• Title/Summary/Keyword: Geometrical Nonlinear

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Geometrical Nonlinear Analysis of Thin-walled Structures by Flat Shell Elements with Drilling D.O.F. (회전자유도를 갖는 평면쉘요소에 의한 박판구조물의 기하비선형해석)

  • 최창근;송명관
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.317-324
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    • 1998
  • A nonlinear anile element formulation of flat shell elements with drilling d.o.f, is presented for the geometrical nonlinear analysis of thin-walled structures. The shell element to be applied in finite element analysis was developed by combining a membrane element named as CLM with drilling rotation d.o.f, and plate bending element. The combined shell element possesses six degrees of freedom per node. The element showed the excellent performance in the linear analysis of the folded plate structures, in which the normal rotational rigidity of folded plates is considered, therefore, using this element geometrical nonlinear analysis of those structures is fulfilled in this study. An incremental total Larangian approach is adopted through out in which displacements are referred to the original configuration. Comparing the results with those of other researches shows the performance of this element and a folded plate structure is analyzed as an example.

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Topology Optimization Using the Element Connectivity Parameterization Method in Three Dimensional Design Domain (3차원 설계 영역에서의 요소 연결 매개법을 이용한 위상 최적 설계)

  • Ho Yoon Gil;Young Kim Yoon;Soo Joung Yuung
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.29 no.7
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    • pp.990-997
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    • 2005
  • The objective of this paper is to present the element connectivity parameterization (ECP) fur three dimensional problems. In the ECP method, a continuum structure is viewed as discretized finite elements connected by zero-length elastic links whose stiffness values control the degree of inter-element connectivity. The ECP method can effectively avoid the formation of the low-density unstable elements. These elements appear when the standard element density method is used for geometrical nonlinear problems. In this paper, this ECP method developed fur two-dimensional problems is expanded to the design of three-dimensional geometrical nonlinear structures. Among others, the automatic procedure converting standard finite element models to the models suitable for the ECP approach is developed and applied for optimization problems defined on general three-dimensional design domains.

Geometrical Nonlinear Analyses of Post-buckled Columns with Variable Cross-section (후좌굴 변단면 기둥의 기하 비선형 해석)

  • Lee, Byoung Koo;Kim, Suk Ki;Lee, Tae Eun;Kim, Gwon Sik
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.1A
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    • pp.53-60
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    • 2009
  • This paper deals with the geometrical nonlinear analyses of post-buckled columns with variable cross-section. The objective columns having variable cross-section of the width, depth and square tapers are supported by both hinged ends. By using the Bernoulli-Euler beam theory, differential equations governing the elastica of post-buckled column and their boundary conditions are derived. The solution methods of these differential equations which have two unknown parameters are developed. As the numerical results, equilibrium paths, elasticas and stress resultants of the post-buckled columns are presented. Laboratory scaled experiments were conducted for validating the theories developed in this study.

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Geometrical nonlinear dynamic analysis of laminated skew plates made of advanced composite materials (적층된 ACM 경사판의 기하학적 비선형 동적 해석)

  • Lee, Sang-Youl;Chang, Suk-Yoon
    • Journal of the Korean Society for Advanced Composite Structures
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    • v.1 no.4
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    • pp.28-34
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    • 2010
  • W e performed a geometrical nonlinear dynamic analysis of laminated skew plates made of advanced composite materials (ACM ) based on the first-order shear deformation plate theory (FSDT). The Newmark method and Newton-Raphson iteration are used for the nonlinear dynamic solution. The effects of skew angles and layup sequences on the nonlinear dynamic response for various parameters are studied using a nonlinear dynamic finite element program developed for this study. The several numerical results were in good agreement with those reported by other investigators for square composite and skew plates, and the new results reported in this paper show the significant interactions between the skew angle and layup sequence in the skew laminate. Key observation points are discussed and a brief design guideline is given.

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Comparison between two geometrical nonlinear methods for truss analyses

  • Greco, M.;Menin, R.C.G.;Ferreira, I.P.;Barros, F.B.
    • Structural Engineering and Mechanics
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    • v.41 no.6
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    • pp.735-750
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    • 2012
  • This paper presents a comparison between two different procedures to deal with the geometric nonlinear analysis of space trusses, considering its structural stability aspects. The first nonlinear formulation, called positional, uses nodal positions rather than nodal displacements to describe the finite elements kinematics. The strains are computed directly from the proposed position concept, using a Cartesian coordinate system fixed in space. The second formulation, called corotational, is based on the explicit separation between rigid body motion and deformed motion. The numerical examples demonstrate the performances and the convergence of the responses for both analyzed formulations. Two numerical examples were compared, including a lattice beam with postcritical behavior. Despite the two completely different approaches to deal with the geometrical nonlinear problem, the results present good agreement.

Comprehensive evaluation of structural geometrical nonlinear solution techniques Part II: Comparing efficiencies of the methods

  • Rezaiee-Pajand, M.;Ghalishooyan, M.;Salehi-Ahmadabad, M.
    • Structural Engineering and Mechanics
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    • v.48 no.6
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    • pp.879-914
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    • 2013
  • In part I of the article, formulation and characteristics of the several well-known structural geometrical nonlinear solution techniques were studied. In the present paper, the efficiencies and capabilities of residual load minimization, normal plane, updated normal plane, cylindrical arc length, work control, residual displacement minimization, generalized displacement control and modified normal flow will be evaluated. To achieve this goal, a comprehensive comparison of these solution methods will be performed. Due to limit page of the article, only the findings of 17 numerical problems, including 2-D and 3-D trusses, 2-D and 3-D frames, and shells, will be presented. Performance of the solution strategies will be considered by doing more than 12500 nonlinear analyses, and conclusions will be drawn based on the outcomes. Most of the mentioned structures have complex nonlinear behavior, including load limit and snap-back points. In this investigation, criteria like number of diverged and complete analyses, the ability of passing load limit and snap-back points, the total number of steps and analysis iterations, the analysis running time and divergence points will be examined. Numerical properties of each problem, like, maximum allowed iteration, divergence tolerance, maximum and minimum size of the load factor, load increment changes and the target point will be selected in such a way that comparison result to be highly reliable. Following this, capabilities and deficiencies of each solution technique will be surveyed in comparison with the other ones, and superior solution schemes will be introduced.

Comprehensive evaluation of structural geometrical nonlinear solution techniques Part I: Formulation and characteristics of the methods

  • Rezaiee-Pajand, M.;Ghalishooyan, M.;Salehi-Ahmadabad, M.
    • Structural Engineering and Mechanics
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    • v.48 no.6
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    • pp.849-878
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    • 2013
  • This paper consists of two parts, which broadly examines solution techniques abilities for the structures with geometrical nonlinear behavior. In part I of the article, formulations of several well-known approaches will be presented. These solution strategies include different groups, such as: residual load minimization, normal plane, updated normal plane, cylindrical arc length, work control, residual displacement minimization, generalized displacement control, modified normal flow, and three-parameter ellipsoidal, hyperbolic, and polynomial schemes. For better understanding and easier application of the solution techniques, a consistent mathematical notation is employed in all formulations for correction and predictor steps. Moreover, other features of these approaches and their algorithms will be investigated. Common methods of determining the amount and sign of load factor increment in the predictor step and choosing the correct root in predictor and corrector step will be reviewed. The way that these features are determined is very important for tracing of the structural equilibrium path. In the second part of article, robustness and efficiency of the solution schemes will be comprehensively evaluated by performing numerical analyses.

Parametric effects on geometrical nonlinear dynamic behaviors of laminated composite skew plates (적층된 복합소재 경사판의 기하학적 비선형 동적 거동에 미치는 매개변수 영향)

  • Lee, Sang-Youl
    • Composites Research
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    • v.25 no.6
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    • pp.217-223
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    • 2012
  • This study investigates a geometrical nonlinear dynamic behaviors of laminated skew plates made of advanced composite materials (ACM). Based on the first-order shear deformation plate theory (FSDT), the Newmark method and Newton-Raphson iteration are used for the nonlinear dynamic solution. The effects of cutout sizes, skew angles and lay up sequences on the nonlinear dynamic response for various parameters are studied using a nonlinear dynamic finite element program developed for this study. The several numerical results were in good agreement with those reported by other investigators for square composite plates with or without central cutouts, and the new results reported in this paper show the significant interactions between the cutout, skew angles and layup sequence in the laminate. Key observation points are discussed and a brief design guideline of skew laminates is given.

Topology Design Optimization of Nonlinear Thermoelasticity Problems (비선형 열탄성 연성 구조물에 대한 위상 최적설계)

  • 문세준;하윤도;조선호
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.347-354
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    • 2004
  • Using an efficient adjoint variable method, we develop a unified design sensitivity analysis (DSA) method considering both steady state nonlinear heat conduction and geometrical nonlinear elasticity problems. Design sensitivity expressions with respect to thermal conductivity and Young's modulus are derived. Beside the temperature and displacement adjoint equations, another coupled one is defined regarding the obtained adjoint displacement field as the adjoint load in temperature field. The developed DSA method is shown to be very efficient and further extended to a topology design optimization method for the nonlinear weakly coupled thermo-elasticity problems using a density approach.

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Initial Shape Finding and Stress-Deformation Analysis of Pretensioned Membrane Structures with Triangular Constants Strain Element (TCS요소론 이용한 인장 막구조물의 초기명상해석 및 응력변형해석)

  • Ko, Hyuk-Jun;Song, Pyung-Hun;Song, Ho-San
    • 한국공간정보시스템학회:학술대회논문집
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    • pp.230-237
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    • 2004
  • In this study, equation of finite element is formulated to analyze relations of large deformation-small deformation considering geometrical nonlinear for membrane structure. Total Lagrangian Formulation(TLF) is introduced to formulate theory and equation of motion considering Triangular Constant Strain(TCS) element in finite, element analysis is formulated. Finite element program is made by equation of motion considering TLF. This study analyzed a variety of examples, so compared with the past results.

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