On the treatment of uncertainties in structural mechanics and analysis

In this paper the need for a rational treatment of uncertainties in structural mechanics and analysis is reasoned. It is shown that the traditional deterministic conception can be easily extended by applying statistical and probabilistic concepts. The so-called Monte Carlo simulation procedure is the key for those developments, as it allows the straightforward use of the currently used deterministic analysis procedures.A numerical example exemplifies the methodology. It is concluded that uncertainty analysis may ensure robust predictions of variability, model verification, safety assessment, etc.     

Correlation between the gradients of the quadratic functional and its clipped prototype

Applicability of clipping of quadratic functional E = −0.5x ⁺ Tx + Bx in the minimization problem is considered (here x is the configurational vector and B ∈ R ^N is real valued vector). The probability that the gradient of this functional and the gradient of clipped functional ɛ = −0.5x ⁺ τx + bx are collinear is shown to be very high (the matrix τ is obtained by clipping of original matrix T: τ_ij = sgnT _ij ). It allows the conclusion that minimization of functional ɛ implies minimization of functional E. We can therefore replace the laborious process of minimizing functional E by the minimization of its clipped prototype ɛ. Use of the clipped functional allows sixteen-times reduction of the computation time and computer memory usage.     

On the quadratic controllability and quadratic feedback minimality

In Swei et al. (2000) the quadratic controllability and quadratic feedback minimality of unstructured norm bounded uncertain linear systems have been studied with explicitly verifiable necessary and sufficient solvability conditions in terms of the so-called "essential subsystem." In this note, we give the geometric interpretation of the main results in the above paper, using the strongly controllable subspace and, hence, provide a deeper understanding of the concept of "essential subsystem" in an earlier work.     

重建代谢网络及其结构与功能的分析

文中研究重建代谢网络及分析其拓扑结构与功能.首先,详细介绍用于重建代谢网络的主要数据类型以及相关数据库.然后,介绍重建和精练代谢网络的方法,及重建苏云金芽胞杆菌(Bacillus thuringiensis)代谢网络的工作.用代谢物图表示该网络,共830个节点,1 132条连线.最后,分析网络的拓扑结构特征,借助代谢网络"蝴蝶结"结构的特征对其予以简化,并从网络的小世界效应、节点度分布和关键代谢物3方面分析其巨强连通体.该巨强连通体的平均路径长度为8.63,节点度分布符合幂律分布,表明它是一个典型的小世界和无标度网络.同时,研究结果表明其关键代谢物均具备重要的生物学功能意义.     

Sequential quadratic programming and the ASTROS structural optimization system

The NLPQL sequential quadratic programming algorithm of Schittkowski is integrated with the Automated Structural Optimization System (ASTROS) and tested on three largescale optimization problems, including one with constraints from multiple disciplines. Furthermore, the traditional solution approach, which involves the formulation and solution of an explicitly defined approximate problem during each iteration, is replaced by a simpler approach, in which the approximate problem is eliminated, and each finite element analysis is followed by one iteration of the optimizer. To compensate for the cost of additional analyses, a much more restrictive active set strategy is used. Although not much computational efficiency is gained, the alternative approach gives accurate solutions. The largest test problem, which had 1527 design variables and 6124 constraints was solved with ASTROS for the first time using a direct method. The resulting design represents the lowest weight feasible design recorded to date.Research done while a graduate student at the Air Force Institute of Technology, Dayton, Ohio. The views expressed in this article are those of the authors, and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the U.S. Government     

On using deterministic FEA software to solve problems in stochastic structural mechanics

Over the last three decades there has been an outstanding growth in the development of deterministic finite element codes with extensive analysis capabilities. Extension of such deterministic codes to solve problems in stochastic mechanics is of much interest to the academic research community and industry. In this paper we discuss some of the issues involved in integrating fully grown third-party deterministic finite element codes with stochastic projection schemes. The objective of this study is to lay the foundation for development of an easy-to-use general-purpose stochastic finite element software for carrying out probabilistic analysis of large-scale engineering systems. We present a brief introduction to stochastic reduced basis projection schemes and the steps involved in coupling them with a typical deterministic finite element software. We demonstrate with the help of a number of case studies how a coupled framework can be used for solving problems in probabilistic mechanics.     

Positive definiteness of a quadratic functional

In a 1975 paper, Molinari [1] proved that under certain continuity and controllability hypotheses, the infinum of a quadratic linear functional subject to linear differential equations constraints and a linear terminal constraint, is a quadratic function of the initial state. We show here how to constructively find this quadratic form under the addition of a positivity assumption. We also show that if a strengthened generalized Legendre-Clebsch condition holds then there is a linear optimal feedback control law.     

Invariant-theoretic methods in scene analysis and structural mechanics

We discuss possible applications of invariant theory to unsolved problems in applied geometry. In particular, we discuss projective conditions for correctness of plane drawings of 3-dimensional geometric forms, and for special mechanical behavior of bar-and-joint structures.     

On a multiscale computational strategy with time and space homogenization for structural mechanics

A new multiscale computational strategy was recently proposed for the analysis of structures described both on a fine space scale and a fine time scale. This strategy, which involves homogenization in space as well as in time, could replace in several domains of application the standard homogenization techniques, which are generally limited to the space domain. It is an iterative strategy which calls for the resolution of problems on both a micro (fine) scale and a macro (homogenized) scale. In this paper, we review the bases of this approach and present improved approximation techniques to solve the micro- and macro-problems.     

A global sensitivity analysis in structural mechanics

A methodology is developed to evaluate the response sensitivity of structural systems to variations in their design parameters. The sensitivity is evaluated by considering the global behavior of the system response when the parameters vary within a bounded region. The design parameters are characterized by means of baseline values plus fluctuating components, and the sensitivity of the system is measured in terms of the global variability of the response with respect to its baseline response. The methodology is then extended into the context of optimum redesign analysis of structural systems. Application of the method is made to a structural system defined by two-dimensional beam-column elements and to a system defined by plate elements. The numerical implementation of the global sensitivity approach is made by means of the finite element method. Several analyses are performed and the results are discussed. Finally, some extensions of the present work are presented.     

Non-overlapping domain decomposition methods in structural mechanics

Summary The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family of large ill-conditioned linear systems. In this paper we study strategies to efficiently solve to linear system based on non-overlapping domain decomposition methods. We present a review of most employed approaches and their strong connection. We outline their mechanical interpretations as well as the practical issues when willing to implement and use them. Numerical properties are illustrated by various assessments from academic to industrial problems. An hybrid approach, mainly designed for multifield problems, is also introduced as it provides a general framework of such approaches.     

Applications of artificial neural nets in structural mechanics

First the fundamentals of neurologically motivated computing are briefly discussed. This is followed by presenting two of the many possible applications in structural mechanics. Both of these are oriented towards structural optimization. In the first mode a neural net model of the structural response is created and then attached to any conventional optimization algorithm. In the second mode a neural net model of an experienced designer is created knowledgeable within a narrow class of structural concepts.Presented at the CISM Course Shape and Layout Optimization in Structural Design, Udine, Italy, July 1990     

On the structural output distinguishability of parametric models, and its relations with structural identifiability

In this note the notion of output distinguishability is extended to parametric models with different structures. Methods are suggested for testing such models for structural output distinguishability. The possible relations of structural output distinguishability with structural identifiability and other structural properties are investigated.     

Nested approach to structural optimization in nonsmooth mechanics

This work applies the nested approach of structural optimization, in the form of the method of moving asymptotes (MMA), to some typical problems of nonsmooth mechanics. Namely, the state problems that arise when mechanical structures, in this case, trusses, are subjected to frictionless contact constraints and/or the constraints arising due to supporting cables that are rigid in tension but do not admit compression. In these problems the state as a function of the design is not everywhere differentiable and since MMA is developed for smooth problems, it is not clear that it is an admissible solution method. However, from the series of test problems in this paper we conclude that it is indeed a valid method: it shows convergence to a solution for all cases except for a class of problems with strict conditions on the magnitude of the contact (cable) forces, but these difficulties could be removed by the introduction of a small modification of MMA in the form of simple move limits.     

Finite-element programs in integrated software for structural mechanics and CAD

The paper discusses integrated FEM (finite-element method) software for structural analysis and CAD applications. The main purpose of this paper is to emphasize the need to use interactive graphics in structural analysis and CAD. An attempt is made to review general-purpose pre- and post-processing programs developed for FEM applications, and integrated FEM programs for structural mechanics applications. Some large integrated systems for sizing and analysing aircraft structures are presented.     

On the linear quadratic minimum-time problem

A nontraditional minimum-time problem that includes quadratic-state and control-weighting terms in the performance index is investigated. This formulation provides a convenient solution to the problem that uses the solution of the Riccati equation to compute the optimal feedback gain and the optimal time. In some cases the latter is simply found using the derivative of the Riccati equation solution     

On polynomial response surfaces and Kriging for use in structural optimization of crashworthiness

The accuracy of different approximating response surfaces is investigated. In the classical response surface methodology (CRSM) the true response function is usually replaced with a low-order polynomial. In Kriging the true response function is replaced with a low-order polynomial and an error correcting function. In this paper the error part of the approximating response surface is obtained from simple point Kriging theory. The combined polynomial and error correcting function will be addressed as a Kriging surface approximation.To be able to use Kriging the spatial correlation or covariance must be known. In this paper the error is assumed to have a normal distribution and the covariance to depend only on one parameter. The maximum-likelihood method is used to find the latter parameter. A weighted least-square procedure is used to determine the trend before simple point Kriging is used for the error function. In CRSM the surface approximation is determined through an ordinary least-square fit. In both cases the D-optimality criterion has been used to distribute the design points.From this investigation we have found that a low-ordered polynomial assumption should be made with the Kriging approach. We have also concluded that Kriging better than CRSM resolves abrupt changes in the response, e.g. due to buckling, contact or plastic deformation.