• Advances in nano research
• /
• 제11권6호
• /
• pp.581-593
• /
• 2021

This model is proposed to describe the buckling behavior of Carbon Nanotubes (CNTs) embedded in an elastic medium taking into account the combined effects of the magnetic field, the temperature, the nonlocal parameter, the number of walls. Using Eringen's nonlocal elasticity theory, thin cylindrical shell theory and Van der Waal force (VdW) interactions, we develop a system of partial differential equations governing the buckling response of CNTs embedded on Winkler, Pasternak, and Kerr foundations in a thermal-magnetic environment. The pre-buckling stresses are obtained by applying airy's stress function and an adjacent equilibrium criterion. To estimate the nonlocal critical buckling load of CNTs under the simultaneous effects of the magnetic field, the temperature change, and the number of walls, an optimization technique is proposed. Furthermore, analytical formulas are developed to obtain the buckling behavior of SWCNTs embedded in an elastic medium without taking into account the effects of the nonlocal parameter. These formulas take into account VdW interactions between adjacent tubes and the effect of terms involving differences in tube radii generally neglected in the derived expressions of the critical buckling load published in the literature. Most scientific research on modeling the effects of magnetic fields is based on beam theories, this motivation pushes me to develop a cylindrical shell model for studying the effect of the magnetic field on the static behavior of CNTs. The results show that the magnetic field has significant effects on the static behavior of CNTs and can lead to slow buckling. On the other hand, thermal effects reduce the critical buckling load. The findings in this work can help us design of CNTs for various applications (e.g. structural, electrical, mechanical and biological applications) in a thermal and magnetic environment.

• 자원환경지질
• /
• 제10권1호
• /
• pp.37-48
• /
• 1977

The earth's crust is unceasingly undergoing deformations because of the forces acting upon it. The relationship between the tectonic forces and the resulting deformations are found from the states of stresses in the earth's crust induced by these forces. The study has been attempted to analyze the deformations of the overlying sedimentary layers, which are deformed by the magma intrusion along its lower boundary. The elastic model is constructed to analyze the geologic structures, by means of the theory of elasticity, and then the appropriate boundary conditions are given. The solution of the Airy stress function which satisfies the given boundary conditions is derived from the analytic method. The internal stress distributions of the deformed elastic model layer are portrayed by principal stress trajetories, and then the corresponding potential faults and joints systems are predicted from the Coulomb-Mohr failure criterion. The internal displacement distributions are shown by the calculated displacement components vectors, namely horizontal, vertical and net components. Results of the numerical calculations show the developments of some geologic structures as follows; (1) one set of shear joints and or two sets of shear joints which are oppisite directions, and one set of extension joints parallel to the ${\sigma}_1$ direction, (2) one set of high angle thrusts and normal faults, (3) symmetric fold; both limbs are dipping in opposite direction with low angle. The field work at the Wall-A San area, located near Jinju City, in southern Korea, had accomplished to compare the field structures with the predicted ones. The results of the comparison exhibits the developments of joint and fault systems satisfactorily consistent with each others. But the area does not show any type of folding, in spite of the intrusion of a granodiorite massif, this fact is one of the important features of the whole Kyungsang sedimentary basins of Mesozoic age distributed at the south-eastern parts of Korea. For this reason, it is thought that the magma intrusion had occurred with extremly low pressure. The geologic structures have been modified by the erosion and weathering throughout the geologic time, and the conditions of the sedimentary layers (width, thickness and radius of magma) are not the same as before, being intruded by the magma. To enlighten this, it is preferable to study these geologic structures with analyses of various types of rheological models.

• Structural Engineering and Mechanics
• /
• 제31권2호
• /
• pp.181-210
• /
• 2009

This paper presents the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of isotropic flat plates. The so-called exact finite strip is assumed to be simply supported out-of-plane at the loaded ends. The strip is developed based on the concept that it is effectively a plate. The present method, which is designated by the name Full-analytical Finite Strip Method in this paper, provides an efficient and extremely accurate buckling solution. In the development process, the Von-Karman's equilibrium equation is solved exactly to obtain the buckling loads and the corresponding form of out-of-plane buckling deflection modes. The investigation of thin flat plate buckling behavior is then extended to an initial post-buckling study with the assumption that the deflected form immediately after the buckling is the same as that obtained for the buckling. It is noted that in the present method, only one of the calculated out-of-plane buckling deflection modes, corresponding to the lowest buckling load, i.e., the first mode is used for the initial post-buckling study. Thus, the postbuckling study is effectively a single-term analysis, which is attempted by utilizing the so-called semi-energy method. In this method, the Von-Karman's compatibility equation governing the behavior of isotropic flat plates is used together with a consideration of the total strain energy of the plate. Through the solution of the compatibility equation, the in-plane displacement functions which are themselves related to the Airy stress function are developed in terms of the unknown coefficient in the assumed out-of-plane deflection function. These in-plane and out-of-plane deflected functions are then substituted in the total strain energy expressions and the theorem of minimum total potential energy is applied to solve for the unknown coefficient. The developed method is subsequently applied to analyze the initial postbuckling behavior of some representative thin flat plates for which the results are also obtained through the application of a semi-analytical finite strip method. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is significantly promoted.

• 대한토목학회논문집
• /
• 제4권1호
• /
• pp.1-10
• /
• 1984

본(本)논문(論文)은 재료(材料)의 성질(性質)이 직교(直交)하는 방향(方向)으로 상이(相異)한 이방성(異方性) 구조체(構造體)에 부분등분포(部分等分布) 전단하중(剪斷荷重)이 경계(境界)에 작용(作用)할 경우의 수직응력(垂直應力)과 전단응력(剪斷應力)을 나태내는 엄밀해법(解法)을 제시(提示)하였다. 이 해법(解法)은 평형조건(平衡條件)과 적합조건(適合條件)을 동시에 만족하는 탄성론적(彈性論的)인 엄밀 해법(解法)이다. 따라서 이러한 문제(問題)를 해석(解析)하기 위하여 Airy 응력함수(應力凾數)를 이용(利用)하였다. 본해법(本解法)의 타당성(妥當性)을 증명(證明)하기 위하여 이방성(異方性)인 경우의 방정식(方程式)들의 이방성상수(異方性常數)들을 등방성(等方性)인 경우의 상수(常數)들로 대치(代置)할 경우에 등방성(等方性)인 경우의 방정식(方程式)들로 변환(變換)되지 않으면 안된다. 이를 검토(檢討)하기 위하여 L'hospital의 법칙(法則)을 이용하였다. 그 결과(結果) 이방성(異方性)인 경우의 모든 방정식(方程式)들은 등방성(等方性)인 경우의 방정식(方程式)들로 정확히 변환(變換)되었고 이 식들은 이미 연구된 자료(資料)의 값들과 비교(比較)된 결과(結果) 정확히 일치(一致)되었다. 또한 집중하중(集中荷重)의 경우와의 관계(關係)에서는 부분등분포하중(部分等分布荷重)의 특별(特別)한 경우가 집중하중(集中荷重)임을 고려하고 L'hospital의 법칙(法則)을 이용(利用)하면 부분등분포하중(部分等分布荷重)의 경우의 방정식(方程式)들은 바로 집중하중(集中荷重)의 경우의 방정식(方程式)들로 변환(變換)됨을 알 수 있다. 본 결과(結果)로 미루어 보아 해법(解法)의 타당성(妥當性)이 입증(立證)되었다고 할 수 있다. 본해법(本解法)의 방정식(方程式)들은 간단(簡單)한 형태(形態)로 구성(構成)되어 있어 수치결과(數値結果)를 정확히 누구나 얻을 수 있는 장점이 있다. 응력(應力)의 값을 나타내는 수치결과(數値結果)를 이방성재료(異方性材料)인 3단합판(合板)과 중첩합판을 예로 들어 나무결을 2가지 방향(方向)으로 강축(强軸)을 바꾸어 각각의 수직(垂直) 및 전단응력(剪斷應力)을 구(求)하여 도표(圖表)로 표시(表示)하였으며, 그 결과 응력(應力)의 분포(分布)는 재료(材料)의 성질과 강축(强軸)의 방향(方向)에 따라 현저하게 달라지는 현상을 볼 수 있다.

• 대한토목학회논문집
• /
• 제5권3호
• /
• pp.95-105
• /
• 1985

본(本) 논문(論文)은 재료(材料)의 성질(性質)이 직교(直交)하는 방향(方向)으로 상이(相異)한 이방성(異方性) 구조체(構造體)에 모멘트 하중(荷重)이 경계(境界)에 작용(作用)할 경우의 수직(垂直) 및 전단응력(剪斷應力)을 나타내는 엄밀 해석(解析)을 제시(提示)하였다. 모멘트하중(荷重)은 물론 탄성하중(彈性荷重)은 물론 탄소성하중(彈塑性荷重)과 극한하중(極限荷重)에 이르기까지의 하중(荷重)의 변화(變化)에 따른 구조체(構造體) 내부(內部)의 응력(應力)들을 해석적(解析的)인 방법(方法)으로 해석(解析)하였다. 이 해법(解法)은 평형조건(平衡條件)과 적합조건(適合條件)을 동시에 만족하는 탄성론적(彈性論的)인 엄밀해법(解法)이다. 따라서 이러한 문제(問題)를 해석(解析)하기 위하여 Airy 응력함수(應力凾數)를 이용(利用)하였다. 본(本) 해법(解法)의 타당성(妥當性)을 증명(證明)하기 위하여 이방성(異方性)인 경우의 방정식(方程式)들의 이방성(異方性) 상수(常數)들을 등방성(等方性)인 경우 상수(常數)들로 대치(代置)할 경우에 등방성(等方性)인 경우의 방정식(方程式)들로 변환(變換)되지 않으면 안된다. 이를 검토하기 위하여 L'hospital 외 법칙(法則)을 이용(利用)하였다. 그 결과(結果) 이방성(異方性)인 경우의 모든 방정식(方程式)들은 등방성(等方性)인 경우 방정식(方程式)들로 정확히 변환(變換)되었고 이 식(式)들은 이미 연구된 자료들의 값들과 비교(比較)된 결과(結果) 동일한 값을 얻었다. 본(本) 해법(解法)의 방정식(方程式)들은 간단(簡單)한 형태(形態)로 구성(構成)되어있어 수치결과(數値結果)를 누구나 정확히 얻을 수 있는 장점이 있다. 응력(應力)의 값을 얻기 위한 재료(材料)의 성질(性質)이나 구조적(構造的) 성질(性質)에 따라 결정되는 이방성상수(異方性常數)를 3 단합판중첩합판과 강보강판(鋼補鋼板), 철근콘크리트판(板)을 예(例)를 들어 표(表)로 표시(表示)하였고 수치결과(數値結果)는 3 단합판(段合板)을 예(例)를 들어 나무결을 두가지 방향(方向)으로 강축(强軸)을 바꾸어 각각의 수직(垂直) 및 전단응력(剪斷應力)을 구(求)하여 도표(圖表)로 표시(表示)하였으며 그 결과 응력(應力)의 분포(分布)는 재료(材料)의 성질(性質)과 보강부재(補强部材)의 배치 내용에 따라 달라지는 강축(强軸)의 방향(方向)에 따라 현저하게 달라지는 현상을 볼 수 있다.