• Structural Engineering and Mechanics
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• v.10 no.1
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• pp.67-79
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• 2000

Critical loads and load-carrying capacities for steel scaffolds used as shoring systems were compared using computational and experimental methods in Part I of this paper. In that paper, a simple 2-D model was established for use in evaluating the structural behavior of scaffold-shoring systems. This 2-D model was derived using an incremental finite element analysis (FEA) of a typical complete scaffold-shoring system. Although the simplified model is only two-dimensional, it predicts the critical loads and failure modes of the complete system. The objective of this paper is to present a closed-form solution to the 2-D model. To simplify the analysis, a simpler model was first established to replace the 2-D model. Then, a closed-form solution for the critical loads and failure modes based on this simplified model were derived using a bifurcation (eigenvalue) approach to the elastic-buckling problem. In this closed-form equation, the critical loads are shown to be function of the number of stories, material properties, and section properties of the scaffolds. The critical loads and failure modes obtained from the analytical (closed-form) solution were compared with the results from the 2-D model. The comparisons show that the critical loads from the analytical solution (simplified model) closely match the results from the more complex model, and that the predicted failure modes are nearly identical.

• Journal of the Korean Geotechnical Society
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• v.22 no.9
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• pp.23-36
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• 2006

This study presents the development of a new closed-form analytical solution for the ultimate bearing capacity of an embedded wall in a granular mass. The closed-form analytical solution consists of upper and lower bound solutions (UB and LB). The calculated values from these bound solutions were compared with the author's two-dimensional laboratory wall model loading test and finite element analysis in the plastic region. The comparison showed that ultimate bearing loads from both the model test and finite element analysis are located between UB and LB. In particular, the ultimate bearing load from LB showed good agreement with the ultimate bearing load values from both the model test and finite element analysis. However, the calculated value from the conventional empirical form subjected to plane-strain conditions was shown to be much smaller than the LB.

• Journal of Ocean Engineering and Technology
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• v.24 no.1
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• pp.34-38
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• 2010

An analytical solution procedure for the dynamic response of beams with variable properties is developed by using an asymptotic solution and the Green's function. This asymptotic closed form solution is derived for the transverse vibration of beams under the assumption of slowly varying properties, such as mass, cross-section, tension etc., along the beam length. However, this solution is still found to be very accurate even in the case of large variation, such as step change in cross-section, mass, and tension. Therefore, this derived asymptotic closed form solution and the Green's function can be easily applied to find dynamic responses for various kind of beam vibration problems.

• Structural Engineering and Mechanics
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• v.51 no.5
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• pp.773-792
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• 2014

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

• Journal of Ocean Engineering and Technology
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• v.33 no.6
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• pp.535-546
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• 2019

The paper presents a closed-form analytical solution for the ultimate strength of sandwich panels with metal faces and an elastic isotropic core during combined in-plane compression and lateral pressure under clamped boundary condition. By using the principle of minimum potential energy, the stress distribution in the faces during uni-axial edge compression and constant lateral pressure was obtained. Then, the ultimate edge compression was derived on the basis that collapse occurs when yield has spread from the mid-length of the sides of the face plates to the center of the convex face plates. The results were validated by nonlinear finite element analysis. Because the solution is analytical and closed-form, it is rapid and efficient and is well-suited for use in practical structural design methods, including repetitive use in structural optimization. The solution applies for any elastic isotropic core material, but the application that stimulated this study was an elastomer-cored steel sandwich panel that had excellent energy absorbing and protective properties against fire, collisions, ballistic projectiles, and explosions.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.289-292
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• 1994

In this paper, the equations of motion are constructed systematically for multibody systems containing closed kinematic loops. For the displacement analysis of the closed loops, we introduce a new mixed coordinates by adding to the reference coordinates, relative coordinates corresponding to the degrees of freedom of the system. The mixed coordinates makes easy derive the explicit closed form solution. The explicit functional relationship expressed in closed form is of great advantages in system dimension reduction and no need of an iterative scheme for the displacement analysis. This forms of equation are built up in the general purpose computer program for the kinematic and dynamic analysis of multiboty systems.

• Journal of the Korean Geotechnical Society
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• v.23 no.4
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• pp.185-197
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• 2007

Limit analysis of upper and lower bound solutions has been well developed to provide the stability numbers for shallow tunnels in cohesive soil ($c_u$ material), cohesive-frictional soil (c'-$\phi$' material) and cohesionless soil ($\phi$'material). However, an extension of these methods to relatively deep circular tunnels in the cohesionless soil has been explored rarely to date. For this reason, the closed-form analytical solutions including lower bound solution based on the stress discontinuity concept and upper bound solution based on the kinematically admissible failure mechanism were proposed for assessing tunnel collapse load in this study. Consequently, the tunnel collapse load from those solutions was compared with both the finite element analysis and the previous analytical bound solutions and shown to be in good agreement with the FE results, in particular with the FE soil elements located on the horizontal tunnel axis.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.11
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• pp.130-139
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• 2004

The Casing Oscillator is a bore file Equipment for the all-casing process. All-casing process is a method of foundation work in construction yard to oscillate steel Casing in the ground. The existing Casing Oscillator has some problem like not boring horizontally with disturbance and not driving Casing othor angle except horizon. To solve problem, the new structure Casing Oscillator is presented and studied. The performance of Casing Oscillator is improved by kinematics analysis. The Casing Oscillator is similar to the parallel manipulator in structure. So we obtain Inverse kinematics solution of Casing Oscillator easily. But it is difficult to solve forward kinematics of Casing Oscillator. T his paper presents a novel pose description corresponding to the structure characteristics of parallel manipulators. Through analysis on geometry theory, we obtain a new method of the closed-form solution to the forward kinematics using Kinematic Inversion. The closed-form solution contains two different meanings -analytical and real-time. So we reach the goal of practical application and control. Closed-form forward kinematics solution is verified by an inverse kinematics analysis. It shows that the method has a practical value for real -time control and inverse kinematics servo control.

• Journal of Korean Tunnelling and Underground Space Association
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• v.4 no.3
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• pp.175-184
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• 2002

Ground reaction curve is very useful information for estimating the installation time of the tunnel support. The ground reaction curve can be estimated by analytical closed form solutions derived in case of circular section and isotropic stress condition. The nature of the ground reaction, however, depends significantly on tunnel configurations. Nevertheless, few purely analytical and experimental studies of this problem due to tunnel configurations appear to have been carried out. Therefore, it is necessary to investigate the influence of tunnel configurations in order to use simply in practical design. This paper describes a numerical study for the intial elastic displacement in the ground reaction curve due to configuration of tunnel excavation. In order to evaluate the applicability of analytical closed form solution in practical design, the parametric studies were carried out by numerical analysis in elastic tunnel behaviour. In the studies, S value, namely configuration factor, defined as the ratio between tunnel height (b) and width (a), varies between 0.5 and 3.0, initial ground vertical stress varies between 5~30 MPa for each S values. The results indicated that the self-supportability of ground is larger in the ground having low S value. It, however, is suggested that the applicability of closed form solution may not be adequate to determine directly the installation time of the support and self-supportability of ground. It should be necessary to perform the additional numerical analysis.

• Advances in Computational Design
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• v.5 no.1
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• pp.55-89
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• 2020

For the first time, an accurate analytical solution, based on coupled three-dimensional (3D) piezoelasticity equations, is presented for free vibration analysis of the angle-ply elastic and piezoelectric flat laminated panels under arbitrary boundary conditions. The present analytical solution is applicable to composite, sandwich and hybrid panels having arbitrary angle-ply lay-up, material properties, and boundary conditions. The modified Hamiltons principle approach has been applied to derive the weak form of governing equations where stresses, displacements, electric potential, and electric displacement field variables are considered as primary variables. Thereafter, multi-term multi-field extended Kantorovich approach (MMEKM) is employed to transform the governing equation into two sets of algebraic-ordinary differential equations (ODEs), one along in-plane (x) and other along the thickness (z) direction, respectively. These ODEs are solved in closed-form manner, which ensures the same order of accuracy for all the variables (stresses, displacements, and electric variables) by satisfying the boundary and continuity equations in exact manners. A robust algorithm is developed for extracting the natural frequencies and mode shapes. The numerical results are reported for various configurations such as elastic panels, sandwich panels and piezoelectric panels under different sets of boundary conditions. The effect of ply-angle and thickness to span ratio (s) on the dynamic behavior of the panels are also investigated. The presented 3D analytical solution will be helpful in the assessment of various 1D theories and numerical methods.