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Finite element method for viscoelastic medium with damage and the application to structural analysis of solid rocket motor grain

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Science China(Physics,Mechanics & Astronomy) 2014年第5期57卷 908-915页

作者： DENG Bin SHEN ZhiBin DUAN JingBo TANG GuoJin College of Aerospace Science and Engineering National University of Defense Technology

This paper studies the damage-viscoelastic behavior of composite solid propellants of solid rocket motors(SRM).Based on viscoelastic theories and strain equivalent hypothesis in damage mechanics,a three-dimensional(3-D)nonlinear viscoelastic constitutive model incorporating with damage is *** resulting viscoelastic constitutive equations are numerically discretized by integration algorithm,and a stress-updating method is presented by solving nonlinear equations according to the Newton-Raphson method.A material subroutine of stress-updating is made up and embedded into commercial code of *** material subroutine is validated through typical *** results indicate that the finite element results are in good agreement with the analytical ones and have high accuracy,and the suggested method and designed subroutine are efficient and can be further applied to damage-coupling structural analysis of practical SRM grain.

关键词： composite solid propellant viscoelasticity with damage f'mite element method integration algorithm stress-updatingmethod

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Review of attitude representations used for aircraft kinematics

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JOURNAL OF AIRCRAFT 2001年第4期38卷 718-737页

作者： Phillips, WF Hailey, CE Gebert, GA Utah State Univ Dept Mech & Aerosp Engn Logan UT 84322 USA Sverdrup Technol Inc Eglin AFB FL 32542 USA

A detailed survey is presented of the literature on attitude representation dating from the early work of Euler and Hamilton to recent publications in fields such as navigation and control. The scope is limited to the development of the aircraft kinematic transformation equations in terms of four different attitude representations, including the well-known Enter angles, the Euler-axis rotation parameters, the direction cosines, and the Euler-Rodrigues quaternion. The emphasis is directed at the application of the quaternion formulation to aircraft kinematics. Results are presented that reinforce observations that the quaternion formulation, typically implemented to eliminate singularities associated with the Enter angle formulation, is far superior to the other commonly used formulations based on computational efficiency alone. A development of quaternion constraints necessary to independently constrain roll, pitch, yaw, bank angle, elevation angle, and/or azimuth angle is presented. For verification of simulation codes, a general closed-form solution to the quaternion formulation, for the case of constant rotation, is also presented. Additionally, a discussion is provided of numerical integration methods and numerical errors for the quaternion formulation. This discussion is especially important for simulations that may still utilize a common error reduction scheme originally developed for analog computers.

关键词： Aircraft Kinematics Quaternions Angular Motion Aerodynamic Moments Earth Numerical integration Pilot Airspeed integration algorithm Numerical algorithms

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GENERALIZED TECHNIQUE FOR INVERSE SIMULATION APPLIED TO AIRCRAFT MANEUVERS

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1991年第5期14卷 920-926页

作者： HESS, RA GAO, C WANG, SH UNIV CALIF DAVIS DEPT ELECT ENGN & COMP SCIDAVISCA 95616

Inverse simulation techniques are computational methods that determine the control inputs to a dynamic system that produce desired system outputs. Such techniques can be powerful tools for the analysis of problems associated with maneuvering flight. An algorithm is developed that serves as an efficient inverse simulation tool for analyzing maneuvering flight. As opposed to current inverse simulation methods, which require numerical time differentiation in their implementation, the generalized technique offered is essentially an integration algorithm. Examples of inverse solutions for a large-amplitude aircraft maneuver and a nap-of-the-Earth helicopter maneuver are presented.

关键词： Aircraft Maneuvers Helicopters Computational Methods Earth integration algorithm Stability and Control Augmentation System Aileron Roll Singular Value Decomposition Inverse Problems Aircraft Flight Control System

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NONLINEAR STRUCTURAL DYNAMIC ANALYSIS USING A MODIFIED MODAL METHOD

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AIAA JOURNAL 1985年第10期23卷 1594-1601页

作者： KNIGHT, NF NASA Langley Research Center Hampton Virginia

A procedure for predicting the nonlinear dynamic response of structural components subjected to a step loading is presented. The procedure is a modified modal method that involves a change of dependent variables from the unknown nodal degrees of freedom of the finite element model of the structure to a smaller set of generalized coordinates. This change of dependent variables uses a combination of the nonlinear static solution and some selected vibration mode shapes. The vibration mode shapes correspond to the eigenvectors obtained by solving a standard free vibration eigenvalue problem wherein the stiffness matrix is expanded about the nonlinear static solution. A strategy is also presented for determining which and how many vibration mode shapes to include in the transformation. The effect of inaccurate representation of the spatial distribution of the applied load on the nonlinear dynamic response is discussed for two classes of structural behavior. Application of the procedure to structures that exhibit a stiffening behavior and to those with a softening behavior is presented. © 1985 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Structural Dynamic Analysis Elastic Modulus Finite Element Modeling Nonlinear Structural Dynamics Spherical Shell Transient Response Free Vibrations integration algorithm Numerical integration Nonlinear Dynamics

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Finite element formulation for modeling nonlinear viscoelastic elastomers

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2008年第51-52期197卷 4702-4717页

作者： Areias, Pedro Matous, Karel Univ Illinois Dept Aerosp Engn Urbana IL 61801 USA

Nonlinear viscoelastic response of reinforced elastomers is modeled using a three-dimensional mixed finite element method with a nonlocal pressure field. A general second-order unconditionally stable exponential integrator based on a diagonal Pade approximation is developed and the Bergstrom-Boyce nonlinear viscoelastic law is employed as a prototype model. An implicit finite element scheme with consistent linearization is used and the novel integrator is successfully implemented. Finally, several viscoelastic examples, including a study of the unit cell for a solid propellant, are solved to demonstrate the computational algorithm and relevant underlying physics. (c) 2008 Elsevier B.V. All rights reserved.

关键词： Stabilized element Implicit gradient integration algorithm Viscoelasticity Propellant unit cell

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On numerical modeling of cyclic elastoplastic response of shell structures

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CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES 2008年第2期26卷 75-90页

作者： Tonkovic, Zdenko Soric, Jurica Skozrit, Ivica Univ Zagreb Fac Mech Engn & Naval Architecture Zagreb 10000 Croatia

An efficient numerical algorithm for modeling of cyclic elastoplastic deformation of shell structures is derived. The constitutive model includes highly nonlinear multi-component forms of kinematic and isotropic hardening functions in conjunction with von Mises yield criterion. Therein, the closest point projection algorithm employing the Reissner-Mindlin type kinematic model, completely formulated in tensor notation, is applied. A consistent elastoplastic tangent modulus ensures high convergence rates in the global iteration approach. The integration algorithm has been implemented into a layered assumed strain isoparametric finite shell element, which is capable of geometrical nonlinearities including finite rotations. Numerical examples, considering the symmetric and nonsymmetric loading controlled tests, illustrate the ratcheting effect and stabilization of the load-displacement response. Accuracy and robustness of the proposed algorithms are demonstrated.

关键词： shell structures finite element analysis cyclic elastoplasticity nonlinear kinematic hardening integration algorithm tensor formulation

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Computing differential equations for integrals associated to smooth Fano polytope

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JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 2013年第2期30卷 307-319页

作者： Nakayama, Hiromasa Takayama, Nobuki Kobe Univ Grad Sch Sci Dept Math Nada Ku Kobe Hyogo 6578501 Japan JST Crest Hibi Team Nada Ku Kobe Hyogo 6578501 Japan

We give an approximation algorithm of computing holonomic systems of linear differential equations for definite integrals of rational functions with parameters. We show that this algorithm gives a correct answer in finite steps, but we have no general stopping condition. We apply the approximation method to find differential equations for integrals associated to smooth Fano polytopes. These are interesting in the study of K3 surfaces and the toric mirror symmetry. In this class of integrals, we can apply Stienstra's rank formula to our algorithm, which gives a stopping condition of the approximation algorithm.

关键词： Grobner Basis D-modules integration algorithm Period map Calabi-Yau variety

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MULTIOBJECTIVE TRAJECTORY OPTIMIZATION BY GOAL PROGRAMMING WITH FUZZY DECISIONS

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1994年第2期17卷 297-303页

作者： SUZUKI, S YOSHIZAWA, T University of Tokyo Bunkyo-ku Tokyo 113 Japan

A sequential goal programming approach is considered for not only well-defined flight trajectory problems but also ill-defined problems that have no feasible solutions satisfying all design requirements due to strict boundary conditions or tight path constraints. By using a time integration algorithm, trajectory optimization problems am transformed into numerical optimization problems that seek optimal control variables at discrete time points to minimize an objective function and satisfy various design constraints. By defining the target goal values of both the constraints and the objective functions and by prioritizing each goal according to its significance, the GP formulation modifies ill-defined problems as multiobjective design problems. Additionally, a fuzzy decision making method is applied for those goals that are prioritized, not precisely, but in a fuzzy manner. Numerical applications for simple ascent trajectory problems show that this method can efficiently find the trajectories when various kinds of design requirements are imposed for the ill-defined problem.

关键词： Trajectory Optimization Flight Trajectory Numerical Optimization integration algorithm Sequential Quadratic Programming Control Optimization Sequential Linear Programming Propellant Finite Difference Method Interplanetary Mission

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An elasto-viscoplastic constitutive model for polymers at finite strains: Formulation and computational aspects

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COMPUTERS & STRUCTURES 2016年 166卷 60-74页

作者： Mirkhalaf, S. M. Andrade Pires, P. M. Simoes, R. Univ Porto Fac Engn Dept Mech Engn Rua Dr Roberto Frias P-4200465 Oporto Portugal Univ Minho Inst Polymers & Composites IPC I3N P-4800058 Guimaraes Portugal Polytech Inst Sch Technol Cavado & AveCampus IPCA P-4750810 Barcelos Portugal

This paper describes a finite strain elasto-viscoplastic constitutive model to predict the non-linear behaviour of polymeric based materials. The theoretical basis of the material model and the computational treatment are presented. The operator split methodology and the Newton-Raphson method are used to derive the state update algorithm and to obtain the numerical solution. The integration algorithm reduces to the solution of only one scalar non-linear equation. A closed formula for the corresponding consistent tangent operator is presented. Different aspects of the constitutive model and its integration algorithm are investigated by considering a comprehensive set of numerical examples. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Polymer Elasto-viscoplastic EGP integration algorithm

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EXTENSION OF STRAPDOWN ATTITUDE algorithm FOR HIGH-FREQUENCY BASE MOTION

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1990年第4期13卷 738-743页

作者： LEE, JG YOON, YJ MARK, JG TAZARTES, DA LITTON SYST INC DIV GUIDANCE & CONTROL SYSTLOS ANGELESCA 91367

In this paper, we have expanded an application of the rotation vector concept to develop an efficient attitude algorithm for a strapdown system under a coning base motion. The proposed algorithm takes four samples of gyroscope data per update. A rotation vector error analysis for a coning motion has been employed to come up with an optimum four-sample algorithm. Also presented is an efficient way to implement the algorithm in a real-time environment. The algorithm is formulated in a recursive form using two time-rate executions and using only integer arithmetic. To compare the performance of the proposed algorithm with an already existing threesample algorithm, a simulation has been performed by varying coning motion frequency and update rate. Results Show that the four-sample algorithm outperforms the three-sample algorithm in case of high-frequency coning motion. The use of the four-sample algorithm is economical since it requires less computing time for an equal accuracy. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Rate Integrating Gyroscope Strapdown System Computing Time Quaternions Inertial Navigation integration algorithm Digital Computers Taylor Series Euler Method

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