• Title/Summary/Keyword: elastic constraints

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Analysis of Valvetrain Dynamics of an Internal Combustion Engine with Elastic Deformation of the Components (부품의 탄성변형을 고려한 내연기관 밸브트레인 동역학 해석)

  • Lee, Ki-Su
    • Transactions of the Korean Society of Automotive Engineers
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    • v.17 no.4
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    • pp.63-71
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    • 2009
  • The elastic effects of the valve train components are analyzed by using the finite element models of the rocker arm and valve. The whole equations of motion of the valvetrain of an internal combustion engine formulated by finite element techniques are solved by imposing the contact conditions with the augmented Lagrange multiplier method. The velocity and acceleration constraints as well as the displacement constraints are imposed on the contact points. The numerical simulations show that, even if the magnitude of the elastic deformation of the components is very small, it may have large effects on the valvetrain dynamics of a high-speed engine.

Effects of deformation of elastic constraints on free vibration characteristics of cantilever Bernoulli-Euler beams

  • Wang, Tong;He, Tao;Li, Hongjing
    • Structural Engineering and Mechanics
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    • v.59 no.6
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    • pp.1139-1153
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    • 2016
  • Elastic constraints are usually simplified as "spring forces" exerted on beam ends without considering the "spring deformation". The partial differential equation governing the free vibrations of a cantilever Bernoulli-Euler beam considering the deformation of elastic constraints is firstly established, and is nondimensionalized to obtain two dimensionless factors, $k_v$ and $k_r$, describing the effects of elastically vertical and rotational end constraints, respectively. Then the frequency equation for the above Bernoulli-Euler beam model is derived using the method of separation of variables. A numerical analysis method is proposed to solve the transcendental frequency equation for the continuous change of the frequency with $k_v$ and $k_r$. Then the mode shape functions are given. Finally, effects of $k_v$ and $k_r$ on free vibration characteristics of the beam with different slenderness ratios are calculated and analyzed. The results indicate that the effects of $k_v$ are larger on higher-order free vibration characteristics than on lower-order ones, and the impact strength decreases with slenderness ratio. Under a relatively larger slenderness ratio, the effects of $k_v$ can be neglected for the fundamental frequency characteristics, while cannot for higher-order ones. However, the effects of $k_r$ are large on both higher- and lower-order free vibration characteristics, and cannot be neglected no matter the slenderness ratio is large or small.

Analysis of Welding Deformation by Equivalent Load Method on Steel Structures (등가하중법을 이용한 강구조물 용접변형 해석)

  • 박정웅;이재원;이해우
    • Journal of Welding and Joining
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    • v.20 no.3
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    • pp.129-137
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    • 2002
  • This study presents a new method to derive the constraint coefficient from the degree of angular deformation caused by welding, as measured experimentally by varying the shape of welded joints and the magnitude of constraints and from analysis results given by the elastic FEM method. The equivalent load was then calculated with this constraint coefficient. The validity of the numerical analysis involved in this new method was confirmed by its agreement with the experimental results. As for the effects of the constraints based on the shape of the welded joints in the case of Butt welding when the constraint coefficients are not considered, the deformed quantity produced by analysis is larger that produced by experiment and consequently is largely affected by the constraints. However, in the case of Fillet welding, the deformed quantity is seldom affected regardless of constraint coefficient considerations.

Influence of Elastic Constraints at Free End on Stability of Timoshenko Cantilever Beam Subjected to a Follower Force (종동력을 받는 Timoshenko 외팔보에서 자유단의 탄성구속이 안정성에 미치는 영향)

  • 윤한익;손종동;김현수
    • Journal of the Korean Society of Safety
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    • v.11 no.2
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    • pp.116-121
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    • 1996
  • On the stability of Timoshenko cantilever beam subjected to a follower force, the influence of the characteristics of elastic constraints at the free end Is studied. The equations of motion and boundary conditions of this nonconservative elastic system are estabilished by using the Hamilton's principle. Upon evaluation of the stability of this system, the effect of shear deformation and rotatory inertia is considered in calculation. Using cowper's formulae Timoshenko's shear coefficient K'are determined. From this imvestigation it is found that the constrain parameter have an appreciable stabilizing effect in this nonconservative system. Moreover, it is obvious that the small values of K'decrease the flutter load of this system.

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Effect of Mechanical Constraints on the Angular Distortion of Welding Joints (용접 각변형에 미치는 구속도의 영향)

  • Park, Jeong Ung;Lee, Jae Won;Lee, Hae Woo
    • Journal of Korean Society of Steel Construction
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    • v.13 no.5
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    • pp.547-556
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    • 2001
  • This study presents new method in which to derive the constraint coefficient from the quantity of angular deformation by welding measured by varying the shape of welded joints and the magnitude of constraints by varying the shape of welded joints and the magnitude of constraints by experiment and from the result analyzed by elastic FEM method and then to decide equivalent load with it The numerical analysis results by this new method verified the validity by agreeing with the experimental result on specimen. In addition These results are applicable to the prediction of the quantity of welding deformation for large structures regardless of the size and the shape While in the effects of the constraints based on the shape of welded joints in the case of Butt welding when the constraint coefficients are not considered the deformed quantity is produced larger than one by the experiment and consequently is largely affected by the constraints But in the case of Fillet welding the deformed quantity is seldom affected regardless of considering the constraint coefficients or not.

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Using multiple point constraints in finite element analysis of two dimensional contact problems

  • Liu, C.H.;Cheng, I.;Tsai, An-Chi;Wang, Lo-Jung;Hsu, J.Y.
    • Structural Engineering and Mechanics
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    • v.36 no.1
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    • pp.95-110
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    • 2010
  • Two-dimensional elastic contact problems, including normal, tangential, and rolling contacts, are treated with the finite element method in this study. Stress boundary conditions and kinematic conditions are transformed into multiple point constraints for nodal displacements in the finite element method. Upon imposing these constraints into the finite element system equations, the calculated nodal stresses and nodal displacements satisfy stress and displacement contact conditions exactly. Frictional and frictionless contacts between elastically identical as well as elastically dissimilar materials are treated in this study. The contact lengths, sizes of slip and stick regions, the normal and the shear stresses can be found.

Stiffness Analysis of a Low-DOF Parallel Manipulator including the Elastic Deformations of Both Joints and Links (ICCAS 2005)

  • Kim, Han-Sung;Shin, Chang-Rok;Kyung, Jin-Ho;Ha, Young-Ho;Yu, Han-Sik;Shim, Poong-Soo
    • 제어로봇시스템학회:학술대회논문집
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    • 2005.06a
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    • pp.631-637
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    • 2005
  • This paper presents a stiffness analysis method for a low-DOF parallel manipulator, which takes into account of elastic deformations of joints and links. A low-DOF parallel manipulator is defined as a spatial parallel manipulator which has less than six degrees of freedom. Differently from the case of a 6-DOF parallel manipulator, the serial chains in a low-DOF parallel manipulator are subject to constraint forces as well as actuation forces. The reaction forces due to actuations and constraints in each limb can be determined by making use of the theory of reciprocal screws. It is shown that the stiffness model of an F-DOF parallel manipulator consists of F springs related to the reciprocal screws of actuations and 6-F springs related to the reciprocal screws of constraints, which connect the moving platform to the fixed base in parallel. The $6{times}6$ stiffness matrix is derived, which is the sum of the stiffness matrices of actuations and constraints. The six spring constants can be precisely determined by modeling the compliance of joints and links in a serial chain as follows; the link can be considered as an Euler beam and the stiffness matrix of rotational or prismatic joint can be modeled as a $6{times}6$ diagonal matrix, where one diagonal element about the rotation axis or along the sliding direction is zero. By summing the elastic deformations in joints and links, the compliance matrix of a serial chain is obtained. Finally, applying the reciprocal screws to the compliance matrix of a serial chain, the compliance values of springs can be determined. As an example of explaining the procedure, the stiffness of the Tricept parallel manipulator has been analyzed.

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Modal Analysis of Suspension System with Kinematic Constraints and Elastic Elements (기구학적 구속조건과 탄성요소를 가진 현가계의 모드해석)

  • 이장무;강주석;윤중락;배상우;탁태오
    • Transactions of the Korean Society of Automotive Engineers
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    • v.8 no.1
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    • pp.110-123
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    • 2000
  • In this Study, the dynamic equation for vibration analysis of mechanical systems with kinematic constraints is derived. This equations are derived in terms of small displacements of Cartesian coordinates, and are applied to compute the dynamic response and the natural modes of the suspension system of a vehicle. The results are validated through the comparison with the results from conventional nonlinear dynamic analysis and modal test.

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An incremental convex programming model of the elastic frictional contact problems

  • Mohamed, S.A.;Helal, M.M.;Mahmoud, F.F.
    • Structural Engineering and Mechanics
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    • v.23 no.4
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    • pp.431-447
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    • 2006
  • A new incremental finite element model is developed to simulate the frictional contact of elastic bodies. The incremental convex programming method is exploited, in the framework of finite element approach, to recast the variational inequality principle of contact problem in a discretized form. The non-classical friction model of Oden and Pires is adopted, however, the friction effect is represented by an equivalent non-linear stiffness rather than additional constraints. Different parametric studies are worked out to address the versatility of the proposed model.

Analysis of Welding Deformation By Equivalent Load Method on Steel Structures (등가하중법을 이용한 강구조물 용접변형 해석)

  • 박정용;이재원;박길현
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2002.04a
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    • pp.93-98
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    • 2002
  • This study presents a new method to derive the constraint coefficient from the degree of angular deformation caused by welding, as measured experimentally by varying the shape of welded joints and the magnitude of constraints and from analysis results given by the elastic FEM method. The equivalent load was then calculated with this constraint coefficient. The validity of the numerical analysis involved in this new method was confirmed by its agreement with the experimental results. As for the effects of the constraints based on the shape of the welded joints in the case of Butt welding when the constraint coefficients are not considered, the deformed quantity produced by analysis is larger that produced by experiment and consequently is largely affected by the constraints.

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