• Journal of KIBIM
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• v.9 no.3
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• pp.1-7
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• 2019

Digital twin technology has been actively developed to monitor and assess the current state of actual structures. The digital twin changes the traditional observation method performed in the field to the real-time observation and detection system using virtual online model. Thus, this study designed a digital twin model for a beam and examined the feasibility of the digital twin for bridges. To reflect the current state of the bridge, model updating was performed according to the field test data to construct an analysis model. Based on the constructed bridge analysis model, the relationship between strain and displacement was used to represent a virtual model that behaves in the same way as the actual structure. The strain and displacement relationship was expressed as a matrix derived using an approximate analytical theory. Then, displacements can be obtained using the measured data obtained from strain sensors installed on the bridge. The coordinates of the obtained displacements are used to construct a virtual digital model for the bridge. For verification, a beam was fabricated and tested to evaluate the digital twin model constructed in this study. The displacements obtained from the strain and displacement relationship agrees well with the actual displacements of the beam. In addition, the displacements obtained from the virtual model was visualized at the locations of the strain sensor.

• Smart Structures and Systems
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• v.3 no.2
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• pp.147-172
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• 2007

The present paper is concerned with the design of distributed sensors and actuators. Strain type sensors and actuators are considered with their intensity continuously distributed throughout a continuous structure. The sensors measure a weighted average of the strain tensor. As a starting point for their design we introduce the concept of collocated sensors and actuators as well as the so-called natural output. Then we utilize the principle of virtual work for an auxiliary quasi-static problem to assign a mechanical interpretation to the natural output of the sensors to be designed. Therefore, we take the virtual displacements in the principle of virtual work as that part of the displacement in the original problem, which characterizes the deviation from a desired one. We introduce different kinds of distributed sensors, each of them with a mechanical interpretation other than a weighted average of the strain tensor. Additionally, we assign a mechanical interpretation to the collocated actuators as well; for that purpose we use an extended body force analogy. The sensors and actuators are applied to solve the displacement tracking problem for continuous structures; i.e., the problem of enforcing a desired displacement field. We discuss feed forward and feed back control. In the case of feed back control we show that a PD controller can stabilize the continuous system. Finally, a numerical example is presented. A desired deflection of a clamped-clamped beam is tracked by means of feed forward control, feed back control and a combination of the two.

• The Journal of Korea Robotics Society
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• v.15 no.4
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• pp.301-308
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• 2020

In this paper, we deal with the static modeling of a continuum robot that can perform surgical interventions. The proposed continuum robot is made of stainless steel wires and a multi lumen flexible tube using a thermoplastic elastomer. This continuum robot could be most severely deformed in physical contact with narrow external environments, when a lateral external force acts at the distal tip of the continuum robot. In order to predict the shape and displacement under the lateral external force loading, the forward kinematics, the statics modeling, the force-moment equilibrium equation, and the virtual work-energy method of the continuum robot are described. The deflection displacements were calculated using the virtual work-energy method, and the results were compared with the displacement obtained by the conventional cantilever beam theories. In conclusion, the proposed static modeling and the virtual work-energy method can be used in arrhythmia procedure simulations.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.20 no.6
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• pp.703-713
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• 2011

In this study, to minimize trial and error in the design and manufacturing processes of a high-precision large-surface micro-grooving machine which is able to fabricate the molds for 42 inch LCD light guide panels, the effects of the structural deformation of the micro-grooving machine according to the positions of the X-axis, Y-axis and Z-axis feed systems were examined on the tool tip displacement errors associated with the machining accuracy. The virtual prototype (finite element model) of the micro-grooving machine was constructed to include the joint stiffnesses of the hydrostatic bearings, hydrostatic guideways and linear motors, and then the tool tip displacement errors were measured from the virtual prototype. Especially, to establish the prediction model of the tool tip displacement errors, which was constructed using the positions of the X-axis, Y-axis and Z-axis feed systems as independent variables, the response surface method based on the central composite design was introduced. The reliability of the prediction model was verified by the fact that the tool tip displacement errors obtained from the prediction model coincided well those measured from the virtual prototype. And the causes of the tool tip displacement errors were identified through the analysis of interactions between the positions of the X-axis, Y-axis and Z-axis feed systems.

• Geomechanics and Engineering
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• v.19 no.3
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• pp.201-215
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• 2019

A new approach of analyzing the displacements and stress of the surrounding rock for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface is investigated in this study. In the proposed approach, by using a virtual image technique, the shear stress of the vertical ground surface is revised to be zero, and elastic solutions of the surrounding rock are obtained before stress revision. To revise the vertical normal stress and shear stress of horizontal ground surface generated by the combined action of the actual and image sinks, the harmonic functions and corresponding stress function solutions were adopted. Based on the Boussinesq's solutions and integral method, the horizontal normal stress of the vertical ground surface is revised to be zero. Based on the linear superposition principle, the final solution of the displacements and stress were proposed by superimposing the solutions obtained by the virtual image technique and the stress revision on the horizontal and vertical ground surfaces. Furthermore, the ground settlements and lateral displacements of the horizontal and vertical ground surfaces are derived by the proposed approach. The proposed approach was well verified by comparing with the numerical method. The discussion based on the proposed approach in the manuscript shows that smaller horizontal ground settlements will be induced by lower tunnel buried depths and smaller limb distances. The proposed approach for the displacement and stress of the surrounding rocks can provide some practical information about the surrounding rock stability analysis of shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface.

• Proceedings of the KSR Conference
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• 2007.11a
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• pp.107-114
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• 2007

In this paper, the equations of motion by which the natural vibration of rotating thick ring can be analyzed accurately are presented. These equations are derived from the theory of finite deformation and the principle of virtual work. The effects of variation in curvature across the ring cross-section can be considered in these equations. The ring models are called as thick ring model and thin ring model respectively as the effects of variation in curvature are considered or neglected. The radial displacement of ring which is rotating at constant angular velocity is determined by a non-linear equation derived from the principle of virtual work. The equations of the in-plane and out-of-plane vibrations at disturbed state are also formulated from the principle of virtual work. They can be expressed as the combination of the radial displacement at the steady state and the disturbed displacements about the steady state. The natural vibrations of rings with different thickness are analyzed by using the presented ring models and 3-dimensional finite element method to verify accuracy of the presented equations of motion. Its results are compared and discussed.

• Structural Engineering and Mechanics
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• v.33 no.2
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• pp.159-177
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• 2009

The aim of this paper is to give a rigorous framework for the interpretation of limit analysis results including large displacements. The presentation is oriented towards unidimensional media (beams) but two-dimensional (plates) or three-dimensional media are also concerned. A single-degree-of-freedom system is first considered: it shows the basic phenomena of large displacement limit analysis or second-order limit analysis. The results are compared to those of a continuous system and the differences between both systems are discussed. Theoretical results are obtained using the kinematical approach of limit analysis. An admissible load-displacement plane is then defined, according to the yield design theory. The methodology used is applied to frame structures. The presented results are nevertheless different from those already published in the literature, as the virtual displacement field can be distinguished from the displacement field at collapse. The simplicity of large displacement limit analysis makes it attractive for practical engineering applications. The load-displacement upper bound can be used for instance in the optimal design of steel frames in seismic areas.

• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.793-807
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• 2015

Constructing the influence lines of forces of statically indeterminate structures is a traditional issue in structural engineering and mechanics. However, the existing kinematic method for establishing these force influence lines is an indirect or mixed approach by combining the force method with the theorem of reciprocal displacements, which is yet inconsistent with the kinematic method for statically determinate structure. This paper proposes the direct kinematic method in conjunction with the load-displacement differential relation for exactly constructing influence lines of reaction and internal forces of indeterminate structures. Firstly, through applying the principle of virtual displacement, the formula for influence lines of reaction and internal forces of indeterminate structure via direct kinematic method is derived based on the released structure. Then, a computational approach with a clear concept and unified procedure as well as wide applicability based on the load-displacement differential relation of beam is suggested to achieve conveniently the closed-form expression of force influence lines, and exactly draw them. Finally, three representative examples for constructing force influence lines of statically indeterminate beams and frame illustrate the superiority of the proposed method.

• Structural Engineering and Mechanics
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• v.51 no.4
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• pp.601-625
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• 2014

Based on continuum mechanics and the principle of virtual displacements, incremental total Lagrangian formulation (T.L.) and incremental updated Lagrangian formulation (U.L.) were presented. Both T.L. and U.L. considered the large displacement stiffness matrix, which was modified to be symmetrical matrix. According to the incremental updated Lagrangian formulation, small strain, large displacement, finite rotation of three dimensional Timoshenko fiber beam element tangent stiffness matrix was developed. Considering large displacement and finite rotation, a new type of tangent stiffness matrix of the beam element was developed. According to the basic assumption of plane section, the displacement field of an arbitrary fiber was presented in terms of nodal displacement of centroid of cross-area. In addition, shear deformation effect was taken account. Furthermore, a nonlinear finite element method program has been developed and several examples were tested to demonstrate the accuracy and generality of the three dimensional beam element.

• Structural Engineering and Mechanics
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• v.50 no.5
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• pp.665-677
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• 2014

A numerical method, using a special mixed finite element associated with the virtual crack extension technique, has been developed to evaluate the energy release rate for kinking cracks. The element is two dimensional 7-node mixed finite element with 5 displacement nodes and 2 stress nodes. The mixed finite element ensures the continuity of stress and displacement vectors on the coherent part and the free edge effect. This element has been formulated starting from a parent element in a natural plane with the aim to model different types of cracks with various orientations. Example problems with kinking cracks in a homogeneous material and bimaterial are presented to assess the computational accuracies.