectively by wheel-rail contact models. The applicability of various wheel-rail contact models has been discussed, and to reveal the effectiveness of this model in solving engineering problems such as the soil elasticity unevenness and the contact break of “hanging sleepers”, numerical examples have also been presented with referencable conclusions.     

变温条件下考虑车辆-路面相互作用的车辙分析

研究沥青路面结构的车辙问题,首先基于车辆与路面的相互耦合作用,建立路面不平整度引起的车辆荷载简化模型;然后根据沥青混合料蠕变试验数据,拟合出基于修正Burgers模型的沥青路面车辙的计算参数;最后结合气温观测数据,借助ABAQUS有限元软件,引入路面温度场,建立了考虑连续变温的日车辙预估计算模型.模拟了考虑车辆 路面相互作用的沥青路面在连续变温条件下的车辙变化规律,并分析研究了温度、车辆荷载以及车速对车辙的影响.结果表明,考虑车辆 路面相互作用得到的日累积车辙深度增大了6.5%,说明这一因素对沥青路面车辙的预测是不可忽略的;轴载及路面不平整度均与车辙量线性相关;而相同轴载作用下,温度越高,车辙增长越快,得到的车辙量越大;随着车速增大,车辙深度呈减小趋势,并且在车辆与路面发生共振的车速下,该文模型得到的结果增大了32%.     

基于等效梁模型的运载火箭动力学特性仿真预示研究

针对运载火箭动力学特性仿真预示问题,提出了一种基于等效梁模型,其是可考虑贮箱内液体推进剂影响高效、准确的仿真预示方法.应用等效厚度法建立了运载火箭的等效梁模型,并将运载火箭精细有限元模型的模态分析结果作为目标,通过有限元模型修正提升了等效梁模型的精度.以某型号运载火箭为算例,应用该文方法,建立了其等效梁模型,并基于集中质量法和耦合质量法两种液体推进剂等效方法对其进行了考虑贮箱内液体推进剂影响的动力学特性预测,比较了两种方法的分析结果.     

Multiscale simulations of concrete mechanical tests

In civil engineering, computational modeling is widely used in the design process at the structural level. In contrast to that, an automated support for the selection or design of construction materials is currently not available. Specification of material properties and model parameters has a strong influence on the results. Therefore, an uncoupled two-step approach is employed to provide relatively quick and reliable simulations of concrete (mortar) tests. First, the Mori–Tanaka method is utilized to include the majority of small aggregates and air voids. The strain incremental form of MT approach serves for the prediction of material properties subsequently used in the finite element simulations of mechanical tests.     

Towards integrated design and analysis

A systems analysis technique is used to investigate and better understand the processes involved in finite element modelling. Two different starting points are considered: engineering drawings and solid models. The breakdown of activities involved in finite element analysis from a solid model is used as a requirements definition and functional specification for software tools to facilitate automation of finite modelling and eventual integration of design and analysis.     

Pseudoelasticity of Shape Memory Alloys - a 1D Material Model and Finite Element Implementation

This contribution is concerned with the formulation of a 1D-constitutive model accounting for the pseudoelastic behavior of shape memory alloys. The stress-strain-relationship is idealized by a hysteresis both in the compression as in the tension loading range. It is characterized by an upper loading path, which is to be ascribed to the transformation of the lattice to a martensitic structure. Unloading the material, a lower path is described, because of the reverse transformation into austenitic lattice. The constitutive model is based on a switching criterion which serves as a potential function for the evolution of the internal state variables. The model distinguishes between local and global variables to describe the hysteresis effects for the compression and tension range. A strain driven algorithm which captures the complete nonlinear material behavior is presented. The boundary value problem is solved for a truss element applying the finite element method. A consistent linearization of the nonlinear equations is derived. Simple examples will demonstrate the applicability of the proposed model. For future developments the usage of shape memory alloys within civil engineering structures is aimed. The advantage of the material is the very good damping behavior and the potential to overcome great strains. Both properties are distinguished to be of engineering interest. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Use of geometry in finite element thermal radiation combined with ray tracing

In heat transfer for space applications, the exchanges of energy by radiation play a significant role. In this paper, we present a method which combines the geometrical definition of the model with a finite element mesh. The geometrical representation is advantageous for the radiative component of the thermal problem while the finite element mesh is more adapted to the conductive part. Our method naturally combines these two representations of the model. The geometrical primitives are decomposed into cells. The finite element mesh is then projected onto these cells. This results in a ray tracing acceleration technique. Moreover, the ray tracing can be performed on the exact geometry, which is necessary if specular reflectors are present in the model. We explain how the geometrical method can be used with a finite element formulation in order to solve thermal situation including conduction and radiation. We illustrate the method with the model of a satellite.     

Development of a higher order finite element on a Winkler foundation

Analyzing thick plates as a construction component has been of interest to structural engineering research for several decades. In particular, thick plates resting on elastic foundations are more specific. Mindlin's plate theory for thick plate analysis and the Winkler theory for elastic foundation analyses have wide applications. The current research considers analysis of isotropic plates on a Winkler foundation according to Mindlin's plate theory. The analysis uses a higher order plate element to avoid shear locking phenomena in the plate. The main features of this element are representation of real displacement functions of the plate perfect and shear locking do not occur at the plates modeled with this element. Derivation of the equations for finite element formulation for thick plate theory uses fourth-order displacement shape functions. A computer program using the finite element method, coded in C++, analyzes the plates resting on an elastic foundation. The analysis involves a 17-noded finite element. The study's graphs and tables assist engineers' designs of thick plates resting on elastic foundations. The study concludes with the computer-coded program, which allows effective use for the shear locking-free analysis of thick Mindlin plates resting on elastic foundations.     

机动车碳税政策下政府、企业与出行者的三方演化博弈模型研究

为促进机动车碳减排,缓解因尾气排放带来的大气污染,本文采用演化博弈理论探究机动车碳税政策下的决策行为。建立政府管理部门、汽车企业和出行者三方利益主体的演化博弈模型,并对模型的演化路径及演化规律进行理论与数值仿真。研究发现:降低机动车碳排放演化是政府、汽车企业和出行者三者博弈互动的结果;政府主动实施机动车碳税政策,能够促进另外两者选择低碳的策略;提高机动车碳税税额与对低碳行为的补贴,加快了汽车企业与出行者朝各自低碳策略演化的速度。     

A beam segment element for dynamic analysis of large aqueducts

Large aqueduct structure is a complex structure that is commonly used in hydraulic engineering, especially in large-scale water conveying projects. The analysis of dynamic response for an aqueduct structure is necessary if the aqueduct is built in an earthquake area. Traditional 3D finite element analysis is time consuming and the existing simplified response method cannot take into account all the effects, such as the bending-torsion coupling effect and the constrained torsion, of the deformations of the thin wall structure of the aqueduct body. For this special structure, a simple and yet accurate model for dynamic analysis is needed. In this paper, a beam segment element is developed and used for the calculation of dynamic response for aqueduct structures. With the frame of the aqueduct being modeled using beam element, the proposed model can calculate the dynamic response of the whole aqueduct structures. Results are compared with that of a general purpose finite element analysis software using 3D finite element model. Good agreement is achieved between the two models. However, the proposed model needs less elements and much less computing time.     

Real-Time Simulation of Elastic Multibody Systems with Application in Vehicle Dynamics

Real-time simulation models are widely used for vehicle development, usually built up as rigid multibody systems. However, since lightweight structures are commonly used, body deformation is no longer negligible and rigid multibody simulations may be inaccurate. This work presents a real-time capable full vehicle model with a flexible car body, derived from a finite element model, whose performance has been improved by model order reduction. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On a coupled system of reaction–diffusion-transport equations arising from catalytic converter

This paper is concerned with two mathematical models which describe the transient behavior of a catalytic converter in automobile engineering. The first model consists of a coupled system of a heat-conduction equation and two integral equations while the second model involves only one integral equation. It is shown that for any nonnegative initial and boundary functions the three-equation model has a unique bounded global solution while the solution of the two-equation model blows up in finite time. The proof for the global existence and finite-time blow-up property of the solution is by the method of upper and lower solutions and its associated monotone iteration. This method can be used to develop computational algorithms for numerical solutions of the coupled systems.     

A stabilized mixed formulation for finite strain deformation for low-order tetrahedral solid elements

A stabilized mixed finite element formulation for four-noded tetrahedral elements is introduced for robustly solving small and large deformation problems. The uniqueness of the formulation lies within the fact that it is general in that it can be applied to any type of material model without requiring specialized geometric or material parameters. To overcome the problem of volumetric locking, a mixed element formulation that utilizes linear displacement and pressure fields was implemented. The stabilization is provided by enhancing the rate of deformation tensor with a term derived using a bubble function approach. The element was implemented through a user-programmable element of the commercial finite element software ANSYS. Using the ANSYS platform, the performance of the element was evaluated by comparing the predicted results with those obtained using mixed quadratic tetrahedral elements and hexahedral elements with a B-bar formulation. Based on the quality of the results, the new element formulation shows significant potential for use in simulating complex engineering processes.