• Title/Summary/Keyword: fundamental formulation theory

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Nonlinear vibration of FG-CNTRC curved pipes with temperature-dependent properties

  • Mingjie Liu;Shaoping Bi;Sicheng Shao;Hadi Babaei
    • Steel and Composite Structures
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    • v.46 no.4
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    • pp.553-563
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    • 2023
  • In the current research, the nonlinear free vibrations of curved pipes made of functionally graded (FG) carbon nanotube reinforced composite (CNTRC) materials are investigated. It is assumed that the FG-CNTRC curved pipe is supported on a three-parameter nonlinear elastic foundation and is subjected to a uniform temperature rise. Properties of the curved nanocomposite pipe are distributed across the radius of the pipe and are given by means of a refined rule of mixtures approach. It is also assumed that all thermomechanical properties of the nanocomposite pipe are temperature-dependent. The governing equations of the curved pipe are obtained using a higher order shear deformation theory, where the traction free boundary conditions are satisfied on the top and bottom surfaces of the pipe. The von Kármán type of geometrical non-linearity is included into the formulation to consider the large deflection in the curved nanocomposite pipe. For the case of nanocomposite curved pipes which are simply supported in flexure and axially immovable, the motion equations are solved using the two-step perturbation technique. The closed-form expressions are provided to obtain the small- and large-amplitude frequencies of FG-CNTRC curved pipes rested on a nonlinear elastic foundation in thermal environment. Numerical results are given to explore the effects of CNT distribution pattern, the CNT volume fraction, thermal environment, nonlinear foundation stiffness, and geometrical parameters on the fundamental linear and nonlinear frequencies of the curved nanocomposite pipe.

New horizon of geographical method (인문지리학 방법론의 새로운 지평)

  • ;Choi, Byung-Doo
    • Journal of the Korean Geographical Society
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    • v.38
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    • pp.15-36
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    • 1988
  • In this paper, I consider the development of methods in contemporary human geography in terms of a dialectical relation of action and structure, and try to draw a new horizon of method toward which geographical research and spatial theory would develop. The positivist geography which was dominent during 1960s has been faced both with serious internal reflections and strong external criticisms in the 1970s. The internal reflections that pointed out its ignorance of spatial behavior of decision-makers and its simplication of complex spatial relations have developed behavioural geography and systems-theoretical approach. Yet this kinds of alternatives have still standed on the positivist, geography, even though they have seemed to be more real and complicate than the previous one, The external criticisms that have argued against the positivist method as phenomenalism and instrumentalism suggest some alternatives: humanistic geography which emphasizes intention and action of human subject and meaning-understanding, and structuralist geography which stresses on social structure as a totality which would produce spatial phenomena, and a theoretical formulation. Human geography today can be characterized by a strain and conflict between these methods, and hence rezuires a synthetic integration between them. Philosophy and social theory in general are in the same in which theories of action and structural analysis have been complementary or conflict with each other. Human geography has fallen into a further problematic with the introduction of a method based on so-called political ecnomy. This method has been suggested not merely as analternative to the positivist geography, but also as a theoretical foundation for critical analysis of space. The political economy of space with has analyzed the capitalist space and tried to theorize its transformation may be seen either as following humanistic(or Hegelian) Marxism, such as represented in Lefebvre's work, or as following structuralist Marxism, such as developed in Castelles's or Harvey's work. The spatial theory following humanistic Marxism has argued for a dialectic relation between 'the spatial' and 'the social', and given more attention to practicing human agents than to explaining social structures. on the contray, that based on structuralist Marxism has argued for social structures producing spatial phenomena, and focused on theorising the totality of structures, Even though these two perspectives tend more recently to be convergent in a way that structuralist-Marxist. geographers relate the domain of economic and political structures with that of action in their studies of urban culture and experience under capitalism, the political ecnomy of space needs an integrated method with which one can overcome difficulties of orthhodox Marxism. Some novel works in philosophy and social theory have been developed since the end of 1970s which have oriented towards an integrated method relating a series of concepts of action and structure, and reconstructing historical materialism. They include Giddens's theory of structuration, foucault's geneological analysis of power-knowledge, and Habermas's theory of communicative action. Ther are, of course, some fundamental differences between these works. Giddens develops a theory which relates explicitly the domain of action and that of structure in terms of what he calls the 'duality of structure', and wants to bring time-space relations into the core of social theory. Foucault writes a history in which strategically intentional but nonsubjective power relations have emerged and operated by virtue of multiple forms of constrainst wihthin specific spaces, while refusing to elaborate any theory which would underlie a political rationalization. Habermas analyzes how the Western rationalization of ecnomic and political systems has colonized the lifeworld in which we communicate each other, and wants to formulate a new normative foundation for critical theory of society which highlights communicatie reason (without any consideration of spatial concepts). On the basis of the above consideration, this paper draws a new norizon of method in human geography and spatial theory, some essential ideas of which can be summarized as follows: (1) the concept of space especially in terms of its relation to sociery. Space is not an ontological entity whch is independent of society and has its own laws of constitution and transformation, but it can be produced and reproduced only by virtue of its relation to society. Yet space is not merlely a material product of society, but also a place and medium in and through which socety can be maintained or transformed.(2) the constitution of space in terms of the relation between action and structure. Spatial actors who are always knowledgeable under conditions of socio-spatial structure produce and reproduce their context of action, that is, structure; and spatial structures as results of human action enable as well as constrain it. Spatial actions can be distinguished between instrumental-strategicaction oriented to success and communicative action oriented to understanding, which (re)produce respectively two different spheres of spatial structure in different ways: the material structure of economic and political systems-space in an unknowledged and unitended way, and the symbolic structure of social and cultural life-space in an acknowledged and intended way. (3) the capitalist space in terms of its rationalization. The ideal development of space would balance the rationalizations of system space and life-space in a way that system space providers material conditions for the maintainance of the life-space, and the life-space for its further development. But the development of capitalist space in reality is paradoxical and hence crisis-ridden. The economic and poltical system-space, propelled with the steering media like money, and power, has outstriped the significance of communicative action, and colonized the life-space. That is, we no longer live in a space mediated communicative action, but one created for and by money and power. But no matter how seriously our everyday life-space has been monetalrized and bureaucratised, here lies nevertheless the practical potential which would rehabilitate the meaning of space, the meaning of our life on the Earth.

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Two Dimensional Flexible Body Response of Very Large Floating Structures (거대 부체구조물의 2차원 유연체 해석 및 거동)

  • Namseeg Hong
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.8 no.4
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    • pp.274-286
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    • 1996
  • Two-dimensional flexible body analysis (hydroelasticity theory) is adopted to a very large floating structure that may be multimodule and extend in the longitudinal direction. The boundary-element method (BEM) and Green function method(GFM) are used to obtain the hydrodynamic coefficients. The structure is considered to be a flexible beam responding to waves in the vertical direction and a consistent formulation for the hydrostatic stiffness is derived. The resulting coupled equations of motion are solved directly. Two designs of the module connectors are considered: a rotationally-flexible hinge connector, and a rotationally-rigid connector Numerical examples are presented to an integrated system of semi-submersibles. The analysis provides basic motions and section forces, which are useful to develop an understanding of the fundamental modes of displacement and force amplitudes for which multi-module VLFSs must be designed. The results show that while the hinge connectors result in greater motion, the rigid connectors increase substantially the sectional moments.

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Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates

  • Younsi, Abderahman;Tounsi, Abdelouahed;Zaoui, Fatima Zohra;Bousahla, Abdelmoumen Anis;Mahmoud, S.R.
    • Geomechanics and Engineering
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    • v.14 no.6
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    • pp.519-532
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    • 2018
  • In this work, two dimensional (2D) and quasi three-dimensional (quasi-3D) HSDTs are proposed for bending and free vibration investigation of functionally graded (FG) plates using hyperbolic shape function. Unlike the existing HSDT, the proposed theories have a novel displacement field which include undetermined integral terms and contains fewer unknowns. The material properties of the plate is inhomogeneous and are considered to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The governing equations which consider the effects of both transverse shear and thickness stretching are determined through the Hamilton's principle. The closed form solutions are deduced by employing Navier method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. In-plane stress components have been determined by the constitutive equations of composite plates. The transverse stress components have been determined by integrating the 3D stress equilibrium equations in the thickness direction of the FG plate. The accuracy of the present formulation is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature.

On mixing the Rayleigh-Ritz formulation with Hankel's function for vibration of fluid-filled functionally graded cylindrical shell

  • Hussain, Muzamal;Naeem, Muhammad Nawaz;Shahzad, Aamir;Taj, Muhammad;Asghar, Sehar;Fatahi-Vajari, Alireza;Singh, Rahul;Tounsi, Abdelouahed
    • Advances in Computational Design
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    • v.5 no.4
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    • pp.363-380
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    • 2020
  • In this paper, a cylindrical shell is immersed in a non-viscous fluid using first order shell theory of Sander. These equations are partial differential equations which are solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. Throughout the computation, simply supported edge condition is used. Expressions for modal displacement functions, the three unknown functions are supposed in such way that the axial, circumferential and time variables are separated by the product method. Comparison is made for empty and fluid-filled cylindrical shell with circumferential wave number, length- and height-radius ratios, it is found that the fluid-filled frequencies are lower than that of without fluid. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

A Bifurcation Analysis of Space Structures by Using 3D Beam-Column Element Considering Finite Deformations and Bowing Effect (유한변형과 굽힘효과가 고려된 3차원 보-기둥요소에 의한 공간구조물의 분기좌굴해석)

  • Lee, Kyung-Soo;Han, Sang-Eul
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.22 no.4
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    • pp.307-314
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    • 2009
  • The present paper briefly describes the space frame element and the fundamental strategies in computational elastic bifurcation theory of geometrically nonlinear, single load parameter conservative elastic spatial structures. A method for large deformation(rotation) analysis of space frame is based on an eulerian formulation, which takes into consideration the effects of large joint translations and rotations with finite deformation(rotation). The local member force-deformation relationships are based on the beam-column approach, and the change in member chord lengths caused by axial strain and flexural bowing are taken into account. and the derived geometric stiffness matrix is unsymmetric because of the fact that finite rotations are not commutative under addition. To detect the singular point such as bifurcation point, an iterative pin-pointing algorithm is proposed. And the path switching mode for bifurcation path is based on the non-negative eigen-value and it's corresponding eigen-vector. Some numerical examples for bifurcation analysis are carried out for a plane frame, plane circular arch and space dome structures are described.

Formulation of Optimal Design Parameters and Failure Map for Metallic Sandwich Plates with Inner Dimpled Shell Structure Subject to Bending Moment (굽힘 하중을 받는 딤플형 내부구조 금속 샌드위치 판재의 최적설계변수의 수식화 및 파손선도)

  • Seong Dae-Yong;Jung Chang-Gyun;Yoon Seok-Joon;Ahn Dong-Gyu;Yang Dong-Yol
    • Journal of the Korean Society for Precision Engineering
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    • v.23 no.8 s.185
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    • pp.127-136
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    • 2006
  • Metallic sandwich plates with inner dimpled shell subject to 3-point bending have been analyzed and then optimized for minimum weight. Inner dimpled shells can be easily fabricated by press or roll with high precision and bonded with same material skin sheets by resistance welding or adhesive bonding. Metallic sandwich plates with inner dimpled shell structure can be optimally designed for minimum weight subject to prescribed combination of bending and transverse shear loads. Fundamental findings for lightweight design are presented through constrained optimization. Failure responses of sandwich plates are predicted and formulated with an assumption of narrow sandwich beam theory. Failure is attributed to four kinds of mechanisms: face yielding, face buckling, dimple buckling and dimple collapse. Optimized shape of inner dimpled shell structure is a hemispherical shell to minimize weight without failure. It is demonstrated that bending stiffness of sandwich plate is 2 or 3 times larger than solid plates with the same strength. Failure mode boundaries and iso-strength lines dependent upon the geometry and yield strain of the material are plotted with respect to geometric parameters on the failure map. Because optimal parameters of maximum strength for given material weight can be selected from the map, analytic solutions for maximum strength are expressed as a function of only material property and proposed strength. These optimal parameters match well with numerical optimal parameters.