Shape optimization of shell structures based on NURBS description using automatic differentiation

The consolidation of the link among four fields in computational mathematics and mechanics is the main objective of this work. Surfaces based on NURBS (non‐uniform rational B‐spline), mathematical optimization, the finite element method (FEM) in structural analysis, and automatic differentiation (AD) are applied in shape optimization of shells. This problem is performed taking into account the fact that material and mechanical characteristics influence both, the structural shape and the thickness variation, in order to obtain the best performance with respect to a specific criterium. Some techniques were implemented to modify the shell geometry conserving the same parameterization without a new finite element mesh generation. The shape modification is carried out using an optimization code based on the data obtained by a finite element analysis and gradients evaluation. In this work the optimization procedure is performed using an SQP (Sequential Quadratic Programming) algorithm, where the variables are the control points in homogeneous coordinates, the knot vectors, and the thickness. The functional value is determined by the FEM and gradients are evaluated using AD. Some examples are analyzed and discussed. As a consequence of the shape optimization, shells with high structural performance and aesthetically beautiful shapes can be obtained. Copyright © 2011 John Wiley & Sons, Ltd.     

数值微分的一类软化子方法

对数值微分问题构造了一类新的软化子求解方法,并在Ｌ＾２意义上证明了该方法可以提高软化解的收敛阶。     

高阶分数阶微分方程系统的解的注记

分数阶导数在描述不同物质的记忆与遗传性质方面提供了有力的工具.在科学和工程的不同领域,都用分数阶微分方程组来描述动力系统.本文主要探讨分数阶微分方程系统初值问题局部解的存在性与唯一性.对于线性系统,运用Schur分解定理,给出其局部解的存在性与唯一性,并通过举例说明该方法是有效的.对于非线性系统,利用Schauder不动点定理,给出了解的存在性;运用Banach不动点定理,给出了解的唯一性.     

Calibration of elastoplastic constitutive model parameters from full-field data with automatic differentiation-based sensitivities

We present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.     

Analysis of transfer procedures in elastoplasticity based on the error in the constitutive equations: Theory and numerical illustration

The aim of this work is to illustrate a methodology for the assessment of adaptive strategies for the solution of associative rate‐independent plasticity problems solved by employing the incremental displacement conforming finite element method. This is the first step towards a more rational definition of transfer operators in terms of the ensuing error. The motivating idea is the observation that change of data and/or finite element mesh from one time interval to the other can be both related to a discontinuity jump of the approximate solution across the time instant t_n. Thus, reliable a posteriori estimates will have to depend not only on the time step and finite element mesh size but also on the value of the jump. A new error estimate based on the error in the constitutive equations is developed which allows characterization of the discontinuity jump. Copyright © 2004 John Wiley & Sons, Ltd.     

汽车底漆自动沉积涂料的研究

自动沉积涂料中的活性物质是影响漆液活性和稳定性的重要因素.其加入量对溶液的稳定性和漆膜具有很大的影响.采用自行研制的丙烯酸乳胶,将乳胶、碳黑浆及活性剂配制成稳定的自泳漆浴液,研究了氢氟酸等物质对浴液活性的影响,找到了一种简便的涂料稳定性的判断方法,为实际应用中确保涂料涂装质量提供了依据.     

基于"地毯式"的电力企业技术标准差异化梳理方法研析

本文评估了电力企业技术标准内容交叉重复矛盾问题的影响,研究确定标准差异化梳理原则,提出标准差异化梳理方法及流程,实现对标准差异化内容的灵活、快捷的"地毯式"比对,为标准差异化协调工作提供前提基础.研究成果能有效防止标出多门,最大限度地保障电力企业不同专业间技术标准的协调一致,促进标准刚性执行有效落地.     

Nanotopographical Cues Augment Mesenchymal Differentiation of Human Embryonic Stem Cells

The production of bone‐forming osteogenic cells for research purposes or transplantation therapies remains a significant challenge. Using planar polycarbonate substrates lacking in topographical cues and substrates displaying a nanotopographical pattern, mesenchymal differentiation of human embryonic stem cells is directed in the absence of chemical factors and without induction of differentiation by embryoid body formation. Cells incubated on nanotopographical substrates show enhanced expression of mesenchymal or stromal markers and expression of early osteogenic progenitors at levels above those detected in cells on planar substrates in the same basal media. Evidence of epithelial‐to‐mesenchymal transition during substrate differentiation and DNA methylation changes akin to chemical induction are also observed. These studies provide a suitable approach to overcome regenerative medical challenges and describe a defined, reproducible platform for human embryonic stem cell differentiation.     

A finite-difference method of improving dynamic measurement accuracy

Finite differences of various orders are used in linear estimation when the measurements contain not only fluctuation noise but also piecewise-continuous interference of degree type. __________ Translated from Izmeritel’naya Tekhnika, No. 4, pp. 16–21, April, 2006.     

Improved finite difference method for equilibrium problems based on differentiation of the partial differential equations and the boundary conditions

A numerical algorithm for producing high-order solutions for equilibrium problems is presented. The approximated solutions are improved by differentiating both the governing partial differential equations and their boundary conditions. The advantages of the proposed method over standard finite difference methods are: the possibility of using arbitrary meshes; the possibility of using simultaneously approximations with different (distinct) orders of accuracy at different locations in the problem domain; an improvement in approximating the boundary conditions; the elimination of the need for ‘fictitious’ or ‘external’ nodal points in treating the boundary conditions. Furthermore, the proposed method is capable of reaching approximate solutions which are more accurate than other finite difference methods, when the same number of nodal points participate in the local scheme. A computer program was written for solving two-dimensional problems in elasticity. The solutions of a few examples clearly illustrate these advantages.     

A shell problem ‘highly sensitive’ to thickness changes

In general, shell structural problems can be identified to fall into one of the categories of membrane‐dominated, bending‐dominated and mixed shell problems. The asymptotic behaviour with a well‐defined load‐scaling factor shows distinctly into which category a given shell problem falls. The objective of this paper is to present a shell problem and its solution for which there is no convergence to a well‐defined load‐scaling factor as the thickness of the shell decreases. Such shells are unduly sensitive in their behaviour because the ratio of membrane to bending energy stored changes significantly and indeed can fluctuate with changes in shell thickness. We briefly review the different asymptotic behaviours that shell problems can display, and then present the specific problem considered and its numerical solution using finite element analysis. Copyright © 2003 John Wiley & Sons, Ltd.     

辨证论治艾滋病

艾滋病是一种获得性免疫缺陷综合征,中医学的观点则是正气严重不足。正气依靠精神的支撑,而精神来源于饮食气味及其精微物质 ,精微物质的转化主要靠脏腑功能的正常运化。脏腑功能活动是生命运动的根本。五脏各有所主,各司其职,并且相互和合与平衡,只有当五 脏功能旺盛,并且相互和合时,人体的生命力才会强大,机体“正气”充足,才会有免疫力。在五脏之中,肝、脾、肾三脏功能要保持平衡, 其他各脏功能才会自然趋向平衡与协调,人体才会健康长寿,这就是“三维守恒”法则。     

Extending the functionality of the general‐purpose finite element package SEPRAN by automatic differentiation

From an abstract point of view, a numerical simulation implements a mathematical function that produces some output from some given input. Derivatives (or sensitivities) of the function's output with respect to its input can be obtained—free from truncation error—by using a technique called automatic differentiation. Given a computer code in a high‐level programming language like Fortran, C, or C++, automatic differentiation generates another code capable of computing not only the original function but also its derivatives. Thus, the application of automatic differentiation significantly extends the functionality of a simulation package. For instance, automatic differentiation enables, in a completely mechanical fashion, the usage of derivative‐based optimization algorithms where the evaluation of the objective function comprises some given large‐scale engineering simulation. In this paper, the automatic differentiation tool ADIFOR is used to transform the general‐purpose finite element package SEPRAN. In doing so, we automatically transform the given 400000 lines of Fortran 77 into a new program consisting of 600000 lines of Fortran 77. We compare our approach with a traditional approach based on numerical differentiation and quantify its advantages in terms of accuracy and computational efficiency for a standard fluid flow problem. Copyright © 2003 John Wiley & Sons, Ltd.     

A hybrid direct‐automatic differentiation method for the computation of independent sensitivities in multibody systems

The usefulness of sensitivity analyses in mechanical engineering is very well‐known. Interesting examples of sensitivity analysis applications include the computation of gradients in gradient‐based optimization methods and the determination of the parameter relevance on a specific response or objective. In the field of multibody dynamics, analytical sensitivity methods tend to be very complex, and thus, numerical differentiation is often used instead, which degrades numerical accuracy. In this work, a simple and original method based on state‐space motion differential equations is presented. The number of second‐order motion differential equations equals the number of DOFs, that is, there is one differential equation per independent acceleration. The dynamic equations are then differentiated with respect to the parameters by using automatic differentiation and without manual intervention from the user. By adding the sensitivity equations to the dynamic equations, the forward dynamics and the independent sensitivities can be robustly computed using standard integrators. Efficiency and accuracy are assessed by analyzing three numerical examples (a double pendulum, a four‐bar linkage, and an 18‐DOF coach) and by comparing the results with those of the numerical differentiation approach. The results show that the integration of independent sensitivities using automatic differentiation is stable and accurate to machine precision. Copyright © 2014 John Wiley & Sons, Ltd.     

基于眼动分析的白酒外包装导向设计的差异化体现

目的 随着生活质量的提高,消费群体逐步追求品质化的生活,消费所带来的不仅是一种物质上的填补,更是一种心理上的满足。然而,如今白酒外包装一成不变的视觉刺激已经使购买者麻木,无法满足其消费需求,且同质化严重的外包装,也无法突显品牌特点。因此,面对消费者日益增长的心理需求和文化需求,有必要在实现包装的主要功能时,对其进行再设计。方法 从消费者的视角出发,利用格式塔理论对白酒外包装现有产品外形进行提取分析,采用眼动实验探究,分析消费者对白酒外包装品牌品名的重视,以及不同白酒包装外形对消费者的视觉引导趋势。结果 得出白酒外包装对消费者视觉引导的3个规律性特征。结论 针对目前同质化严重的外包装设计,基于品牌文化、消费者心理需求等感性视角,与用户视觉流向特点等理性因素,总结白酒外包装形态对视觉引导的基本规律,并通过该规律对白酒外包装进行差异化设计,达到白酒外在品牌品名优先识别与内在文化突显的最终目的。     

现代性别差异化包装设计

以性别差异影响消费行为为启示,分析了两性在各层面的差异以及消费者需求对设计走向的影响,论述了性别差异化设计对企业提升自身竞争力的重要帮助。在此基础上,对性别差异化包装设计在今后的发展方向加以展望,并提出性别差异化包装设计要素,以期为今后的性别差异化包装设计提供一定的参考和帮助。     

工业射线胶片自动洗片机的应用技术研讨

研讨工业射线胶片自动洗片机在锅炉、压力容器行业的应用技术和实际经验，指出机、片、液、人、法五大要素对此新技术推广应用的重要作用。     

Shape optimization of axisymmetric preform tools in forging using a direct differentiation method

A method for computing shape sensitivity in the frame of non‐linear and non‐steady‐state forging is presented. Derivatives of tool geometry, velocity and state variables with respect to the shape parameters are calculated by a direct differentiation of discrete equations. Because of the important part played by the accuracy of finite element calculations, an efficient transfer method is used between meshes during remeshings and the contact algorithms are carefully differentiated. The resulting inverse design procedure is successfully applied to two industrial examples of forging of automobile parts, with fold‐over and piping defects occurring during the intermediate designs. It makes it possible to suggest reasonable preform shapes, with or without any available knowledge of the forging process. Copyright © 2001 John Wiley & Sons, Ltd.     

Optimal control of an induction heating process using automatic differentiation

We consider an optimal control problem arising in an induction heating process. The main difficulty is to obtain accurate and efficient derivatives of the discrete form of the cost function. In this work we use automatic differentiation. Unlike numerical differentiation based on finite differences, derivatives generated by automatic differentiation are free of truncation error. Numerical results show the performance of the method in terms of accuracy and computational efficiency. Copyright © 2005 John Wiley & Sons, Ltd.     

整体产品概念下的产品市场差异化分析

通过分析产品市场的差异化趋势,总结了产品的差异化形式和特点,为企业创造差异化产品提供一种思路和策略框架。