• 대한기계학회논문집
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• 제11권2호
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• pp.234-242
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• 1987

본 논문에서는 변분법으로 유도한 최적조건을 수치계산에 적용키 위해 영역적 응법이 사용되었으며 불규칙한 형상의 방지에는 격자 적응법이 제시되었다. 설계 문 제로는 '국부 응력치의 일정 한도내에서 구조물 무게의 최소화' 또는 대등한 문제로 '제한된 구조물의 무게한도내에서 최대 국부응력치의 최소화'를 다루었다.

• Advances in nano research
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• 제14권2호
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• pp.141-154
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• 2023

Effects of viscoelastic foundation on vibration of curved-beam structure with clamped and simply-supported boundary conditions is investigated in this study. In doing so, a micro-scale laminate composite beam with two piezoelectric face layer with a carbon nanotube reinforces composite core is considered. The whole beam structure is laid on a viscoelastic substrate which normally occurred in actual conditions. Due to small scale of the structure non-classical elasticity theory provided more accurate results. Therefore, nonlocal strain gradient theory is employed here to capture both nano-scale effects on carbon nanotubes and microscale effects because of overall scale of the structure. Equivalent homogenous properties of the composite core is obtained using Halpin-Tsai equation. The equations of motion is derived considering energy terms of the beam and variational principle in minimizing total energy. The boundary condition is assumed to be clamped at one end and simply supported at the other end. Due to nonlinear terms in the equations of motion, semi-analytical method of general differential quadrature method is engaged to solve the equations. In addition, due to complexity in developing and solving equations of motion of arches, an artificial neural network is design and implemented to capture effects of different parameters on the inplane vibration of sandwich arches. At the end, effects of several parameters including nonlocal and gradient parameters, geometrical aspect ratios and substrate constants of the structure on the natural frequency and amplitude is derived. It is observed that increasing nonlocal and gradient parameters have contradictory effects of the amplitude and frequency of vibration of the laminate beam.

• Journal of Welding and Joining
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• 제19권2호
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• pp.221-227
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• 2001

Based on the principle of complementary energy, an analytical method is developed which focuses on the end effects for determining thermal stress distributions in a three-layered beam. This method gives the stress distributions which completely satisfy the stress-free boundary conditions. A numerical example is given in order to verify this method. The results show that the present analytical solutions have the values of stress in excellent agreement with the solutions derived by other investigators. Using this method, the effects of the thickness of bond coat on the thermal stresses of a typical sprayed thermal barrier coating, which consists of IN738LC substrate, MCrAIY bond coat and ZrO$_2$-8wt%Y$_2$O$_3$top coat, were investigated.

• Structural Engineering and Mechanics
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• 제52권1호
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• pp.115-136
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• 2014

In this study, an extended Kantorovich method, employing multi-term displacement functions, is applied to analyze the vibration problem of symmetrically laminated plates with arbitrary boundary conditions. The vibration behaviors of laminated plates are determined based on the variational principle of total energy minimization and the iterative Kantorovich method. The out-of-plane displacement is represented in the form of a series of a sum of products of functions in x and y directions. With a known function in the x or y directions, the formulation for the variation of total potential energy is transformed to a set of governing equations and a set of boundary conditions. The equations and boundary conditions are then numerically solved for the natural frequency and vibration mode shape. The solutions are verified with available solutions from the literature and solutions from the Ritz and finite element analysis. In most cases, the natural frequencies compare very well with the reference solutions. The vibration mode shapes are also very well modeled using the multi-term assumed displacement function in the terms of a power series. With the method used in this study, it is possible to solve the angle-ply plate problem, where the Kantorovich method with single-term displacement function is ineffective.

• Structural Engineering and Mechanics
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• 제30권3호
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• pp.263-278
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• 2008

Structural pipe-in-pipe cross-sections have significant potential for application in offshore oil and gas production systems because of their property that combines insulation performance with structural strength in an integrated way. Such cross-sections comprise inner and outer thin walled pipes with the annulus between them fully filled by a selectable thick filler material to impart an appropriate combination of properties. Structural pipe-in-pipe cross-sections can exhibit several different collapse mechanisms and the basis of the preferential occurrence of one over others is of interest. This paper presents an elastic analyses of a structural pipe-in-pipe cross-section when subjected to external hydrostatic pressure. It formulates and solves the static and elastic buckling problem using the variational principle of minimum potential energy. The paper also investigates a simplified formulation of the problem where the outer pipe and its contact with the filler material is considered as a 'pipe on an elastic foundation'. Results are presented to show the variation of elastic buckling pressure with the relative elastic modulus of the filler and pipe materials, the filler thickness and the thicknesses of the inner and outer pipes. The range of applicability of the simplified 'pipe on an elastic foundation' analysis is also presented. A brief review of the types of materials that could be used as the filler is combined with the results of the analysis to draw conclusions about elastic buckling behaviour of structural pipe-in-pipe cross-sections.

• 한국강구조학회 논문집
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• 제10권4호통권37호
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• pp.667-676
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• 1998

본 연구에서는 부분지지되어 있고 사각형의 개구부를 갖는 적층복합판의 과도해석을 유한요소법을 이용하여 연구하였다. 수학적 지배방정식은 변분과 일차전단변형이론을 고려하여 유도하였고 적층판의 폭-두께비, 재료의 특성, 적층각도, 지지조건이 중앙점의 동적응답에 미치는 영향에 대하여 연구하였다. 수치적인 결과는 그래프와 표로 나타내었으며 참고문헌의 결과와 비교 분석하였다.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2004년도 추계학술대회 논문집 Vol.17
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• pp.218-221
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• 2004

The electronic state of ZnO doped with Al, Ga and In, which belong to III family elements in periodic table, was calculated using the density functional theory. In this study, the program used for the calculation on theoretical structures of ZnO and doped ZnO was Vienna Ab-initio Simulation Package (VASP), which is a sort of pseudo potential method. The detail of electronic structure was obtained by the describe variational $X{\alpha}(DV-X{\alpha})$(DV-Xa) method, which is a sort of molecular orbital full potential method. The optimized crystal structures obtained by calculations were compared to the measured structure. The density of state and energy levels of dopant elements was shown and discussed in association with properties.

• 한국전기전자재료학회논문지
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• 제18권7호
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• pp.589-593
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• 2005

The electronic states of ZnO doped with Al, Ga and In, which belong to III family elements in periodic table, were calculated using the density functional theory. In this study, the calculation was performed by two Programs; the discrete variational Xa (DV-Xa) method, which is a sort of molecular orbital full potential method; Vienna Ab-initio Simulation Package (VASP), which is a sort of pseudo potential method. The fundamental mixed orbital structure in each energy level near the Fermi level was investigated with simple model using DV-Xa. The optimized crystal structures calculated by VASP were compared to the measured structures. The density of state and the energy levels of dopant elements were shown and discussed in association with properties.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2002년도 봄 학술발표회 논문집
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• pp.303-308
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• 2002

A governing differential equation (GDE) of PSC flexural member with constant eccentricity considering the long-term losses including concrete creep, shrinkage, and PS steel relaxation is derived based on the two approaches. The first approach utilizes the force and moment equilibrium equations derived based on the geometry of strains of the uniform and curvature strains while the second one utilizes the principle of minimum total potential energy formulation. The identity of the two GDE's is verified by comparing the coefficients consisting of the GDE's. The boundary conditions resulting from the functional analysis of the variational calculus are investigated. Rayleigh-Ritz method provides a way to get the explicit form of the continuous deflection function in which the total potential energy is minimized with respect to the unknown coefficients consisting of the trial functions. As a closure, the analytically calculated results are compared with the experiments and show good agreements.

• Geomechanics and Engineering
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• 제32권6호
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• pp.553-566
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• 2023

A circular tank foundation resting on the ground and subjected to axisymmetric horizontal and vertical loads and moments is analyzed using the variational principles of mechanics. The circular foundation is assumed to behave as a Kirchhoff plate with in-plane and transverse displacements. The soil beneath the foundation is assumed to be a multi-layered continuum in which the horizontal and vertical displacements are expressed as products of separable functions. The differential equations of plate and soil displacements are obtained by minimizing the total potential energy of the plate-soil system and are solved using the finite element and finite difference methods following an iterative algorithm. Comparisons with the results of equivalent two-dimensional finite element analysis and other researchers establish the accuracy of the method.