• 대한기계학회논문집A
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• 제24권7호
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• pp.1878-1884
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• 2000

In multibody dynamic analysis, one of the most important problems is to reduce computation times for real time simulation. In this paper, a symbolic computation method is implemented and tested for each dynamic analysis step. Applying symbolic formulations to the vehicle dynamics program AutoDyn7, the effectiveness of the symbolic computation method is verified.

• Structural Engineering and Mechanics
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• 제27권6호
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• pp.713-739
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• 2007

Nowadays computers can perform symbolic computations in addition to mere number crunching operations for which they were originally designed. Symbolic computation opens up exciting possibilities in Structural Mechanics and engineering. Classical areas have been increasingly neglected due to the advent of computers as well as general purpose finite element software. But now, classical analysis has reemerged as an attractive computer option due to the capabilities of symbolic computation. The repetitive cycles of simultaneous - equation sets required by the finite element technique can be eliminated by solving a single set in symbolic form, thus generating a truly closed-form solution. This consequently saves in data preparation, storage and execution time. The power of Symbolic computation is demonstrated by six examples by applying symbolic computation 1) to solve coupled shear wall 2) to generate beam element matrices 3) to find the natural frequency of a shear frame using transfer matrix method 4) to find the stresses of a plate subjected to in-plane loading using Levy's approach 5) to draw the influence surface for deflection of an isotropic plate simply supported on all sides 6) to get dynamic equilibrium equations from Lagrange equation. This paper also presents yet another computationally efficient and accurate numerical method which is based on the concept of derivative of a function expressed as a weighted linear sum of the function values at all the mesh points. Again this method is applied to solve the problems of 1) coupled shear wall 2) lateral buckling of thin-walled beams due to moment gradient 3) buckling of a column and 4) static and buckling analysis of circular plates of uniform or non-uniform thickness. The numerical results obtained are compared with those available in existing literature in order to verify their accuracy.

• Journal of Mechanical Science and Technology
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• 제19권spc1호
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• pp.395-402
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• 2005

This paper deals with modeling and computer simulation of a full multibody vehicle model for a driving simulator. The multibody vehicle model is based on the recursive formulation and a corresponding simulation code is generated automatically from AUTOCODE, which is a symbolic computation package developed by the authors using MAPLE. The paper describes a procedure for automatically generating a highly efficient simulation code for the full vehicle model, while incorporating realistically modeled components. The following issues have been accounted for in the procedure, including software design for representing a mechanical system in symbolic form as a set of computer data objects, a multibody formulation for systems with various types of connections between bodies, automatic manipulation of symbolic expressions in the multibody formulation, interface design for allowing users to describe unconventional force-and torque-producing components, and a method for accommodating external computer subroutines that may have already been developed. The effectiveness and efficiency of the proposed method have been demonstrated by the simulation code developed and implemented for driving simulation.

• 대한기계학회논문집
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• 제17권6호
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• pp.1509-1517
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• 1993

본 연구에서는 3차원 운동을 하는 다물체 기구가 물체 수와 조인트 연결상태 만 주어진 상태에서 구성상태에 따라 절점 좌표계를 이용하여 모델링하고 MACSYMA를 써서 복잡단조로운 대수 계산을 하여 모든 운동학적 정보를 얻어내며 수치계산이 필요 하면 별도의 프로그램을 이용 수치해석을 하는 과정을 밟는다.

• 대한기계학회논문집A
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• 제33권12호
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• pp.1433-1441
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• 2009

In multibody dynamic analysis, one of the most important problems is to reduce computation times for real-time simulation. This paper presents the derivation procedure of equations of motion of a 6${\times}$6 autonomous vehicle in terms of chassis local coordinates which do not require coordinates transformation matrix to enhance efficiency for real-time dynamic analysis. Also, equations of motion are derived using the VT(velocity transformation) technique and symbolic computation method coded by MATLAB. The Jacobian matrix of the equations of motion of a system is derived from symbolic operations to apply the implicit integration method. The analysis results were compared with ADAMS results to verify the accuracy and approve the feasibility of real time analysis.

• 한국정밀공학회지
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• 제16권4호통권97호
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• pp.26-36
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• 1999

A general procedure for determining the optimum location of suspension hard points with respect to kinematic design parametes is presented. Suspensions are modeled as connection of rigid bodies by ideal kinematic joints. Constraint equations of the kinematic joints are expressed in terms of the generalized coordinates and hard points. By directly differentiating the constraint equations with respect to the hard points, kinematic sencitivity equations are obtained. In order to cope with algebraic complexity associated with the differentiation process, a symbolic computation technique is used. A performance index is defined in terms of static design parameters such as camber, caster, toe, ect.. Gradient of the performance index can be analytically computed from the kinematic sensitivity equations. Optimization results show the effectiveness and validity of the procedure, which is applicable to any type of suspension if its kinematic configurations are given.

• 한국자동차공학회논문집
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• 제4권6호
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• pp.247-259
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• 1996

Kinematic design sensitivity analysis for vehicle in suspension systems design is performed. Suspension systems are modeled using composite joins to reduce the number of the constraint equations. This allows a semi-analytical approach that is computerized symbolic manipulation before numerical computations and that may compensate for their drawbacks. All the constraint equations including design variables are derived in symbolic equations for sensitivity analysis. By directly differentiating the equations with respect to design variables, sensitivity equations are obtained. Since the proposed method only requires the hard point data, sensitivity analysis is possible in suspension design stage.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제6권5호
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• pp.1463-1478
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• 2012

Based on the theory of local-world network, the composition self-similarity (CSS) of network traffic is presented for the first time in this paper for the study of DoS detection. We propose the concept of composition distribution graph and design the relative operations. The $(R/S)^d$ algorithm is designed for calculating the Hurst parameter. Based on composition distribution graph and Kullback Leibler (KL) divergence, we propose the composition self-similarity anomaly detection (CSSD) method for the detection of DoS attacks. We evaluate the effectiveness of the proposed method. Compared to other entropy based anomaly detection methods, our method is more accurate and with higher sensitivity in the detection of DoS attacks.

• 한국항공운항학회지
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• 제23권2호
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• pp.69-74
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• 2015

We propose a rigorous and practical methodology to evaluate the performance of symbolic manipulation program such as Mathematica, Maple, and Maxima. First, we demonstrate an inverse method to construct the benchmark problems of an initial value problems. The benchmark problems associated with the discrete version of the Chebyshev polynomials provide a rigorous and objective measure to evaluate the performance of symbolic manipulation programs. We compare three symbolic manipulation programs, which are Mathematica, Maple and Maxima, using this methodology. The computation time, the used memory and the perturbation terms are chosen for comparison parameters.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.81-94
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• 2007

In this paper we investigate symbolic implementation of two modifications of the Leverrier-Faddeev algorithm, which are applicable in computation of the Moore-Penrose and the Drazin inverse of rational matrices. We introduce an algorithm for computation of the Drazin inverse of rational matrices. This algorithm represents an extension of the papers [11] and [14]. and a continuation of the papers [15, 16]. The symbolic implementation of these algorithms in the package MATHEMATICA is developed. A few matrix equations are solved by means of the Drazin inverse and the Moore-Penrose inverse of rational matrices.