Sensitivity analysis for product design selection with an implicit value function

In product design selection the decision maker (DM) often does not have enough information about the end users’ needs to state the “preferences” with precision, as is required by many of the existing selection methods. We present, for the case where the DM gives estimates of the preferences, a concept for calculating a “robustness index.” The concept can be used with any iterative selection method that chooses a trial design for each iteration, and uses the DM’s preference parameters at that trial design to eliminate some design options which have lower value than the trial design. Such methods, like our previously published method, are applicable to cases where the DM’s value function is implicit. Our robustness index is a metric of the allowed variation between the actual and estimated preferences for which the set of non-eliminated trial designs (which could be singleton) will not change. The DM, through experience, can use the robustness index and other information generated in calculating the index to determine what action to take: make a final selection from the present set of non-eliminated designs; improve the precision of the preference estimates; or otherwise cope with the imprecision. We present an algorithm for finding the robustness index, and demonstrate and verify the algorithm with an engineering example and a numerical example.     

Application of an anisotropic growth formulation to computational structural design

Common structural optimisation problems consist of problem-specific objective functions which have to be minimised mathematically with respect to design and state variables taking into account particular constraints. In contrast to this, we adopt a conceptually different approach for the design of a structure which is not based on a topology-optimisation technique. Instead, we apply a one-dimensional energy-driven constitutive evolution equation for the referential density–originally proposed for the simulation of remodelling effects in bones–and embed this into the micro-sphere-concept to end up with a three-dimensional anisotropic growth formulation. The objective of this contribution is to investigate this approach with emphasis on its application to structural design problems by means of two three-dimensional benchmark-type boundary value problems. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analysis of uncertainties in the effective material behaviour of disordered structural foams

The present contribution is concerned with a numerical analysis of the uncertainties in the structural response of threedimensional structural foams with partially open cells. The effective thermo mechanical material response is determined by means of an energy based homogenization procedure. Stochastic effects in the geometry and topology of the microstructure are treated by means of a repeated analysis of small-scale representative volume elements with prescribed relative density and prescribed cell size distribution. The results are evaluated by stochastic methods. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability and Hopf bifurcation analysis of an eco-epidemic model with a stage structure

In this paper, an eco-epidemiological model with a stage structure is considered. The asymptotical stability of the five equilibria, the existence of stability switches about positive equilibrium, is investigated. It is found that Hopf bifurcation occurs when the delay τ passes though a critical value. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, biological explanations and main conclusions are given.     

Optimization of structural design

Typical problems of optimal structural design are discussed to indicate mathematical techniques used in this field. An introductory example (Section 2) concerns the design of a beam for prescribed maximal deflection and shows how suitable discretization may lead to a problem of nonlinear programming, in this case, convex programming. The problem of optimal layout of a truss (Section 3) is discussed at some length. A new method of establishing optimality criteria (Section 4) is illustrated by the optimal design of a statically indeterminate beam of segmentwise constant or continuously varying cross section for given deflection under a single concentrated load. Other applications of this method (Section 5) are briefly discussed, and a simple example of multipurpose design (Section 6) concludes the paper.     

Model selection for regression on a fixed design

We deal with the problem of estimating some unknown regression function involved in a regression framework with deterministic design points. For this end, we consider some collection of finite dimensional linear spaces (models) and the least-squares estimator built on a data driven selected model among this collection. This data driven choice is performed via the minimization of some penalized model selection criterion that generalizes on Mallows' C _p . We provide non asymptotic risk bounds for the so-defined estimator from which we deduce adaptivity properties. Our results hold under mild moment conditions on the errors. The statement and the use of a new moment inequality for empirical processes is at the heart of the techniques involved in our approach. Received: 2 July 1997 / Revised version: 20 September 1999 / Published online: 6 July 2000     

Evolution of structural damage and macrofailure of inhomogeneous media at the supercritical stage of deformation

The article deals with the evolution of structural damage of an inhomogeneous body as a function of the properties of the loading system whose characteristics are taken into account by supplementing the boundaryvalue problem (1), (2) with the boundary conditions of the third kind (3) and (4). With the numerical solution by the finite-element method these boundary conditions are satisfied in accordance with the Eqs. (6) and (7) by changing the rigidity matrix of the discretized body (8). The material loses its load-bearing capacity at some point of the descending branch of the stress-strain diagram (Fig. 1a) at the instant the conditions of stability (9) are infringed. Normalized correlation functions of a damaged structure plotted for different equilibrium states of a granular composite (Fig. 2) make it possible to identify characteristic stages of failure. Macroscopic failure of material is regarded as the concluding stage of the processes of the onset, localization of structural disruptions, and formation of a macrodefect. Increased rigidity of the loading system makes it possible to stabilize the process of damage calculation, and this leads to an increase of limit deformations. The realization of the supercritical stage of deformation, together with energy dissipation upon structural destruction is the mechanism of adaptation of an inhomogeneous body to the loading conditions.Perm State Technical University, Russia. Translated from Mekhanika Komozitnykh Materialov, Vol. 33, No. 3, pp. 329–339, May–June, 1997.     

The onset of stochastic pulsations at the early non-linear stage of the development of perturbations in the jet of an incompressible fluid propagating along a wall

The Korteweg-De Vries equation, which describes the non-linear propagation of perturbations in a jet of incompressible fluid emanating from a slit in a planar screen and propagating along a wall is considered. When account is taken of the natural vibrations of the wall, the equation becomes inhomogeneous. If an external action is specified in the form of a running wave, the particular solution of the inhomogeneous equation may be sought in an analogous form. As a result, the simplest problem in the theory of dynamical systems in the Hamiltonian formulation arises. As usual, the existence of a homoclinic structure in the neighbourhood of the separatrices is deduced from an analysis of a Poincaré transformation. Among the trajectories belonging to the homoclinic structure in the secant plane, there are some with properties which are formulated in terms of determinate chaos. A fundamentally important conclusion concerning the dual role of solitons at the non-linear stage of the wave motion of the fluid follows: on the one hand, they serve as the nuclei of large-scale coherent structures and, on the other hand, they are responsible for the onset of stochastic pulsations.     

The balance of material momentum at a shock wave propagating in a thermo-elastic material

At a surface of discontinuity, the mechanical balance laws are represented by jump conditions. It is shown how the balance of material momentum at an adiabatic shock propagating in a thermo-elastic material is obtained from the discontinuous balances of physical momentum and energy. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On a class of optimum problems in structural design

The paper deals with the existence of solutions for a class of optimal design problems. The notion of relaxation of an integral functional with respect toG-convergence is introduced, and a general integral representation theorem is obtained for the relaxed functional. For a particular class of functionals, this integral representation is computed explicitly.This work has been realized in a National Research Project in Mathematics supported by the Ministero della Pubblica Istruzione (Italy).     

Stability analysis for an epidemic model with stage structure

An epidemic model with stage structure is formulated. The period of infection is partitioned into the early and later stages according to the developing process of infection, and the infectious individuals in the different stages have the different ability of transmitting disease. The constant recruitment rate and exponential natural death, as well as the disease-related death, are incorporated into the model. The basic reproduction number of this model is determined by the method of next generation matrix. The global stability of the disease-free equilibrium and the local stability of the endemic equilibrium are obtained; the global stability of the endemic equilibrium is got under the case that the infection is not fatal.     

Optimal structural design of a planar parallel platform for machining

Parallel manipulators have many advantages over traditional serial manipulators. These advantages include high accuracy, high stiffness and high load-to-weight ratio, which make parallel manipulators ideal for machining operations where high accuracy is required to meet the requirements that modern standards demand.Recently, the finite element method has been used by some workers to determine the stiffness of spatial manipulators. These models are mainly used to verify stiffness predicted using kinematic equations, and are restricted to relatively simple truss-like models. In this study, state-of-the-art finite elements are used to determine the out of plane stiffness for parallel manipulators. Euler–Bernoulli beam elements and flat shell elements with drilling degrees of freedom are used to model the platform assembly.The main objective of this study is to quantify the stiffness, particularly the out of plane stiffness, of a planar parallel platform to be used for machining operations. The aim is to obtain a design that is able to carry out machining operations to an accuracy of 10 μm for a given tool force.Reducing the weight of a parallel manipulator used in machining applications has many advantages, e.g. increased maneuverability, resulting in faster material removal rates. Therefore the resulting proposed design is optimized with respect to weight, subject to displacement and stress constraints to ensure feasible stiffness and structural integrity. The optimization is carried out by means of two gradient-based methods, namely LFOPC and Dynamic-Q.     

Multi-objective design optimization of an engine accessory drive system with a robustness analysis

Designing a good engine accessory drive system becomes a hard work with its increasingly complicated configuration and high demands on its dynamic characteristics. In this work, a hybrid mutation particle swarm optimization (HMPSO) algorithm is presented to optimize the key structure parameters of an engine accessory drive system for its vibration control. The superiority of the HMPSO algorithm against several other concerned metaheuristic algorithms in terms of solution quality and stability are verified by non-parametric statistical tests on ten benchmark functions. The design problem of the engine accessory drive system is a multi-objective optimization problem; the weighted sum method and main target method are applied to convert it to a single-objective one. Optimization on an example engine accessory drive system using the HMPSO algorithm demonstrates obvious improvement in system vibration after optimization. A robustness analysis is conducted to identify the robustness of dynamic responses of the engine accessory drive system with respect to small variations of the design variables relative to the optimal design in the design space, and suggestions on design of an engine accessory drive system are given according to it.     

Eigenvalue analysis for a crack in a power-law material

A nonlinear eigenvalue problem related to determining the stress and strain fields near the tip of a transverse crack in a power-law material is studied. The eigenvalues are found by a perturbation method based on representations of an eigenvalue, the corresponding eigenfunction, and the material nonlinearity parameter in the form of series expansions in powers of a small parameter equal to the difference between the eigenvalues in the linear and nonlinear problems. The resulting eigenvalues are compared with the accurate numerical solution of the nonlinear eigenvalue problem.     

判别分析在小儿支原体肺炎早期诊断中的应用

本文对辽宁中医学院附属医院儿科收治的 90例肺炎病例进行了判别分析 ,求得判别函数 ,并应用于临床 ,收到了较为满意的效果。     

Optimal control of a variational inequality with applications to structural analysis. I. Optimal design of a beam with unilateral supports

A class of optimal design problems is considered, where the state problem is governed by a variational inequality. The latter includes an elliptic operator, the coefficients of which are chosen as the design (control) variables.Existence of an optimal design is proven on the abstract level. Some applications are presented to the problems of elastic or elasto-plastic beams with unilateral supports. Finite element approximations are proposed and a theoretical convergence result is proven in case of elastic beams.     

Crosslinked polychlorostyrene as an optically sensitive material for photoelastic stress analysis

The photoelastic properties of chlorostyrene-ethylene glycol dimethacrylate copolymers have been investigated. Thanks to the high segmental polarizability anisotropy of chlorostyrene and the possibility of regulating the crosslink density in the crosslinked polymer, these materials possess high optical sensitivity combined with a broad range of moduli of elasticity at the "freezing" temperature.Institute of High-Molecular Compounds, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 554–556, May–June, 1969.