• Steel and Composite Structures
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• 제47권5호
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• pp.551-568
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• 2023

In this research, a new two-dimensional (2D) and quasi three-dimensional (quasi-3D) higher order shear deformation theory is devised to address the bending problem of functionally graded plates resting on an elastic foundation. The displacement field of the suggested theories takes into account a parabolic transverse shear deformation shape function and satisfies shear stress free boundary conditions on the plate surfaces. It is expressed as a combination of trigonometric and exponential shear shape functions. The Pasternak mathematical model is considered for the elastic foundation. The material properties vary constantly across the FG plate thickness using different distributions as power-law, exponential and Mori-Tanaka model. By using the virtual works principle and Navier's technique, the governing equations of FG plates exposed to sinusoidal and evenly distributed loads are developed. The effects of material composition, geometrical parameters, stretching effect and foundation parameters on deflection, axial displacements and stresses are discussed in detail in this work. The obtained results are compared with those reported in earlier works to show the precision and simplicity of the current formulations. A very good agreement is found between the predicted results and the available solutions of other higher order theories. Future mechanical analyses of three-dimensionally FG plate structures can use the study's findings as benchmarks.

• 한국해양공학회지
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• 제26권4호
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• pp.42-49
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• 2012

A numerical method is presented for an out-of-plane structural intensity analysis of rectangular thick plates with arbitrary elastic edge constraints. The method adapts an assumed mode method based on Timoshenko beam functions to obtain the velocities and internal forces needed for a structural intensity analysis. To verify the presented method, the structural intensity of a square thick plate under harmonic force excitation, for which four edges are simply supported, is analyzed, and the result is compared with existing solutions using the assumed mode method based on trigonometric functions. In addition, numerical analyses are carried out for a rectangular-shaped thick plate under harmonic force excitations, of which three edges are simply supported and one edge utilizes an arbitrary elastic edge constraint. These numerical examples show the good accuracy and applicability of the presented method for rectangular thick plates with arbitrary edge constraints.

• Advances in aircraft and spacecraft science
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• 제2권1호
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• pp.57-76
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• 2015

We investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the Ritz method, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the layers was modeled using the complex modulus. Simply-supported, cantilever, and viscously supported boundary conditions were considered in this study. Simple trigonometric functions were used as admissible functions in the Ritz method. The key idea behind sandwich structure is to increase damping in a beam as affected by the presence of a highly-damped core layer vibrating mainly in shear. Different assumptions are utilized in the literature, to model shear deformation in the core layer. In this manuscript, we used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, where the base and constraining layers were also damped. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically and viscously damped structures. The numerical results were compared with those available in the literature, and the results were found to be satisfactory.

• 한국강구조학회 논문집
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• 제21권4호
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• pp.433-442
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• 2009

본 연구는 V노치 또는 예리한 균열이 존재하는 N 다변형 단면 입체 실린더에 대한 새로운 3차원 진동 데이터를 제시한다. 본 논문에서는 수학적으로 완전한 대수삼각다항식과 V노치 선단을 따라 존재하는 3차원 응력특이도를 명확히 다루는 허용에지함수와 함께 Ritz방법이 적용된다. 응력특이도를 포함하는 다변형 입체 실린더의 정확한 고유진동수 및 모드형상을 얻기 위해서는 에지함수가 필요하다는 것이 수렴도 분석을 통하여 입증된다.

• Transactions on Control, Automation and Systems Engineering
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• 제4권2호
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• pp.156-163
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• 2002

This paper presents a new formulation to simplify the three resulting constraint equations of the direct kinematics of the 3-6 (Stewart-Gough) Platform. The conventional direct kinematics of the 3-6 Platform has been formulated through complicated steps with trigonometric functions in three angle variables and thus results in the computational burden. In order to reduce the formulation complexity, we replace an angle variable into a length one and express three connecting joints on the moving platform in the same frame. The proposed formulation yields considerable abbreviation of the number of the calculation terms involved in the direct kinematics. It is verified through a series of simulation results.

• 한국학교수학회논문집
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• 제4권2호
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• pp.1-9
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• 2001

Since the computer is becoming more and more indispensible tool in every fields of the modern society, it is needed and desirable to utilize the computer as a basic tool from the very early stage of the education process. Recently Maple is gaining its popularity as a comprehensive mathematical software with its power of symbolic calculations and graphics as well as its great numerical computational ability. We demonstrate the suitability of this software as a tool for the mathematical education and presents several examples of the applications of Maple. For the middle and the high school mathematics courses, we give the application examples for the quadratic functions and their graphs, statistics, the three dimensional shapes, algebraic problems. Through the examples, we confirm that mathematical education can be much more effective and simple by using Maple. If we establish computer-assisted mathematical classes, we can draw more attention and excitement from the attendants than traditional classes and eventually improve more rapidly their problem-solving ability On the other hand, the excess of the computer-aided education give to obstacle of psychological, not to be passing over the fact.

• Journal of Power Electronics
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• 제15권3호
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• pp.796-805
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• 2015

New direct and indirect current control methods for a fault-tolerant active power filter topology are presented in this paper. Since a three-phase four-switch topology has a phase bridge current which cannot be directly controlled, a hysteresis control method in the α-β plane which controls the three-phase current in the two-phase stationary coordinate system is proposed. The improved SVPWM algorithm is able to eliminate the operation of the trigonometric functions in the traditional algorithm by rotating the α-β coordinates and alternating the sequence of the output vectors, which in turn simplifies the algorithm and reduces the switching frequency. The selection of the DC-side reference voltage and DC-side capacitor equalization strategy are also discussed. Simulation and experiments demonstrate that the proposed control method is correct and feasible.

• 전자공학회논문지CI
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• 제40권6호
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• pp.1-8
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• 2003

Global carry propagation이 없는 redundant signed number에 의한 CORDIC 회로를 제안하였다. 이 number format은 Booth recording과 유사한 새로운 receding scheme을 가지고 가감산에서 carry 전파의 문제를 효과적으로 해결하였다. 여기서는 상수 scale factor를 갖고 삼각함수 계산을 하는 pipeline구조를 채택하였다. 이 CORDIC 회로의 동작시간은 채택한 operand bit에 상관없이 일정하다.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.317-324
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• 2008

This paper shows the degree of simultaneous neural network approximation for a target function in $C^r$[-1, 1] and its first derivative. We use the Jackson's theorem for differentiable functions to get a degree of approximation to a target function by algebraic polynomials and trigonometric polynomials. We also make use of the de La Vall$\grave{e}$e Poussin sum to get an approximation order by algebraic polynomials to the derivative of a target function. By showing that the divided difference with a generalized translation network can be arbitrarily closed to algebraic polynomials on [-1, 1], we obtain the degree of simultaneous approximation.

• Communications for Statistical Applications and Methods
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• 제15권1호
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• pp.87-94
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• 2008

Andrews (1972) proposed to combine trigonometric functions to represent n observations of p variates, where the coefficients in linear sums are taken from the values of corresponding observation's respective variates. By viewing Andrews' plot as a collection of n trajectories of p-dimensional objects (observations) as a weighting point loaded with dimensional weights moves along a certain path on the hyper-dimensional sphere, we develop graphical techniques for further uses in data visualization. Specifically, we show that the parallel coordinate plot is a special case of Andrews' plot and we demonstrate the versatility of Andrews' plot with a projection pursuit engine.