On the Reliable Solution of Contact Problems in Engineering Design

In this paper we examine briefly the reliability of solution needed for the accurate and effective analysis of engineering design problems involving contact conditions. A general finite element formulation for treating the frictional contact problem using constraint functions is first summarized. Then we address general reliability issues and those related to the selection of appropriate elements that provide optimal performance. These elements of course do not lock and would provide the best solution an analyst can expect when simulating a design problem. Reliability issues specific to the contact formulation are also presented. A promising procedure to increase the reliability of an analysis is the method of finite spheres. The method does not require a mesh and in particular can be used with a finite element discretization as described in the paper. Finally, the results of several illustrative analysis problems are given.     

特征值问题迭代伽略金法与Rayleigh商加速

该文讨论特征值问题非协调有限元和混合有限元的加速计算方法。基于迭代伽略金法和Rayleigh商加速技巧,我们建立了特征值问题Wilson非协调有限元和Ciarlet-Raviart混合有限元的加速计算方案。这些新方案把在细网格上解一个特征值问题简化为在粗网格上解一个特征值问题和在细网格上解一个线性方程。文中证明了新方案的计算结果仍然保持了渐近最优精度阶,并用数值实验验证了理论结果。     

A simple solution strategy for coupled piezo-diffusion in elastic solids

In this work, a simple solution strategy for the fully coupled problem of the diffusion of a mobile constituent into an elastic solid is proposed. The key features of the proposed solution strategy are a superconvergent strain recovery and a final stress filtering, suitably arranged with a standard recursive staggering scheme. The strategy is devised to overcome some shortcomings arising when solving the problem within the standard finite element framework and can be easily implemented by using existing finite element packages for uncoupled elasticity and diffusion problems. Numerical applications show the effectiveness of the proposed solution strategy.     

CALCULATION OF THE STRESS INTENSITY FACTOR AND ESTIMATION OF ITS ERROR BY A SHAPE SENSITIVITY ANALYSIS

Abstract— The precision with which the stress intensity factor (SIF) can be calculated from a finite element solution depends essentially on the extraction method and on the discretization error. In this paper, the influence of the discretization error in the SIF calculation was studied and a method for estimating the resulting error was developed. The SIF calculation method used is based on a shape design sensitivity analysis; this assures that the resulting error in the extracted SIF depends solely on the global discretization error present in the finite element solution. Moreover, this method allows us to extend the Zienkiewicz-Zhu discretization error estimator to the SIF calculation. The reliability of the proposed method was analysed solving a two-dimensional problem using an h -adaptive process. Also the convergence of the error with the h -adaptive refinement was studied.     

Shape optimal design of elastic planar frames with non-linear response

This paper describes an approach to shape optimal design of elastic planar frames with non-linear response. The foundation of the proposed approach forms an appropriate strategy of shape representation of the structure, based on the design element technique. A frame structure is treated as to be assembled from several frame design elements, which in turn may consist of several appropriately joined beam finite elements. The shape of each frame design element is defined by convenient functions involving Bezier blending polynomials. The original formulation of the beam finite element, proposed by Saje, is modified in order to fit nicely into the context of the frame design element technique. The formulation of the shape optimal design problem in a form of a problem of non-linear mathematical programming and its solution by employing gradient-based methods of mathematical programming are discussed briefly. The theory is illustrated with two numerical examples.     

Design of a recursive,shape controlling mesh generator

A recursive, shape controlling triangulation method is described. The method is designed to produce a labelling which implies reduced fill in the solution of (finite element) equations assembled from such a triangulation and allows simple implementation of a nested disection algorithm for irregular domains. This approach saves a substantial amount of time usually spent on discovering a suitable relabelling of the triangulation. In addition, the matrix of the resulting system is then endowed with a recursive doubly bordered block diagonal form. This allows us to develop a recursive parallel bisection method for the solution of the system of equations.     

The domain composition method applied to Poisson's equation in two dimensions

Domain composition, a recently described method for formulating continuum field problems, removes certain restrictions on the construction of finite element models such that it is possible to solve a finite element problem without using a global compatible mesh. The domain composition method couples or otherwise constrains meshes in local regions to obtain a solution equivalent to that produced by conventional finite element methods. In particular, the domain composition method enables finite element models to be formulated with overlapping elements. Several advantages come from this, including an ability to automatically generate a finite element model from a solid geometric model, an ability to use a variety of element types in a single finite element model and an ability to exactly match element boundaries to the local geometry. This paper shows in detail a finite element formulation of Poisson's equation using domain composition and presents certain key algorithms that incorporate the domain composition method into well-established finite element procedures.     

基于时间有限元的弹簧摆动力学新解法EI北大核心CSCD

弹簧摆问题是一种刚柔耦合的非线性动力学问题,随着电力技术的发展,弹簧摆在高压电塔减震方面获得了大规模的应用,但其动力学仿真还存在很多不完善之处。对此该文提出了一种利用时间有限元与保辛递推算法求解弹簧摆问题的新方法。该方法通过对弹簧摆的非线性摆动问题进行了近似积分处理,并对作用量采用矩形和梯形积分的方法获得保辛递推的形式。在提高求解速度的同时,提高了长时间求解的数值稳定性。为了体现了该文方法在求解内共振系统上的速度和稳定性优势,同已有结果进行两次对比,显示本算法较传统算法的计算速度、时间稳定性与精度上均存在一定优势。最后初步讨论了采用该方法求解大摆角混沌问题的途径。     

An updated Lagrangian finite element sensitivity analysis of large deformations using quadrilateral elements

A continuum parameter and shape sensitivity analysis is presented for metal forming processes using the finite element method. The sensitivity problem is posed in a novel updated Lagrangian framework as suitable for very large deformations when remeshing operations are performed during the analysis. In addition to exploring the issue of transfer of variables between meshes for finite deformation analysis, the complex problem of transfer of design sensitivities (derivatives) between meshes for large deformation inelastic analyses is also discussed. A method is proposed that is shown to give accurate estimates of design sensitivities when remeshing operations are performed during the analysis. Sensitivity analysis for the consistent finite element treatment of near incompressibility within the context of the assumed strain methods is also proposed. In particular, the performance of four‐noded quadrilateral elements for the sensitivity analysis of large deformations is studied. The results of the continuum sensitivity analysis are validated by a comparison with those obtained by a finite difference approximation (i.e. using the solution of a perturbed deformation problem). The effectiveness of the method is demonstrated by applications in the design optimization of metal forming processes. Copyright © 2001 John Wiley & Sons, Ltd.     

Optimum design of weaving structure of 3-D woven fabric composites by using genetic algorithms

This paper discusses the optimum design method of the weaving structure of three-dimensional (3-D) reinforced composites. We propose the design method which combines the genetic algorithms (GA) and the finite element analysis. GA is one of the optimization techniques for the combinatorial optimization problem. In the finite element analysis, we used the original structure model which can express the fiber arrangement state in the 3-D composites faithfully. In this study, the original weaving structure model is constructed by combining the basic structure which has the fiber bundle and the cubic grid of resin. From analysis results, in the small design region, we can obtain the optimum weaving structure. Moreover, we proposed a new genetic operation, to design the weaving structure at the larger design region. These operations aim to prevent the failure of the partial weaving structure in the analytical model as much as possible. From the analysis results, the optimum weaving structure is obtained at the large design region, similar to above results. Consequently, it seems that the proposed method enables the design of the optimum weaving structure in the 3-D composites.     

Robust optimization based on the Propagation of Variance method for analytic design models

The robust optimisation is performed in the preliminary design phase dealing with analytic models. The analytic models come either from the finite element models or from the physical laws approximation. The variability on the design parameters is defined using random variables identified by their first two Moments, the Mean and the Standard deviation. A robust design approach is proposed that determines whether a robust design solution exists or not to the given design problem. This approach combines a reformulation of the analytic model with the new design specifications. It integrates the parameter uncertainties (Mean and Standard deviation) and a deterministic optimisation algorithm (SQP algorithm). The Means and the Standard deviation are computed using the Propagation of Variance method. The engineering application of an electrical actuator design is introduced and used to show the implementation and the effectiveness of the proposed robust approach.     

基于分布式计算的复合材料机翼优化设计

将遗传算法与高精度的通用有限元分析软件相结合, 并将其应用于复合材料机翼满足气动弹性要求的优化设计中。为了提高采用遗传算法的复合材料机翼优化设计的效率, 探讨了将分布式计算与遗传算法进行集成, 形成了基于分布式计算和遗传算法的复合材料机翼优化设计方法, 并应用该方法解决某大展弦比复合材料机翼副翼和舵面操纵反效问题。计算结果表明, 该方法可用于解决工程上复杂结构优化问题。      

基于代理模型的空投装备气囊缓冲系统多目标优化

基于有限元法和控制体积法建立装备-气囊系统有限元模型,并采用试验数据对模型进行验证。复杂气囊系统着陆缓冲过程仿真计算资源消耗大,难以应用传统迭代方法进行参数优化。为克服这些问题,结合扩展拉丁超立方设计,以最大着陆冲击加速度和最大翻转角度为响应,采用径向基函数构建代理模型。在代理模型基础上,利用多目标遗传算法对主气囊高度、横向宽度及排气孔面积等气囊缓冲系统参数进行了多目标优化。优化结果表明:优化后最大冲击加速度减小了15.5%,最大翻转角度减小了70.3%,缓冲性能与横向稳定性均有所提高。     

The element connectivity parameterization formulation for the topology design optimization of multiphysics systems

In spite of the success of the element‐density‐based topology optimization method in many problems including multiphysics design problems, some numerical difficulties, such as temperature undershooting, still remain. In this work, we develop an element connectivity parameterization (ECP) formulation for the topology optimization of multiphysics problems in order to avoid the numerical difficulties and yield improved results. In the proposed ECP formulation, finite elements discretizing a given design domain are not connected directly, but through sets of one‐dimensional zero‐length links simulating elastic springs, electric or thermal conductors. The discretizing finite elements remain solid during the whole analysis, and the optimal layout is determined by an optimal distribution of the inter‐element connectivity degrees that are controlled by the stiffness values of the links. The detailed procedure for this new formulation for multiphysics problems is presented. Using one‐dimensional heat transfer models, the problem of the element‐density‐based method is explained and the advantage of the ECP method is addressed. Copyright © 2005 John Wiley & Sons, Ltd.     

钢铝板材压力连接模具几何参数多目标优化

为解决钢铝混合车身中钢和铝异种材料间的连接问题,对无铆钉自冲铆连接钢铝异种材料的可行性进行了实验研究和仿真分析.在实验验证的基础上,为得到连接接头处的最优机械性能,以接头颈厚值和自锁值为评价指标,综合运用实验设计、统计分析、代理模型构造响应面以及遗传算法对钢铝压力连接模具几何参数进行多目标优化,得到了接头颈厚值和自锁值...     

Dimensional model reduction in non‐linear finite element dynamics of solids and structures

A general approach to the dimensional reduction of non‐linear finite element models of solid dynamics is presented. For the Newmark implicit time‐discretization, the computationally most expensive phase is the repeated solution of the system of linear equations for displacement increments. To deal with this, it is shown how the problem can be formulated in an approximation (Ritz) basis of much smaller dimension. Similarly, the explicit Newmark algorithm can be also written in a reduced‐dimension basis, and the computation time savings in that case follow from an increase in the stable time step length. In addition, the empirical eigenvectors are proposed as the basis in which to expand the incremental problem. This basis achieves approximation optimality by using computational data for the response of the full model in time to construct a reduced basis which reproduces the full system in a statistical sense. Because of this ‘global’ time viewpoint, the basis need not be updated as with reduced bases computed from a linearization of the full finite element model. If the dynamics of a finite element model is expressed in terms of a small number of basis vectors, the asymptotic cost of the solution with the reduced model is lowered and optimal scalability of the computational algorithm with the size of the model is achieved. At the same time, numerical experiments indicate that by using reduced models, substantial savings can be achieved even in the pre‐asymptotic range. Furthermore, the algorithm parallelizes very efficiently. The method we present is expected to become a useful tool in applications requiring a large number of repeated non‐linear solid dynamics simulations, such as convergence studies, design optimization, and design of controllers of mechanical systems. Copyright © 2001 John Wiley & Sons, Ltd.     

Topology Design of Planar Cross-Sections with a Genetic Algorithm: Part 2--Bending,Torsion and Combined Loading Applications

A topology design approach provides freedom to design a structure of any size, shape and connectivity within a defined domain. The binary chromosome storage and global search capabilities of the Genetic Algorithm (GA) make it an excellent tool for structural topology applications. A companion paper (Fanjoy, D. W. and Crossley, W. A. (2000), Topology design of planar cross-sections with a genetic algorithm: Part1--overcoming the obstacles. Engineering Optimization, (this issue)) investigated and demonstrated a successful GA approach for topology design of planar cross-sections subject to bending, torsion and combined loading. In this paper, the structural topology design applications are investigated in greater detail. The finite element method used for section analysis is described. Several applications are presented, highlighting different features of the GA/finite-element method combination for topology design. Designs generated for simple bending and torsion problems are presented first, with discussion and comparison to theoretical or known solutions. A combined loading application is presented, and the generated solution is compared to a baseline design. Finally, a multiobjective problem demonstrates the ability of the GA to generate a family of design trade-off solutions; a capability not normally associated with topology design approaches. The GA method for topology design presented here shows promise for application to a wider range of structural design problems than previous GA approaches.     

Autonomous decentralized finite element method and its applications

In this paper, a new solution procedure using the finite element technique in order to solve problems of structure analysis is proposed. This procedure is called the autonomous decentralized finite element method because it is based on the characteristic autonomy and decentralization in life or biological systems (life‐like approach). The fundamental approach is developed according to an idea of cellular automata manipulation by the new neighbourhood model. The finite element method with an algorithm of the relaxation method is adopted as the solution procedure in this approach. The proposed procedure demonstrates that it is a powerful means of numerical analysis for many kinds of structural problems that are structural morphogenesis, structural optimization and structural inverse problems. Our procedure is applied to numerical analysis of three simple plane models: (1) The structural shape analysis problem for the prescribed displacement mode of a truss structure, (2) An adaptive structure remodelling problem on an elastic continuum, (3) An identification problem of thermal conductivity on a continuum. The effectiveness and validity of our idea are shown from their numerical results. Copyright © 2003 John Wiley & Sons, Ltd.     

杆系结构自由振动精确求解的理论和算法

杆系结构的自由振动特性对结构的抗震设计至关重要。与常规有限元方法采用近似形函数将原问题化为线性特征值问题不同,本文的精确方法从杆件精确的形函数出发获得精确的动力刚度,将原问题化为非线性特征值问题。已有的Wittrick-Willliams算法很好地解决了该问题的频率求解。在此基础上,进一步提出了求解该非线性问题的导护型Newton法格式,并优化了各个算法环节。该法能同时求出频率和振型,求解结果精确可靠且具有二阶收敛速度,是一种快速精确、可靠实用的工程计算方法。     

Optimal design of multi-response experiments using semi-definite programming

Optimal design of multi-response experiments for estimating the parameters of multi-response linear models is a challenging problem. The main drawback of the existing algorithms is that they require the solution of many optimization problems in the process of generating an optimal design that involve cumbersome manual operations. Furthermore, all the existing methods generate approximate design and no method for multi-response n-exact design has been cited in the literature. This paper presents a unified formulation for multi-response optimal design problem using Semi-Definite Programming (SDP) that can generate D-, A- and E-optimal designs. The proposed method alleviates the difficulties associated with the existing methods. It solves a one-shot optimization model whose solution selects the optimal design points among all possible points in the design space. We generate both approximate and n-exact designs for multi-response models by solving SDP models with integer variables. Another advantage of the proposed method lies in the amount of computation time taken to generate an optimal design for multi-response models. Several test problems have been solved using an existing interior-point based SDP solver. Numerical results show the potentials and efficiency of the proposed formulation as compared with those of other existing methods. The robustness of the generated designs with respect to the variance-covariance matrix is also investigated.