• Geomechanics and Engineering
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• v.4 no.3
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• pp.209-218
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• 2012

This paper presents the derivation of an analytical expression for the dynamic active thrust from c-${\phi}$ (c = cohesion, ${\phi}$ = angle of shearing resistance) soil backfill on rigid retaining walls with wall friction and adhesion. The derivation uses the pseudo-static approach considering tension cracks in the backfill, a uniform surcharge on the backfill, and horizontal and vertical seismic loadings. The development of an explicit analytical expression for the critical inclination of the failure plane within the soil backfill is described. It is shown that the analytical expression gives the same results for simpler special cases previously reported in the literature.

• Structural Engineering and Mechanics
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• v.57 no.5
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• pp.877-895
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• 2016

This paper is concerned with the analytical derivation of natural sloshing frequencies of liquid in annular cylindrical tank and its verification by experiment. The whole liquid domain is divided into three simple sub-regions, and the region-wise linearized velocity potentials are derived by the separation of variables. Two sets of matrix equations for solving the natural sloshing frequencies are derived by enforcing the boundary conditions and the continuity conditions at the interfaces between sub-regions. In addition, the natural sloshing frequencies are measured by experiment and the numerical accuracy of the proposed analytical method is verified through the comparison between the analytical and experimental results. It is confirmed that the present analytical method provides the fundamental sloshing frequencies which are in an excellent agreement with the experiment. As well, the effects of the tank radial gap, the bottom flow gap and the liquid fill height on the fundamental sloshing frequency are parametrically investigated.

• International journal of steel structures
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• v.18 no.4
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• pp.1440-1463
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• 2018

The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner's coefficient have been presented due to the limitation of Vlasov's buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler-Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair's formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.

• Proceedings of the Korean Radioactive Waste Society Conference
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• 2007.11a
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• pp.192-193
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• 2007

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1991.10a
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• pp.63-68
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• 1991

The frequency window method has been extended to include strong coupling and multiple connections between the primary structure and the secondary structures. The rational polynomial expansion of the eigenvalue problem and the analytical methods for its solution are novel and distinguish this work from other eigenvalue analysis methods. The key results are the identification of parameters which quantify the resonance and coupling characteristics; the derivation of analytical dosed-form expressions describing the fundamental modal properties of the frequency windows; and the development of an iterative procedure which yields accurate convergent results for strongly-coupled primary-secondary structures.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.378-382
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• 1996

This paper presents a 'mixed' method for performing the sensitivity analysis for multibody dynamics. The mixed method uses both the analytical derivation and the numerical evaluation, in which premitive derivations rely on the analytical process and their associated individual terms are evaluated by the numerical precess. Therefore, this method can eliminate difficulty in dervation of the direct differentiation. Furthermore, by using the joint coordinate formulation for the equations of motion, compulational efficiencyand numerical accuracy are achieved.

• Structural Engineering and Mechanics
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• v.62 no.1
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• pp.85-95
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• 2017

This paper presents an explicit analytical iteration method for form-finding analysis of suspension bridges. By extending the conventional analytical form-finding method predicated on the elastic catenary theory, two nonlinear governing equations are derived for calculating the accurate unstrained lengths of the entire cable systems both the main cable and the hangers. And for the gradient-based iteration method, the derivation of explicit calculation for the Jacobian matrix while solving the nonlinear governing equation enhances the computational efficiency. The results from sensitivity analysis show well performance of the explicit Jacobian matrix compared with the traditional finite difference method. According to two numerical examples of long span suspension bridges studied, the proposed method is also compared with those reported approaches or the fundamental criterions in suspension bridge structural analysis, which eventually confirms the accuracy and efficiency of the proposed approach.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.20 no.5
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• pp.461-471
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• 2008

An analytical solution of one dimensional mild slope equation is derived by use of the WKB method, which has a form similar to Porter's solution(2003). The present solution is so general in the sense of application that it is comparable to the corresponding numerical solutions. In the derivation we also presented the solution of refraction equation in terms of surface displacement. Some numerical results of the present solution by use of Bremmer's method are presented which agree with existing numerical solutions.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.54 no.12
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• pp.576-585
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• 2005

This paper deals with the electromagnetic field analysis of slotless brushless permanent magnet machines with three different magnetization patterns such as Halbach, parallel and radial magnetization. The magnetization modeling of Halbach, parallel and radial magnetization is performed analytically. And then, analytical solutions for open-circuit field distributions, armature reaction field distributions, flux linkages due to PMs and stator windings, torque, back-emf and inductance are derived in terms of magnetic vector potential and two-dimensional (2-d) polar coordinate systems. The analytical results are validated extensively by finite element (FE) analyses. The magnet volume required in order to produce identical flux density is compared with each magnetization. Finally, analytical solutions and derivation procedures of those presented in this paper can be applied to slotless and slotted brushless permanent magnet AC and DC machines.

• Wind and Structures
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• v.25 no.5
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• pp.459-474
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• 2017

In this study an analytical expression is derived for the natural frequency of the wind turbine towers supported on flexible foundation. The derivation is based on a Euler-Bernoulli beam model where the foundation is represented by a stiffness matrix. Previously the natural frequency of such a model is obtained from numerical or empirical method. The new expression is based on pure physical parameters and thus can be used for a quick assessment of the natural frequencies of both the real turbines and the small-scale models. Furthermore, a relationship between the diagonal and non-diagonal element in the stiffness matrix is introduced, so that the foundation stiffness can be obtained from either the p-y analysis or the loading test. The results of the proposed expression are compared with the measured frequencies of six real or model turbines reported in the literature. The comparison shows that the proposed analytical expression predicts the natural frequency with reasonable accuracy. For two of the model turbines, some errors were observed which might be attributed to the difference between the dynamic and static modulus of saturated soils. The proposed analytical solution is quite simple to use, and it is shown to be more reasonable than the analytical and the empirical formulas available in the literature.