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A self-scaling implicit SQP method for large scale structural optimization

INTERNATIONAL JOURNAL FOR numerical METHODS IN ENGINEERING 1996年第11期39卷 1933-1953页

作者： Huang, MW Arora, JS Optimal Design Laboratory College of Engineering The University of Iowa Iowa City IA 52242 U.S.A. [*]Optimal Design Laboratory College of Engineering The University of Iowa Iowa City IA 52242 U.S.A.

The basic idea bf an implicit sequential quadratic programming (ISQP) method for constrained problems is to use the approximate Hessian of the Lagrangian without explicitly calculating and storing it. This overcomes one of the major drawbacks of the traditional SQP method where a large matrix needs to be calculated and stored. This concept of an implicit method is explained and an algorithm based on it is presented. The proposed method extends a similar algorithm for unconstrained problems where a two-loop recursion formula is used for the inverse Hessian matrix. The present paper develops a similar algorithm for not only the constrained problem but also the direct Hessian updates. Several scaling procedures for the Hessian are also presented and evaluated. The basic method and some of its variations are evaluated using a set of mathematical programming test problems, and a set of structural design test problems-small to larger scale. The ISQP method performs much better than a method that does not use any approximate Hessian matrix. Its performance is better than the full SQP method for larger scale problems. The test results also show that an appropriate scaling of the Hessian can improve both efficiency and reliability substantially.

关键词： structures optimization large scale structural design sequential quadratic programming self-scaling numerical algorithms algorithm evaluation test problems

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Feasible direction algorithm for optimal control problems with state and control constraints: Implementation

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1999年第3期101卷 623-649页

作者： Pytlak, R Vinter, RB Mil Univ Technol Fac Cybernet Warsaw Poland Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London England

In this paper, we describe the implementation aspects of an optimization algorithm for optimal control problems with control, state, and terminal constraints presented in our earlier paper. The important aspect of the implementation is that, in the direction-finding subproblems, it is necessary only to impose the state constraint at relatively few points in the time involved. This contributes significantly to the algorithmic efficiency. The algorithm is applied to solve several optimal control problems, including the problem of the abort landing of an aircraft in the presence of windshear.

关键词： optimal control state-constrained problems numerical algorithms

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SENSITIVITY CONTROLLER FOR UNCERTAIN SYSTEMS

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1990年第2期13卷 321-329页

作者： OKADA, K SKELTON, RE PURDUE UNIV DEPT AERONAUT & ASTRONAUTW LAFAYETTEIN 47906

In this paper a new controller design, which we Shall call the "trajectory sensitivity optimization" method, is presented to improve the robustness for parameter variations. The method uses the sensitivity trajectory to model the parameter uncertainty and introduces a special quadratic cost function involving an input and output sensitivity term. Necessary conditions are derived to obtain the dynamic controller. The necessary conditions consist of two Lyapunov equations and two controller gain equations that have no closed-form solution. Therefore, a special iterative algorithm was developed to obtain the numerical solution. The method can deal with a wider class of parameter uncertainty than existing methods. numerical examples show that the method is effective in improving the robustness to parameter variations. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Closed Loop System Iterative Algorithm Linear Quadratic Gaussian Simply Supported Beams Multivariable Control Flexible Structures White Noise Lagrange Multipliers numerical algorithms Riccati Equations

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Particle swarm optimisation for hybrid electric drive-train sizing

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INTERNATIONAL JOURNAL OF VEHICLE DESIGN 2012年第2-4期58卷 181-199页

作者： Ebbesen, Soren Doenitz, Christian Guzzella, Lino Inst Dynam Syst & Control CH-8092 Zurich Switzerland

Electric hybridisation of vehicles aims at reducing fuel consumption but increases production costs. Hence, automobile manufacturers are confronted with the multi-objective optimisation problem of sizing the drive-train components. In this paper, we evaluated Particle Swarm Optimisation (PSO) for solving this problem. The results showed that PSO performs significantly better than competing methods. Parameter sensitivities indicated that the optimal solution, the vehicle performance constraints, and the preference between fuel consumption and production cost are intimately coupled. Finally, a Pareto analysis confirmed that a relatively small increase in cost accounts for a majority of the total fuel saving potential.

关键词： PSO particle swarm optimisation HEV hybrid electric vehicles drive-train sizing vehicle design fuel consumption cost numerical algorithms search methods

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Generalized characteristic boundary conditions for computational aeroacoustics

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AIAA JOURNAL 2000年第11期38卷 2040-2049页

作者： Kim, JW Lee, DJ Korea Adv Inst Sci & Technol Dept Aerosp Engn Yusong Gu Taejon 305701 South Korea

An extended conservative formalism of the characteristic boundary conditions is presented on the basis of the generalized coordinates for practical computational aeroacoustics. The formalism is derived for solving the entire conservative form of the compressible Euler or Navier-Stokes equations on the body-fitted grid mesh system by using the high-order and high-resolution numerical schemes. It includes the matrices of transformation between the conservative and the characteristic variables, which were already derived In the literature to analyze the eigenvalue-eigenvector modes in an arbitrary direction. The conservation-form governing equations with their full terms are solved at the boundaries, and no kind of extrapolation or simplification of the equations is included in this formalism. Additional correction terms are devised to preserve the conservative form of flux derivative terms in the generalized coordinates. Especially, the soft inflow conditions are presented to keep the nonreflecting features, as well as to maintain the mean value of inflow velocity at the inlet boundary. These boundary conditions are applied to the actual computation of two-dimensional viscous cylinder flows with Reynolds number of 400 on the grid meshes clustered on the cylinder surface and the downstream region. The Strouhal number due to von Karman vortex streets, root-mean-square lift coefficient, and mean drag coefficient are evaluated correctly in comparison,vith experimental data. The far-field sound pressure levels are measured directly in this computation, and the accuracy is validated by an analytic formula derived in the literature.

关键词： Computational Aeroacoustics Karman Vortex Street Freestream Mach Number Navier Stokes Equations Conservation Equations Convection numerical algorithms Static Pressure Courant Friedrichs Lewy Acoustic Phenomena

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Finite-discrete element modelling of sea ice sheet fracture

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INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 2021年 217卷 228-258页

作者： Lilja, Ville-Pekka Polojarvi, Arttu Tuhkuri, Jukka Paavilainen, Jani Aalto Univ Sch Engn Dept Mech Engn POB 14300 FI-00076 Aalto Finland Rand Simulat Ltd Vantaa Finland

A rate-independent, de-cohesive damage model for the fracture modelling of large, cellular, plate-like, quasi-brittle structures is proposed. A hybrid, three-dimensional finite-discrete element method to investigate sea ice sheet fracture is then introduced, followed by three applications. The uniaxial tensile fracture of an ice sheet of varying physical sizes is examined first. The effects of both the size of an ice sheet and the loading rate applied on the effective tensile strength are investigated. The vertical penetration fracture of an ice sheet loaded by a rigid, flat-ended, cylindrical indenter is examined next. The breakthrough loads and strengths of an ice sheet of varying physical sizes are computed, applicable scaling rules as regards to the vertical breakthrough strength searched for. To conclude, the breaking of an ice sheet containing a circular hole by a surfacing, rigid, truncated cone is studied (an axisymmetric contact problem). The loads on the cone are computed and then compared with loads that can be obtained analytically for a case in which a structure is stationary, a sheet moves, and the contact is unilateral. While computing the tensile and the breakthrough strengths, a set of self-similar sheet samples with an inplane size range of 1:16 is examined. The samples are square;have a side length of either L = 10, 20, 40, 80, or 160 m;and a thickness of either h = 0.5, 1.0, or 1.5 m. With the sheets containing holes, only the largest samples (L = 160 m) are investigated. The results indicate that 1) both the tensile and the breakthrough strengths are strong functions of both L and h;ii) the tensile strength is a strong function of the applied loading rate;iii) the failure mode as regards to the vertical penetration fracture changes drastically as a function of L;iv) the model is able to demonstrate both radial and circumferential cracking;and that v) the proposed (in-direct) approach to compute ice loads on a conical offshore structure provides

关键词： Dynamic fracture Plates numerical algorithms Size effect Ice and snow

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Eigenstrains and the elastic field of an adatom

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 1998年第9期46卷 1557-1579页

作者： Peralta, A Kouris, D Knap, J Sieradzki, K Arizona State Univ Dept Mech & Aerosp Engn Tempe AZ 85287 USA

A harmonic lattice model for an adatom at the (001) surface of a cubic crystal is developed, based on the concept of eigenstrains. In this context, eigenstrains represent the distortion introduced by the adatom, affecting the substrate atoms in its vicinity. The distortions which model the relaxations associated with an adatom are obtained directly using embedded atom method (EAM) potentials. The eigenstrains are translated into a set of forces which, in the case of second-neighbor interactions, are applied to five 'substrate' atoms in the immediate vicinity of the adatom. Four of these atoms are located at the surface and one in the first layer below the surface. The resulting set of forces is self-equilibrated as expected by the nature of the adatom. The elastic field of the adatom is described and the limitations of the continuum theory are discussed. Calculations of the interaction energy between adatoms indicate agreement with existing, long-range results. The strength of the leading singularity of the interaction energy changes, however, when the adatoms are closely spaced. Anisotropy plays a significant role in this process;in certain directions, identical adatoms actually attract each other. Independent simulations using EAM potentials clearly demonstrate the accuracy of the elastic field produced by the eigenstrain model. The restrictive assumptions regarding the adatom/force system found in existing models are removed in this distortion-based model. The eigenstrain approach can also be used to represent surface steps and vacancies. (C) 1998 Elsevier Science Ltd. All rights reserved.

关键词： diffusion surface surface energy surface tension thin films numerical algorithms

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Deep drawing simulations using the finite element method embedding a multi-level crystal plasticity constitutive law: Experimental verification and sensitivity analysis

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2019年第Sep.1期354卷 245-270页

作者： Barrett, Timothy J. Knezevic, Marko Univ New Hampshire Dept Mech Engn 33 Acad WayKingsbury HallW119 Durham NH 03824 USA

This paper presents experimental verification of a multi-level simulation framework aimed at sheet metal forming analysis. Specifically, deep drawing of a cylindrical cup simulations from alloy AA6022-T4 sheets are carried out using a physically based elasto-plastic self-consistent (EPSC) polycrystalline homogenization model embedded in implicit finite elements and verified experimentally. The EPSC model takes into account the evolution of microstructure and directionality of deformation mechanisms acting at the single-crystal level in predicting material behavior. It is calibrated and validated as a standalone model using flow stress and R-ratio data as well as iso-shear contours measured along several directions of the sheet through uniaxial and plane strain tension experiments. Furthermore, the particularities pertaining to cyclic response including non-linear unloading and the Bauschinger effect are also calibrated through large strain tension-compression data. Consistent with experimental measurements, the process simulations in finite elements predict directionally dependent thinning of the cup, especially around the punch radius and variation in the cup height around the rim of the cup, referred to as earing. By comparing experiments and predictions, role of the R-ratio is revealed as critical for the accurate prediction of the cup height. Further sensitivity analysis shows that initial texture has a strong influence on the R-ratio, while introducing a minor effect on hardening. The analysis into the choice of finite element types in terms of their accuracy and efficiency shows that the 3D 8 nodal elements (C3D8R) and continuum shell 3D 8 nodal elements (SC8R) are superior over the planar shell 3D 4 nodal elements (S4R) with the former being the most accurate and the latter being computationally efficient. It is demonstrated that the simulation framework presented in this paper can be used to predict phenomena pertaining to material behavior and resulting geo

关键词： Microstructures Crystal plasticity Anisotropic material numerical algorithms AA6022-T4

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On-line performance optimisation of aero engine control system

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AUTOMATICA 2003年第12期39卷 2115-2121页

作者： Lyantsev, OD Breikin, TV Kulikov, GG Arkov, VY Univ Sheffield Dept Automat Control & Syst Engn Sheffield S1 3JD S Yorkshire England Ufa State Aviat Tech Univ Dept Automat Control Syst Ufa 450000 Russia

This paper is focused on on-line performance optimisation of gas turbine engine control systems. Practical problems of optimal engine control design and implementation are considered. An algorithm for on-line resolution of the engine control optimisation problem is proposed. The example of turbo-jet engine on-line specific fuel consumption minimisation is presented. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： aero engine optimal control on-line performance optimisation numerical algorithms

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Influence of anisotropic elasticity on the mechanical properties of fivefold twinned nanowires

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2015年 84卷 358-379页

作者： Niekiel, Florian Spiecker, Erdmann Bitzek, Erik Univ Erlangen Nurnberg Dept Mat Sci & Engn D-91058 Erlangen Germany

Previous atomistic simulations and experiments have shown an increased Young's modulus and yield strength of fivefold twinned (FT) face-centered cubic metal nanowires (NWs) when compared to single crystalline (SC) NWs of the same orientation. Here we report the results of atomistic simulations of SC and FT Ag, Al, Au, Cu and Ni NWs with diameters between 2 and 50 nm under tension and compression. The simulations show that the differences in Young's modulus between SC and FT NWs are correlated with the elastic anisotropy of the metal, with Al showing a decreased Young's modulus. We develop a simple analytical model based on disclination theory and constraint anisotropic elasticity to explain the trend in the difference of Young's modulus between SC and FT NWs. Taking into account the role of surface stresses and the elastic properties of twin boundaries allows to account for the observed size effect in Young's modulus. The model furthermore explains the different relative yield strengths in tension and compression as well as the material and loading dependent failure mechanisms in FTNWs. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Fivefold twinning numerical algorithms Anisotropic material Microstructures Strengthening and mechanisms

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