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An improved, fully symmetric, finite-strain phenomenological constitutive model for shape memory alloys

FINITE ELEMENTS IN ANALYSIS AND DESIGN 2011年第2期47卷 166-174页

作者： Arghavani, J. Auricchio, F. Naghdabadi, R. Reali, A. Univ Pavia Dipartimento Meccan Strutturale I-27100 Pavia Italy Sharif Univ Technol Dept Mech Engn Tehran 111559567 Iran IUSS CeSNA Pavia Italy European Ctr Training & Res Earthquake Engn EUCEN Pavia Italy Sharif Univ Technol Inst Nanosci & Technol Tehran 111559567 Iran

The ever increasing number of shape memory alloy applications has motivated the development of appropriate constitutive models taking into account large rotations and moderate or finite strains. Up to now proposed finite-strain constitutive models usually contain an asymmetric tensor in the definition of the limit (yield) function. To this end, in the present work, we propose an improved alternative constitutive model in which all quantities are symmetric. To conserve the volume during inelastic deformation, an exponential mapping is used to arrive at the time-discrete form of the evolution equation. Such a symmetric model simplifies the constitutive relations and as a result of less nonlinearity in the equations to be solved, numerical efficiency increases. Implementing the proposed constitutive model with in a user-defined subroutine UMAT in the nonlinear finite element software ABAQUS/Standard, we solve different boundary value problems. Comparing the solution CPU times for symmetric and asymmetric cases, we show the effectiveness of the proposed constitutive model as well as of the solution algorithm. The presented procedure can also be used for other finite-strain constitutive models in plasticity and shape memory alloy constitutive modeling. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Shape memory alloys Finite strain solution algorithm Finite element Exponential mapping UMAT

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DYNAMIC UNSTRUCTURED METHOD FOR FLOWS PAST MULTIPLE OBJECTS IN RELATIVE MOTION

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AIAA JOURNAL 1995年第4期33卷 641-649页

作者： SINGH, KP NEWMAN, JC BAYSAL, O OLD DOMINION UNIV DEPT AEROSP ENGNNORFOLKVA 23529

A new methodology is developed to simulate unsteady hows about objects in relative motion and compute the trajectory of their motion as determined by this flowfield. The method couples the quid dynamics and rigid-body dynamics equations to capture the time-dependent interference between stationary and moving boundaries. The unsteady, compressible, inviscid (Euler) equations are solved on dynamic unstructured grids by an explicit, finite-volume, upwind method. For efficiency, the grid adaptation is perfomed within a window around the moving object. The Eulerian equations of the rigid-body dynamics are solved by a Runge-Kutta method in a noninertial frame of reference. This dynamic, unstructured flow solver is validated by computing the flow past a sinusoidally pitching airfoil and comparing these results with, the experimental data. The trajectory code is tested by computing the six-degree-of-freedom trajectory of a store separating from a wing using the experimentally determined force and moment fields, then comparing with the experimental trajectory. Finally, the overall methodology is used for two two-dimensional examples: the flow past a pitching and plunging airfoil, and the free fall of a store after separation from a wing section.

关键词： Pitching Airfoil Unsteady Flows Conservation of Mass Three Degrees of Freedom Unstructured Grid Runge Kutta Methods Computing Angle of Attack Freestream Mach Number solution algorithm

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Entry Trajectory Optimization by Second-Order Cone Programming

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2016年第2期39卷 227-241页

作者： Liu, Xinfu Shen, Zuojun Lu, Ping Beihang Univ Sch Aeronaut Sci & Engn Beijing 100191 Peoples R China Iowa State Univ Dept Aerosp Engn Ames IA 50011 USA

Convex optimization has found wide applications in recent years due to its unique theoretical advantages and the polynomial-time complexity of state-of-the-art solution algorithms for convex programming. This paper represents an attempt to apply second-order cone programming, a branch of convex optimization, to the class of highly nonlinear trajectory optimization problems in entry flight. The foremost challenge in applying convex optimization in most aerospace engineering problems lies in the nonlinearity and nonconvexity of the problem. Exclusive reliance on linearization does not always work well, as is the case in entry trajectory optimization. This paper focuses on how to formulate realistic, highly constrained entry trajectory optimization problems in a fashion suitable to be solved by second-order cone programming with a combination of successive linearization and relaxation techniques. Rigorous analysis is conducted to support the soundness of the approach. Numerical demonstrations are provided to show the efficacy and effectiveness of the proposed method.

关键词： Pseudospectral Optimal Control Nonlinear Programming Aerospace Engineering solution algorithm Aerodynamic Force Dynamic Pressure Angle of Attack Flight Path Angle Earth Three Degrees of Freedom

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SOLID ROCKET MOTOR GRAIN BURNBACK ANALYSIS USING ADAPTIVE GRIDS

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JOURNAL OF PROPULSION AND POWER 1995年第5期11卷 1006-1011页

作者： HEJL, RJ HEISTER, SD Purdue University West Lafayette Indiana 47907

This article describes a solid racket motor ballistics tool capable of calculating burning surface area progressions in either axisymmetric or two-dimensional grains using adaptive gridding techniques. The main advantages of this tool are its ease of use and generalized capabilities in handling spatially dependent burning rate information. The solution algorithm determines optimal locations for the number of grain surface points desired by utilizing weighting factors. Wall proximity, surface curvature, and spatial burning rate variations are considered in assigning the value of this weighting factor.

关键词： Solid Rocket Motor Burning Rate Propellant Burn Rate Ballistics Chamber Pressure solution algorithm Solid Propellant Rocket Surface Modeling Rocket Propulsion Computer Programs

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CALCULATION OF INCOMPRESSIBLE ROUGH-WALL BOUNDARY-LAYER FLOWS

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AIAA JOURNAL 1978年第7期16卷 730-735页

作者： CEBECI, T CHANG, KC California State University at Long Beach Long Beach Calif.

The algebraic eddy viscosity model of Cebeci and Smith has been modified to account for wall roughness by incorporating a suggestion of Rotta. The boundary-layer equations are solved, with this model, by the accurate and efficient Keller Box scheme for a wide variety of experimental configurations. These include adverse, zero and favorable pressure gradients, and roughness elements that approach the upper limits of Rotta's model. Comparison of calculated and measured values of skin friction and integral thickness confirms the applicability of the procedure for all cases presented.

关键词： Boundary Layer Equations Kinematic Viscosity Skin Friction Coefficient Nonequilibrium Flows Adverse Pressure Gradient Freestream Conditions Shear Stress solution algorithm Surface Roughness Turbulence Models

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Differential Aerodynamic Force-Based Formation Control of Nanosatellites Using Yaw Angle Deviation

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2021年第12期44卷 2199-2213页

作者： Hu, Yuandong Lu, Zhengliang Liao, Wenhe Zhang, Xiang Nanjing Univ Sci & Technol Sch Mech Engn Nanjing 210094 Peoples R China

This paper investigates a formation control technique for low-Earth-orbit nanosatellites based on the differential aerodynamic drag and lift. An innovative method of using only the yaw angle deviation, instead of the three-axis attitude rotation, is proposed to simultaneously control the in-plane and out-of-plane relative motions. This method can be used for the formation control of the Earth-pointing satellite. A control scheme consisting of four steps is designed considering complex input constraints. In this scheme, two control inputs are defined based on the predicted atmospheric density, and the explicit expressions of their time-varying feasible regions are analyzed. To obtain the yaw angle of each nanosatellite, a yaw angle solution algorithm based on the grid interpolation method is designed with online solving nonlinear optimization avoided. A dynamic surface control algorithm based on the hyperbolic tangent function and a linear model predictive control algorithm are, respectively, used to limit two control inputs within their feasible regions. In addition, a nonlinear finite-time disturbance observer is used to track the total system disturbance. Numerical simulations are carried out for along-track and circular formations, in which the uncertainties of aerodynamic forces, the attitude dynamics, and the unknown perturbation are taken into account.

关键词： Aerodynamic Coefficients Yaw Satellite Formation solution algorithm Atmospheric Environment Earth Model Predictive Control Numerical Simulation Attitude Dynamics Aerodynamic Performance

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Equivalent nonlinear potential systems: Review of previous assumptions

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PROBABILISTIC ENGINEERING MECHANICS 2010年第1期25卷 142-152页

作者： Floris, Claudio Politecn Milan Dept Struct Engn I-20133 Milan Italy

Few exact solutions for the response of stochastic dynamical systems are available. Thus, the methods of the equivalent linearization and of the equivalent nonlinear system are often used. While the former yields a Gaussian response to a Gaussian excitation, the latter gives a non-Gaussian response, which is nearer to the exact unknown response of a nonlinear system. Among the equivalent nonlinear system methods the one based on the replacement of the actual dynamic system by means of a potential system is promising, Cavaleri and Di Paola (2000) 1411, as it leads to a fixed procedure differently from other methods. The procedure is developed under the assumption that the ratio of the moments E[Lambda(j)(X) over dot(2) and E [Lambda(j+1)] is a constant alpha not depending on j, A being the mechanical energy of the oscillator and (X) over dot its velocity. This relationship is demonstrated only for the so called Robert's oscillator, that is an oscillator with restoring force g(X) = omega(0) sgn(X) . |X|(nu), but in the above mentioned reference it is argued that it is valid in general. In this paper, numerical analyses are presented to ascertain its validity in order to apply the method to systems with different restoring forces. It is found that in some cases it is true, some others are doubtful, while there are cases in which alpha clearly depends on j. The effects of considering alpha constant when it is not are ascertained for a Duffing oscillator with linear plus cubic damping. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Stochastic dynamics Nonlinear systems Equivalent nonlinear system Potential systems solution algorithm

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A study of mixed discrete bilevel programs using semidefinite and semi-infinite programming

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OPERATIONS RESEARCH LETTERS 2023年第1期51卷 84-91页

作者： Kue, Floriane Mefo Dempe, Stephan Univ Yaounde I Higher Training Coll Dept Math POB 812 Yaounde Cameroon AIMS Cameroon Res Ctr POB 608 Limbe Cameroon TU Bergakad Freiberg Dept Math & Comp Sci Akad str 6 D-09596 Freiberg Germany

In this paper, we study the bilevel programming problem with discrete polynomial lower level problem. We start by transforming the problem into a bilevel problem comprising a semidefinite program (SDP for short) in the lower level problem. Then, we are able to deduce some conditions of existence of solutions for the original problem. After that, we again change the bilevel problem with SDP in the lower level problem into a semi-infinite program. With the aid of the exchange technique, for simple bilevel programs, an algorithm for computing a global optimal solution is suggested, the convergence is shown, and a numerical example is given.(c) 2022 Elsevier B.V. All rights reserved.

关键词： Bilevel programming Semidefinite programming Semi -infinite programming solution algorithm

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Coupled ordinates method for multigrid acceleration of radiation calculations

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JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER 1999年第4期13卷 467-473页

作者： Mathur, SR Murthy, JY Fluent Inc Lebanon NH 03766 USA Carnegie Mellon Univ Dept Mech Engn Pittsburgh PA 15213 USA

The finite volume and discrete ordinates methods are known to converge increasingly slowly as the optical thickness is increased. This is a result of the sequential nature of the solution procedure;the equations for energy and the directional intensities are solved one by one, assuming prevailing values for other variables. The coupled ordinates method is proposed whereby the discrete energy and intensity equations at each cell are solved simultaneously assuming spatial neighbors to be known. The point-coupled procedure is used as a relaxation sweep in a multigrid scheme. The formulation of coarse-level discrete equations admits arbitrary nonconvex polyhedra, making the scheme suitable for use with arbitrary unstructured polyhedral meshes. The scheme is shown to substantially accelerate convergence over a range of optical thicknesses.

关键词： Optical Thickness Energy Intensity Aspect Ratio Radiative Transfer Thermal Conductivity Numerical Integration Convection Radiation Heat Transfer solution algorithm Unstructured Grid

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HELICOPTER ROTOR BLADE AEROELASTICITY IN FORWARD FLIGHT WITH AN IMPLICIT STRUCTURAL FORMULATION

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AIAA JOURNAL 1992年第9期30卷 2274-2282页

作者： CELI, R University of Maryland College Park Maryland 20742

This paper describes an aeroelastic stability and response analysis in which the structural operator is formulated numerically, without expanding analytically the various algebraic expressions that make up the beam model. No ordering schemes need to be invoked to simplify the algebraic manipulations, and the various components of the mathematical model of the beam can be implemented and modified independently. The formulation is compatible with most solution algorithms. Two different implicit formulations are presented. The results of four illustrative examples are also presented. The first focuses on the effects of higher order kinematic nonlinearities on the aeroelastic stability and response of a hingeless rotor blade. The remaining three show how to introduce, using the implicit formulation, a nonlinear stress-strain relation in table look-up form, a composite cross section, and cross-sectional warping. Aeroelastic stability results are presented for all examples.

关键词： Aeroelastic Stability Helicopter Rotor Bernoulli Euler Beams Stress Strain Curve Hingeless Rotor Blade Composite Materials Mathematical Models Rotary Wing Elastic Deformation solution algorithm

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