• Structural Engineering and Mechanics
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• v.52 no.5
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• pp.1051-1067
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• 2014

The structures of concern in this study are subject to two types of forces: dead loads from the acceleration imposed on the structures as well as the installed operation machines and the additional adjustable forces. We wish to determine the critical values of the adjustable forces when buckling of the structures occurs. The mathematical statement of such a problem gives rise to a constrained eigenvalue problem (CEVP) in which the dominant eigenvalue is subject to an equality constraint. A numerical algorithm for solving the CEVP is proposed in which an iterative method is employed to identify an interval embracing the target eigenvalue. The algorithm is applied to four engineering application examples finding the critical loads of a fixed-free beam subject to its own body force, two plane structures and one wide-flange beam using shell elements when acceleration force is present. The accuracy is demonstrated using the first example whose classical solution exists. The significance of the equality constraint in the EVP is shown by comparing the solutions without the constraint on the eigenvalue. Effectiveness and accuracy of the numerical algorithm are presented.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.376-382
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• 1991

In the analysis of constrained holonomic systems, the Lagange multiplier method yields a system of second-order ordinary differential equations of motion and algebraic constraint equations. Conventional holonomic or nonholonomic constraints are defined as geometric constraints in this paper. Previous works concentrate on the geometric constraints. However, if the total energy of a dynamic system can be computed from the initial energy plus the time integral of the energy input rate due to external or internal forces, then the total energy can be artificially treated as a constraint. The violation of the total energy constraint due to numerical errors can be used as information to control these errors. It is a necessary condition for accurate simulation that both geometric and energy constraints be satisfied. When geometric constraint control is combined with energy constraint control, numerical simulation of a constrained dynamic system becomes more accurate. A new convenient and effective method to implement energy constraint control in numerical simulation is developed based on the geometric interpretation of the relation between constraints in the phase space. Several combinations of energy constraint control with either Baumgarte's Constraint Violation Stabilization Method (CVSM) are also addressed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.8 s.239
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• pp.1123-1131
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• 2005

In this paper, a formulation for a spatial sliding joint, which a general multibody can move along a very flexible cable, is derived using absolute nodal coordinates and non-generalized coordinate. The large deformable motion of a spatial cable is presented using absolute nodal coordinate formulation, which is based on the finite element procedures and the general continuum mechanics theory to represent the elastic forces. And the non-generalized coordinate, which is neither related to the inertia forces nor external forces, is used to describe an arbitrary position along the centerline of a very flexible cable. In the constraint equation for the sliding joint, since three constraint equations are imposed and one non-generalized coordinate is introduced, one constraint equation is systematically eliminated. Therefore, there are two independent Lagrange multipliers in the final system equations of motion associated with the sliding joint. The development of this sliding joint is important to analyze many mechanical systems such as pulley systems and pantograph/catenary systems for high speed-trains.

• Proceedings of the Korea Concrete Institute Conference
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• 2006.05a
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• pp.346-349
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• 2006

Superstructure of reinforced concrete bridges are shortened or elongated due to creep, drying shrinkage, temperature and so on. Most of bridge superstructures are free to shortening and elongation without constraint and stresses will not be induced by creep, drying shrinkage and temperature. But if bridge superstructure are constraint due to wrong setting and functional defects of bridge bearing, very large constraint forces can be induced. In this study, PSCI-Beam by tilt-constructed with constraint and deviation of bearings are presented and the effects of time-dependent constraint stress and temperature loads are investigated.

• Wind and Structures
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• v.25 no.5
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• pp.493-506
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• 2017

Wind-induced response behavior of long-span roof structures is very complicated, showing significant contributions of multiple vibration modes. The largest load effects in a huge number of members should be considered for the sake of the equivalent static wind loads (ESWLs). Studies on essential matters and necessary conditions of the universal ESWLs are discussed. An efficient method for universal ESWLs on long-span roof structures is proposed. The generalized resuming forces including both the external wind loads and inertial forces are defined. Then, the universal ESWLs are given by a combination of eigenmodes calculated by proper orthogonal decomposition (POD) analysis. Firstly, the least squares method is applied to a matrix of eigenmodes by using the influence function. Then, the universal ESWLs distribution is obtained which reproduces the largest load effects simultaneously. Secondly, by choosing the eigenmodes of generalized resuming forces as the basic loading distribution vectors, this method becomes efficient. Meanwhile, by using the constraint equations, the universal ESWLs becomes reasonable. Finally, reproduced largest load effects by load-response-correlation (LRC) ESWLs and universal ESWLs are compared with the actual largest load effects obtained by the time domain response analysis for a long-span roof structure. The results demonstrate the feasibility and usefulness of the proposed universal ESWLs method.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.7
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• pp.595-601
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• 2015

This paper presents an unified chassis control with electronic stability control (ESC) and active front steering (AFS) under lateral force constraint on AFS. When generating the control yaw moment, an optimization problem is formulated in order to determine the tire forces, generated by ESC and AFS. With Karush-Kuhn-Tucker optimality condition, the optimum tire forces can be algebraically calculated. On low friction road, the lateral force in front wheels is easily saturation. When saturated, AFS cannot generate the required control yaw moment. To cope with this problem, new constraint on the lateral tire force is added into the original optimization problem. To check the effectiveness of the propose method, simulation is performed on the vehicle simulation package, CarSim.

• Journal of Navigation and Port Research
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• v.27 no.4
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• pp.397-402
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• 2003

Generally, container arrangement has been carried out based on the Classification guidelines. However, guidelines provide only container securing forces for the given container arrangement and Classification requirements of the forces. In order to design container arrangement additional information is needed such as container securing forces and arrangement that accounts for lashing bridges, vertical lashing, vertical center of gravity (VCG), and maximum stack weight. Trial and error method using the existing guidelines requires excessive amount of calculation time and cannot provide accurate results of the calculations. In order to fulfill this need, a new container securing system has been established based on the equilibrium conditions that include lashing bridges and vertical lashing. An optimization algorithm has been developed for the new system since current optimization methods such as genetic algorithms and evolution strategies are unsuitable for the container securing problems, which involve equality constraint. Design variables are container weights of tier and objective function is either total container weight or VCG of a stack. The newly developed system provides optimum arrangement of containers for both maximum stack weight and maximum VCG. It also greatly reduces time for designing container arrangement.

• Journal of Mechanical Science and Technology
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• v.19 no.3
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• pp.731-742
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• 2005

A magnetic bearing even with multiple coil failure can produce the same decoupled magnetic forces as those before failure if the remaining coil currents are properly redistributed. This fault-tolerant, force invariance control can be achieved with simply replacing the distribution matrix with the appropriate one shortly after coils fail, without modifying feedback control law. The distribution gain matrix that satisfies the necessary constraint conditions of decoupling linearized magnetic forces is determined with the Lagrange Multiplier optimization method.

• The Journal of Korean Association of Computer Education
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• v.8 no.1
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• pp.73-80
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• 2005

To achieve a natural and plausible interaction with deformable objects and to setup the desirable initial conditions of simulation, user should be able to define and control the geometric constraints intuitively. In addition, user should be able to utilize the simulation as a problem solving platform by experimenting various simulation situations without major modification of the simulator. The proposed physically based geometric constraint simulation system solves the problem using a non-linear finite element method approach to represent deformable objects and constraint forces are generated by defining geometric constraints on the nodes of the object to maintain the restriction. It allows user to define and modify geometric constraints and an algorithm converts these geometric constraints into constraint forces which seamlessly integrate controllability to the simulation system. Simulator can handle linear, angular, inequality based geometric constraints on the objects. Our experimental results show that constraints are maintained in the tight error bound and preserve desired shape of deformable object during the entire simulation.

• Journal of Mechanical Science and Technology
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• v.16 no.8
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• pp.1072-1078
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• 2002

The constrained motion requires the determination of constraint force acting on unconstrained systems for satisfying given constraints. Most of the methods to decide the force depend on numerical approaches such that the Lagrange multiplier method, and the other methods need vector analysis or complicated intermediate process. In 1992, Udwadia and Kalaba presented the generalized inverse method to describe the constrained motion as well as to calculate the constraint force. The generalized inverse method has the advantages which do not require any linearization process for the control of nonlinear systems and can explicitly describe the motion of holonomically and/or nongolonomically constrained systems. In this paper, an explicit equation to describe the constrained motion is derived by minimizing the performance index, which is a function of constraint force vector, with respect to the constraint force. At this time, it is shown that the positive-definite weighting matrix in the performance index must be the inverse of mass matrix on the basis of the Gauss's principle and the derived differential equation coincides with the generalized inverse method. The effectiveness of this method is illustrated by means of two numerical applications.