• Structural Engineering and Mechanics
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• v.58 no.6
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• pp.949-966
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• 2016

The second order analysis taking place due to non-linear behavior of the structures under the mechanical and geometric factors through implementing exact and approximate methods is an indispensible issue in the analysis of such structures. Among the exact methods is the slope-deflection method that due to its simplicity and efficiency of its relationships has always been in consideration. By solving the differential equations of the modified slope-deflection method in which the effect of axial compressive force is considered, the stiffness matrix including trigonometric entries would be obtained. The complexity of computations with trigonometric functions causes replacement with their Maclaurin expansion. In most cases only the first two terms of this expansion are used but to obtain more accurate results, more elements are needed. In this paper, the effect of utilizing higher order terms of Maclaurin expansion on reducing the number of required elements and attaining more rapid convergence with less error is investigated for the Bernoulli beam with various boundary conditions. The results indicate that when using only one element along the beam length, utilizing higher order terms in Maclaurin expansion would reduce the relative error in determining the critical buckling load and kinematic parameters in the second order analysis.

• Structural Engineering and Mechanics
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• v.39 no.1
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• pp.21-46
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• 2011

The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

• Bulletin of the Society of Naval Architects of Korea
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• v.26 no.1
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• pp.24-38
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• 1989

In this study, an attempt for formulating a new and simplified rectangular finite element having only four corner nodal points is made to analyze the elastic-plastic large deformation behaviour up to the ultimate limit state of plates with initial imperfections. The present finite element contains the geometric nonlinearity caused by both in-plane and out-of-plane large deformation because for very thin plates the influence of the former may not be negligible. Treatment of expanded plastic zone in the plate thickness direction of the element is simplified based upon the concept of plastic node method so that the elastic-plastic stiffness matrix of the element is derived by the simple matrix operation without performing complicated numerical integration. Thus, a considerable saving of the computational efforts is expected. A computer program is also completed based on the present formulation and numerical calculation for some examples is performed so as to verify the accuracy and validity of the program.

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.1
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• pp.24-34
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• 1990

In this paper, the formulation of a new simplified finite element is made to analyze the ultimate strength of damaged tubular members subjected to combined axial force and end moment. A damaged tubular member that has the bending deformation and the local dent is modeled by beam elements. Tangent elastic stiffness matrix of a beam element which contains the effect of the geometric nonlinearity is derived by using the updated Lagrangian approach. Here the contribution of the stiffness in the dented area is neglected since its resistance against the external loads is considered to be small. A fully plastic interaction curve of the element under combined loads taking account of the local dent effect is selected as a yielding criterion at each nodal point. Also tangent elasto-plastic stiffness matrix of the element is formulated by plastic node method. Comparison with the present solution and the existing experimental results is made showing that the present method gives quite an accurate solution.

• Steel and Composite Structures
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• v.24 no.1
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• pp.65-77
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• 2017

The purpose of this research is to study the nonlinear free vibration and post-buckling analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams resting on a nonlinear elastic foundation. Uniformly and functionally graded distributions of single walled carbon nanotubes as reinforcing phase are considered in the polymeric matrix. The modified form of rule of mixture is used to estimate the material properties of CNTRC beams. The governing equations are derived employing Euler-Bernoulli beam theory along with energy method and Hamilton's principle. Applying von $K\acute{a}rm\acute{a}n's$ strain-displacement assumptions, the geometric nonlinearity is taken into consideration. The developed governing equations with quadratic and cubic nonlinearities are solved using variational iteration method (VIM) and the analytical expressions and numerical results are obtained for vibration and stability analysis of nanocomposite beams. The presented comparative results are indicative for the reliability, accuracy and fast convergence rate of the solution. Eventually, the effects of different parameters, such as foundation stiffness, volume fraction and distributions of carbon nanotubes, slenderness ratio, vibration amplitude, coefficients of elastic foundation and boundary conditions on the nonlinear frequencies, vibration response and post-buckling loads of FG-CNTRC beams are examined. The developed analytical solution provides direct insight into parametric studies of particular parameters of the problem.

• Structural Engineering and Mechanics
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• v.39 no.1
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• pp.47-75
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• 2011

An accurate substructural synthesis method including random responses synthesis, frequency-response functions synthesis and mid-order modes synthesis is developed based on rigorous substructure description, dynamic condensation and coupling. An entire structure can firstly be divided into several substructures according to different functions, geometric and dynamic characteristics. Substructural displacements are expressed exactly by retained mid-order fixed-interfacial normal modes and residual constraint modes. Substructural interfacial degree-of-freedoms are eliminated by interfacial displacements compatibility and forces equilibrium between adjacent substructures. Then substructural mode vibration equations are coupled to form an exact-condensed synthesized structure equation, from which structural mid-order modes are calculated accurately. Furthermore, substructural frequency-response function equations are coupled to yield an exact-condensed synthesized structure vibration equation in frequency domain, from which the generalized structural frequency-response functions are obtained. Substructural frequency-response functions are calculated separately by using the generalized frequency-response functions, which can be assembled into an entire-structural frequency-response function matrix. Substructural power spectral density functions are expressed by the exact-synthesized substructural frequency-response functions, and substructural random responses such as correlation functions and mean-square responses can be calculated separately. The accuracy and capacity of the proposed substructure synthesis method is verified by numerical examples.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2002.10a
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• pp.191-196
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• 2002

The paper presents a numerical and experimental investigation on dynamic behaviors of a towed low tension cable. In the numerical study, an implicit finite difference algorithm is employed for three-dimensional cable equations. Fluid and geometric non-linearity and bending stiffness are considered and solved by Newton-Raphson iteration. Block tri-diagonal matrix method is applied for the fast calculation of the huge size of matrices. In order to verify the numerical results and to see real physical phenomena, an experiment is carried out for a 6m cable in a deep and long towing tank. The cable is towed in two different ways; one is towed at a constant speed and the other is towed at a constant speed with top end horizontal oscillations. Cable tension and shear forces are measured at the top end. Numerical and experimental results are compared with good agreements in most cases but with some differences in a few cases. The differences are due to drag coefficients caused by vortex shedding. In the numerical modeling, non-uniform element length needs to be employed to cope with the sharp variation of tension and shear forces at near top end.

• Journal of Korea Multimedia Society
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• v.15 no.3
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• pp.323-335
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• 2012

In this paper, we propose an AR(augmented reality) system using user's bare hand based on computer vision. It is important for registering a virtual object on the real input image to detect and track correct feature points. The AR systems with markers are stable but they can not register the virtual object on an acquired image when the marker goes out of a range of the camera. There is a tendency to give users inconvenient environment which is limited to control a virtual object. On the other hand, our system detects fingertips as fiducial features using adaptive ellipse fitting method considering the geometric characteristics of hand. It registers the virtual object stably by getting movement of fingertips with determining the shortest distance from a palm center. We verified that the accuracy of fingertip detection over 82.0% and fingertip ordering and tracking have just 1.8% and 2.0% errors for each step. We proved that this system can replace the marker system by tacking a camera projection matrix effectively in the view of stable augmentation of virtual object.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.4 s.70
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• pp.395-404
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• 2005

This paper presents a reliable numerical procedure for nonlinear time-history analysis of space steel frames subjected to dynamic loads. Geometric nonlinearities of member (P-$\delta$) and frame (P-$\Delta$) are taken into account by the use of stability functions in framed stiffness matrix formulation. The gradual yielding along the member length and over the cross section is included by using a tangent modulus concept and a softening plastic hinge model based on the New-Orbison yield surface. A computer program utilizing the average acceleration method for the integration scheme is developed to numerically solve the equation of motion of framed structure formulated in an incremental form. The results of several numerical examples are compared with those derived from using beam element model of ABAQUS program to illustrate the accuracy and the computational efficiency of the proposed procedure.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.2
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• pp.95-109
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• 1993

In this study, the optimal configuration of arch structure has been tested by a decomposition technique. The object of this study is to provide the method of optimizing the shapes of both two hinged and fixed arches. The problem of optimal configuration of arch structures includes the interaction formulas, the working stress, and the buckling stress constraints on the assumption that arch ribs can be approximated by a finite number of straight members. On the first level, buckling loads are calculated from the relation of the stiffness matrix and the geometric stiffness matrix by using Rayleigh-Ritz method, and the number of the structural analyses can be decreased by approximating member forces through sensitivity analysis using the design space approach. The objective function is formulated as the total weight of the structures, and the constraints are derived by including the working stress, the buckling stress, and the side limit. On the second level, the nodal point coordinates of the arch structures are used as design variables and the objective function has been taken as the weight function. By treating the nodal point coordinates as design variable, the problem of optimization can be reduced to unconstrained optimal design problem which is easy to solve. Numerical comparisons with results which are obtained from numerical tests for several arch structures with various shapes and constraints show that convergence rate is very fast regardless of constraint types and configuration of arch structures. And the optimal configuration or the arch structures obtained in this study is almost the identical one from other results. The total weight could be decreased by 17.7%-91.7% when an optimal configuration is accomplished.