• Steel and Composite Structures
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• 제39권3호
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• pp.291-306
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• 2021

Based on Reissner's mixed variational theorem (RMVT), the authors develop a semi-analytical finite element (FE) method for a three-dimensional (3D) bending analysis of nonhomogeneous orthotropic, complete and incomplete toroidal shells subjected to uniformly-distributed loads. In this formulation, the toroidal shell is divided into several finite annular prisms (FAPs) with quadrilateral cross-sections, where trigonometric functions and serendipity polynomials are used to interpolate the circumferential direction and meridian-radial surface variations in the primary field variables of each individual prism, respectively. The material properties of the toroidal shell are considered to be nonhomogeneous orthotropic over the meridianradial surface, such that homogeneous isotropic toroidal shells, laminated cross-ply toroidal shells, and single- and bi-directional functionally graded toroidal shells can be included as special cases in this work. Implementation of the current FAP methods shows that their solutions converge rapidly, and the convergent FAP solutions closely agree with the 3D elasticity solutions available in the literature.

• Composite Materials and Engineering
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• 제3권3호
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• pp.241-262
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• 2021

In this article, we studied the effect of two-temperature in a two-dimensional orthotropic thermoelastic media with fractional order heat transfer in generalized thermoelasticity with three-phase-lags due to thermomechanical sources. The boundary of the surface is subjected to linearly distributed and concentrated loads (mechanical and thermal source). The solution of the problem is obtained with the help of Laplace and Fourier transform techniques. The expressions for displacement components, stress components and conductive temperature are derived in transformed domain. Numerical inversion technique is used to obtain the results in physical domain. The effect of two-temperature on all the physical quantities has been depicted with the help graphs. Some special cases are also discussed in the present investigation.

• Steel and Composite Structures
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• 제42권6호
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• pp.723-732
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• 2022

The present research is concerned to study the effect of fractional parameter and rotation on the propagation of Rayleigh waves in an orthotropic magneto-thermoelastic media with three-phase-lags in the context of fractional order theory of generalized thermoelasticity with combined effect of rotation and hall current. The secular equations of Rayleigh waves are derived by using the appropriate boundary conditions. The wave properties such as phase velocity, attenuation coefficient are computed numerically and the numerical simulated results are presented through graphs to show the effect on all the components. Some special cases are also discussed in the present investigation.

• Structural Engineering and Mechanics
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• 제81권4호
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• pp.503-511
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• 2022

In this article, we have examined the effect of fractional order parameter in a two-dimensional orthotropic magneto-thermoelastic solid in generalized thermoelasticity without energy dissipation with fractional order heat transfer in the context of hall current, rotation and two-temperature due to normal force. Laplace and Fourier transform techniques are used to obtain the solution of the problem. The expressions for displacement components, stress components, current density components and conductive temperature are obtained in transformed domain and then in physical domain by using numerical inversion method. The effect of fractional parameter on all the components has been depicted through graphs. Some special cases are also discussed in the present investigation.

• 한국강구조학회 논문집
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• 제18권1호
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• pp.93-100
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• 2006

본 논문에서는 축방향 하중을 받는 사변단순지지된 특별직교이방성 적층복합판의 고유진동수를 간편하게 계산하는 방법을 제시한다. 이 방법은 진동해석을 위해, 임의 방법으로 얻어질 수 있는 영향계수를 사용하며 공명상태하에서 관성력에 의한 부재의 변형된 모드 형상을 결정하는 과정으로 이루어진다. 최초에 가정된 임의의 모드 형상으로 시작하여 정확한 모드 형상이 반복적인 과정을 통해 얻어진다. 또한 ${[{\alpha}{\beta}]_r}$, ${[{\alpha}{\beta}{\beta}{\alpha}{\alpha}{\beta}]_r}$그리고 ${[{\alpha}{\beta}{\beta}{\gamma}{\alpha}{\alpha}{\beta}]_r}$와 같이 적층의 수가 증가함에 따라 ${B_1_6}$, ${B_2_6}$, ${D_1_6}$, 그리고 ${D_2_6}$ 가 무시될 수 있어서 특별직교이방성 적층복합판 이론과 본 방법을 적용할 수 있는 형태를 제시하고 이들에 대한 진동해석 결과를 제시한다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1998년도 봄 학술발표회 논문집
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• pp.327-334
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• 1998

A method of calculating the natural frequency corresponding to the first mode of vibration of beams and toll.or structures, with irregular cross sections and with arbitrary boundary conditions was developed and reported by Kim, D. H. in 1974. In this paper, the result of application of this method to the special orthotropic plates with free edges supported on elastic foundation and with a pair of opposite edges under axial forces is presented. Such plates represent the concrete highway slab and hybrid composite pavement of bridges. The reinforced concrete slab can be assumed as a special orthotropic plate, as a close approximation. The highway slab is supported on elastic foundation, with free boundaries. Sometimes, the pair of edges perpendicular to the traffic direction may be subject to the axial forces. The plate is subject to the concentrated load/loads, in the form of traffic loads, or the test equipments. Any method nay be used to obtain the deflection influence surfaces needed for this vibration analysis. Finite difference method is used for this purpose, in this paper. The influence of the modulus of the foundation, the aspect ratio of the plate, and the magnitudes of the axial forces and the concentrated attached mass on the plate, on the natural frequency is thoroughly studied.

• 한국강구조학회 논문집
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• 제16권2호통권69호
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• pp.191-200
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• 2004

본 연구에서는 보강판을 직교이방성 판으로 해석하는 경우 보강판의 제원에 따라 정확도에 큰 차이를 보이는 단점을 해결하기 위하여, 개단면 리브를 갖는 보강판에 대하여 직교이방성 강성을 보정하는 방법을 제안하였다. 여러 가지 보강판에 대하여 등방성 및 직교이방성 판 요소로 모델링하여 해석하고 최대 처짐을 비교한 결과, 특정 강성비를 중심으로 이보다 강성비가 작아질수록 직교이방성 판이 더 작은 처짐을, 이보다 커질수록 더 큰 처짐을 나타내어 정확도의 향상을 위해서는 강성비에 따른 직교이방성 강성 수정이 이루어져야 함을 알 수 있었다. 거동 분석을 토대로, 직교이방성 판의 처짐식과 판만의 처짐과 관련한 처짐 비율을 이용하는 두 가지 강성 수정 방법을 제안하였으며, 두 경우 모두 오차율 및 오차율의 분포폭이 크게 감소하여 정확도가 크게 향상되지만, 처짐 비율의 방법이 처짐식을 이용한 방법보다 사용성 및 안정성 측면에서 더 적절한 것으로 나타났다. 또한, 개단면 리브를 갖는 보강판을 직교이방성 판으로 해석하는 경우, 본 연구에서 제안한 강성 수정 방법을 사용하여 보강판의 직교이방성 휨강성을 보정하게 되면, 상당한 정확성의 증가로 보강판에 대한 간편하고 타당한 결과를 얻을 수 있을 것으로 판단된다.

• Structural Engineering and Mechanics
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• 제51권6호
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• pp.923-937
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• 2014

The rational finite element method is different from the standard finite element method, which is constructed using basic solutions of the governing differential equations as interpolation functions in the elements. Therefore, it is superior to the isoparametric approach because of its obvious physical meaning and accuracy; it has successfully been applied to the isotropic elasticity problem. In this paper, the formulation of rational finite elements for plane orthotropic elasticity problems is deduced. This method is formulated directly in the physical domain with full consideration of the requirements of the patch test. Based on the number of element nodes and the interpolation functions, different approaches are applied with complete polynomial interpolation functions. Then, two special stiffness matrixes of elements with four and five nodes are deduced as a representative application. In addition, some typical numerical examples are considered to evaluate the performance of the elements. The numerical results demonstrate that the present method has a high level of accuracy and is an effective technique for solving plane orthotropic elasticity problems.

• Composites Research
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• 제12권4호
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• pp.25-32
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• 1999

불규칙단면과 다양한 경계조건을 갖는 보와 타워구조물의 1모드 하에서 고유진동수를 계산하는 방법은 1974년 Kim, D.H에 의해 개발되었다. 이 논문에서는 자유경계를 갖고 탄성지지된 특별직교 이방성 적층복합판에 대한 이 방법의 응용결과가 주어진다. 이러한 판들은 고속도로 콘크리트 슬래브와 교량 혼성 복합 포장에서 볼 수 있다. 이 진동해석을 위해 어떤 방법이라도 처짐에 대한 영향면을 구하는데 사용될 수 있다. 이 논문에서는 유한차분법이 사용되었다. 고유진동수에 대한 기초 탄성계수의 영향과 판의 형상비의 영향이 연구되었다. 고유진동수에 대한 판 자중의 무시효과가 또한 심도있게 연구되었다.

• Steel and Composite Structures
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• 제17권4호
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• pp.453-470
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• 2014

This article is the result of an investigation on the influence of a Pasternak elastic foundation on the stability of exponentially graded (EG) cylindrical shells under hydrostatic pressure, based on the first-order shear deformation theory (FOSDT) considering the shear stresses. The shear stresses shape function is distributed parabolic manner through the shell thickness. The governing equations of EG orthotropic cylindrical shells resting on the Pasternak elastic foundation on the basis of FOSDT are derived in the framework of Donnell-type shell theory. The novelty of present work is to achieve closed-form solutions for critical hydrostatic pressures of EG orthotropic cylindrical shells resting on Pasternak elastic foundation based on FOSDT. The expressions for critical hydrostatic pressures of EG orthotropic cylindrical shells with and without an elastic foundation based on CST are obtained, in special cases. Finally, the effects of Pasternak foundation, shear stresses, orthotropy and heterogeneity on critical hydrostatic pressures, based on FOSDT are investigated.