• Structural Engineering and Mechanics
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• 제52권3호
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• pp.595-601
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• 2014

For analysis of the plates and membranes by numerical or analytical methods, the question of choice of the system of functions satisfying the different boundary conditions remains a major challenge to address. It is to this issue that is dedicated this work based on an approach of choice of combinations of trigonometric functions, which are shape functions of a bended beam with the boundary conditions corresponding to the plate support mode. To do this, the shape functions of beam vibrations for strength analysis of the rectangular plates by Kantorovich-Vlasov's method is considered. Using the properties of quasi-orthogonality of those functions allowed assessing to differential equation for every member of the series. Therefore it's proposed some new forms of integration of the beam functions, in order to simplify the problem.

• Earthquakes and Structures
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• 제10권6호
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• pp.1291-1314
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• 2016

The paper presents the development of experimental fragility functions for exterior RC beam-column connections based on results obtained from extensive testing carried out in the present study. Three typical types of seismically deficient beam-column connections, which are commonly prevalent in Indian sub-continent, were considered. These specimens were tested under cyclic displacement histories with different characteristics to induce different damage states. Rehabilitation specific fragility functions for damaged specimens were developed considering drift angle as a demand parameter. Four probability distributions were fit to the data and suitability of each distribution was evaluated using standard statistical method. Specimens with different damage states were rehabilitated appropriately and rehabilitated specimens were tested under similar displacement histories. Fragility functions for rehabilitated specimens have also been developed following similar procedure. Comparison of fragility functions for both original and rehabilitated specimens for each rehabilitation method showed close agreement, which establishes the effectiveness of the adopted rehabilitation strategies and hence would provide confidence in field application.

• 대한기계학회논문집
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• 제14권2호
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• pp.310-323
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• 1990

A three-noded, with three degree-of-freedom at each node, in-plane curved beam element is formulated and employed in eigen-analysis of constant curvature beam. The conventional quadratic shape functions used in a three noded C .deg. type curved beam element produce such an undesirable large stiffness that a significant error is introduced in displacements and stresses. These phenomena are called 'Stiffness Locking Phenomena', which result from spurious strain energy due to inappropriate assumptions on independent isoparametric quadratic interpolation functions. Stiffness locking phenomena can be alleviated by using modified interpolation functions which get rid of spurious constraints of conventional interpolation functions. Eigenvalues and their modes as well as displacements and stresses may be locked because they are related to stiffness. Using modified curved beam element in eigenvalue problem of cantilever and arch, the property and performance of modified curved beam element are examined by numerical experimentations. In these eigen-analyses, mass matrices are calculated by using both modified and unmodified curved beam element, are compared with theoretical solutions. These comparisons show that the performance of the modified curved beam element is better than that of the unmodified curved beam element.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2009년도 춘계학술대회 논문집
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• pp.573-578
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• 2009

Starting from the rotating beam finite element in which the interpolating shape functions satisfies the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfies the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beam.

• Structural Engineering and Mechanics
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• 제39권1호
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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.

• 대한기계학회논문집A
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• 제24권12호
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• pp.3003-3009
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• 2000

In this paper, we propose a new efficient hybrid-mixed C(sup)0 curved beam element with the optimal interpolation functions determined from numerical tests, which gives very accurate locking-free two-node curved beam element. In the element level, the stress parameters are eliminated from the stationary condition and the nodeless degrees of freedom are also removed by static condensation so that a standard six-by-six stiffness matrix is finally obtained. The numeri cal benchmark problems show that the element with cubic displacement functions and quadratic stress functions is the most efficient.

• 한국소음진동공학회논문집
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• 제19권6호
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• pp.591-598
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• 2009

Starting from the rotating beam finite element in which the interpolating shape functions satisfy the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfy the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beams.

• Structural Engineering and Mechanics
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• 제30권6호
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• pp.763-785
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• 2008

In this study, a flexibility-based finite element method considering geometric and material nonlinearities is developed for analyzing steel-concrete frame structures. The stability functions obtained from the exact buckling solution of the beam-column subjected to end moments are used to accurately capture the second-order effects. The proposed method uses the force interpolation functions, including a moment magnification due to the axial force and lateral displacement. Thus, only one element per a physical member can account for the interaction between the bending moment and the axial force in a rational way. The proposed method applies the Newton method based on the load control and uses the secant stiffness method, which is computationally both efficient and stable. According to the evaluation result of this study, the proposed method consistently well predicts the nonlinear inelastic behavior of steel-concrete composite frames and gives good efficiency.

• ETRI Journal
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• 제38권6호
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• pp.1135-1144
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• 2016

Fractal antenna arrays are geometry-based thinned arrays having multiband applications. The major challenge of these arrays is their large number of elements at higher expansion factors. This article presents the thinning of fractal antenna arrays while maintaining an appropriate balance between the side lobe level and beam width by using various quantized fractal distribution functions. A 2D square fractal antenna array and 3DSierpinski gasket antenna array are considered in this article to validate the proposed distribution functions. Nearly one third of the antenna elements are thinned in each successive iteration except in the case of a one-count distribution function. The proposed technique can simplify practical implementation and exhibits better performance for various parameters such as the side lobe level, side lobe angle, and half power beam width than fully populated fractal antenna arrays.

• Advances in materials Research
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• 제5권1호
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• pp.1-9
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• 2016

The bending problem of a functionally graded cantilever beam subjected to uniformly distributed load is investigated. The material properties of the functionally graded beam are assumed to vary continuously through the thickness, according to a power-law distribution of the volume fraction of the constituents. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. A practical example is presented to show the application of the method.