• 한국철도학회:학술대회논문집
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• 한국철도학회 2007년도 추계학술대회 논문집
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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.

• Smart Structures and Systems
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• 제3권2호
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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.

• Structural Engineering and Mechanics
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• 제54권4호
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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.

• 한국추진공학회지
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• 제7권2호
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• pp.36-43
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• 2003

탄소섬유 T700/Epoxy로 만든 직교이방성 구조로 된 두께가 얇은 압력용기의 반경방향의 변위에 관한 해를 곡선좌표계의 평형방정식을 사용하여 구하였다. 3차원 곡선좌표계의 변형율과 변위의 관계를 간단히 하면서 지배방정식을 유도하기 위해 변분이론과 가상일의 원리를 사용하였다. 다른 여러 종류의 직교이방성 압력용기에 대한 계산 결과를 제시했으며 수압시험을 한 결과와 비교 검토하였다. 계산결과와 시험결과는 비교적 잘 일치하였다.

• Geomechanics and Engineering
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• 제19권3호
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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.

• 한국소음진동공학회논문집
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• 제16권1호
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• pp.57-65
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• 2006

In this paper, we present the principle of virtual work, from which the exact non-linear equations of motion of a rotating ring can be derived, by using the theory of finite deformation. For a thin ring of which the effect of variation in curvature across the cross-section is neglected, the radial displacement and the extensional stress are determined from the principle of virtual work at the steady state where the ring is rotating with a constant angular velocity. And also we formulate systematically the governing equations concerned to the in-plane vibrations and the out-of-plane vibrations at the disturbed state by using the principle of virtual work which is expressed with the disturbed displacements about the steady state. The formulated governing equations are classified by four models along the cases of considering or neglecting all or partly the secondary effects of flexural shear, rotary inertia, circumferential extension, and twist inertia. The natural vibrations of thin rings are analyzed, and its results are compared and discussed.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 추계학술대회논문집
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• pp.585-592
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• 2005

In this paper, we present the principle of virtual work, from which the exact non-linear equations of motion of a rotating ring can be derived, by using the theory of finite deformation For a thin ring of which the effect of variation in curvature across the cross-section is neglected, the radial displacement and the extensional stress are determined from the principle of virtual work at the steady state where the ring is rotating with a constant angular velocity. And also we formulate systematically the governing equations concerned to the in-plane vibrations and the out-of-plane vibrations at the disturbed state by using the principle of virtual work which is expressed with the disturbed displacements about the steady state. The formulated governing equations are classified by four models along the cases of considering or neglecting all or partly the secondary effects of flexural shear, rotary inertia, circumferential extension, and twist inertia. The natural vibrations of thin rings are analyzed, and its results are compared and discussed.

• Wind and Structures
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• 제32권1호
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• pp.19-30
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• 2021

This study presents buckling analysis of a simply supported sandwich plate with functionally graded porous layers. In the kinematic relation of the plate, a hyperbolic shear displacement model is used. The governing equations of the problem are derived by using the principle of virtual work. In the solution of the governing equations, the Navier procedure is implemented. In the porosity effect, four different porosity types are used for functionally graded sandwich layers. In the numerical examples, the effects of the porosity parameters, porosity types and geometry parameters on the critical buckling of the functionally graded sandwich plates are investigated.

• Structural Engineering and Mechanics
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• 제51권4호
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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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• 제67권3호
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• pp.291-300
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• 2018

In this work, a new trigonometry theory of shear deformation is developed for the static analysis of thick isotropic beams. The number of variables used in this theory is identical to that required in the theory of Euler-Bernoulli, sine function is used in the displacement field in terms of the coordinates of the thickness to represent the effects of shear deformation. The advantage of this theory is that shear stresses can be obtained directly from the relationships constitute, while respecting the boundary conditions at the free surface level of the beam. Therefore, this theory avoids the use of shear correction coefficients. The differential equilibrium equations are obtained using the principle of virtual works. A thick isotropic beam is considered, whose numerical study to show the effectiveness of this theory.