• Title/Summary/Keyword: form-finding

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New Form-Finding Method combined Genetic Algorithms and Force Density Method (유전알고리즘과 내력밀도법을 결합한 새로운 형상탐색방법)

  • Yoon, Byoung-Wook;Lee, Jae-Hong;Kang, Joo-Won
    • Journal of the Architectural Institute of Korea Structure & Construction
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    • v.30 no.8
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    • pp.3-8
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    • 2014
  • Tensegrity structures are pre-stressed pin-joint structures inclusive tensile members and compressive members. Form-finding is very important for Tensegrity structures need to determine shape and pre-stress value for self-equilibrium. In the form-finding of tensegrity structures, Infomation are usually introduced for initial geometry and pre-determined member types. In this study, Form-finding of tensegrity structures by using genetic easy and versatile form-finding processing requires only a minimal information 'topology'. Genetic Algorithms was determined the type of members. The form-finding of tensegrity structures are found by a full iteration pocedure until a state of self-stress is obtained.

Linear Form Finding Approach for Regular and Irregular Single Layer Prism Tensegrity

  • Moghaddas, Mohammad;Choong, Kok Keong;Kim, Jae-Yeol;Kang, Joo-Won
    • International journal of steel structures
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    • v.18 no.5
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    • pp.1654-1665
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    • 2018
  • In an irregular prism tensegrity, the number of force equilibrium equations is less than the number of unknown parameters of nodal coordinates and member force ratios. As a result, the form-finding process normally becomes nonlinear with additional conditions or needs to be carried out with the use of iterative procedures. For cases of irregular prism tensegrity which involves large number of members, it was found that previously proposed methods of form-finding are not practical. Moreover, there is a need for a form-finding approach which is able to cater to different requirements on final configuration. In this paper, the length relation condition is introduced to be used in combination with the force equilibrium equation. With the combined use of length relation and equilibrium conditions, a linear form-finding approach for irregular prism tensegrity was successfully formulated and developed. An easy-to-use interactive form-finding tool has been developed which can be used for form-finding of irregular prism tensegrities with large number of elements as well as under diverse specific requirements on their configurations.

Comparison of viscous and kinetic dynamic relaxation methods in form-finding of membrane structures

  • Labbafi, S. Fatemeh;Sarafrazi, S. Reza;Kang, Thomas H.K.
    • Advances in Computational Design
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    • v.2 no.1
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    • pp.71-87
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    • 2017
  • This study focuses on the efficiency and applicability of dynamic relaxation methods in form-finding of membrane structures. Membrane structures have large deformations that require complex nonlinear analysis. The first step of analysis of these structures is the form-finding process including a geometrically nonlinear analysis. Several numerical methods for form-finding have been introduced such as the dynamic relaxation, force density method, particle spring systems and the updated reference strategy. In the present study, dynamic relaxation method (DRM) is investigated. The dynamic relaxation method is an iterative process that is used for the static equilibrium analysis of geometrically nonlinear problems. Five different examples are used in this paper. To achieve the grading of the different dynamic relaxation methods in form-finding of membrane structures, a performance index is introduced. The results indicate that viscous damping methods show better performance than kinetic damping in finding the shapes of membrane structures.

A Form-finding of Planar Tensegrity Structures

  • Lee, Sang Jin
    • Architectural research
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    • v.14 no.4
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    • pp.143-152
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    • 2012
  • A form-finding procedure is presented for planar tensegrity structures. Notably, a simple decision criteria is proposed to select the desirable candidate position vector from the unitary matrix produced by the eigenvalue decomposition of force density matrix. The soundness of the candidate position vector guarantees faster convergence and produces a desirable form of tensegrity without any member having zero-length. Several numerical examples are provided to demonstrate the capability of the proposed form-finding process.

A Comparison of the Form-Finding Method of Tensegrity Structures (텐세그리티 구조물의 형상탐색 기법 비교)

  • Lee, Seunghye;Lee, Jaehong
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.27 no.4
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    • pp.313-320
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    • 2014
  • A tensegrity structure consists of a set of continuous cables in tension and a set of discontinuous struts in compression. The tensegrity structure can be classified into self-stressed and pre-stressed pin-jointed structure. A key step in the design of tensegrity structures is the determination of their equilibrium configuration, known as form-finding. In this paper, three effective methods are presented for form-finding of tensegrity structures. After performing form-finding process, a set of force density and corresponding topology results can be obtained. Then the force density method combined with a genetic algorithm is adopted to uniquely define a single integral feasible set of force densities. Numerical examples are presented that demonstrate the excellent performance of the algorithms.

A Form-finding Technique for Three-dimensional Spatial Structures

  • Lee, Sang Jin
    • Architectural research
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    • v.15 no.4
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    • pp.207-214
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    • 2013
  • A form-finding technique is proposed for three-dimensional spatial structures. Two-step discrete finite element (FE) mesh generator based on computer aided geometric design (CAGD) is introduced and used to control the shape of three-dimensional spatial structures. Mathematical programming technique is adopted to search new forms (or shapes) of spatial structures. For this purpose, the strain energy is introduced as the objective function to be minimized and the initial volume (or the initial weight) is considered as constraint function. Numerical examples are carried out to test the capability of the proposed form-finding techniques and provided as benchmark tests.

Form-finding analysis of suspension bridges using an explicit Iterative approach

  • Cao, Hongyou;Zhou, Yun-Lai;Chen, Zhijun;Wahab, Magd Abdel
    • Structural Engineering and Mechanics
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    • v.62 no.1
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    • pp.85-95
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    • 2017
  • This paper presents an explicit analytical iteration method for form-finding analysis of suspension bridges. By extending the conventional analytical form-finding method predicated on the elastic catenary theory, two nonlinear governing equations are derived for calculating the accurate unstrained lengths of the entire cable systems both the main cable and the hangers. And for the gradient-based iteration method, the derivation of explicit calculation for the Jacobian matrix while solving the nonlinear governing equation enhances the computational efficiency. The results from sensitivity analysis show well performance of the explicit Jacobian matrix compared with the traditional finite difference method. According to two numerical examples of long span suspension bridges studied, the proposed method is also compared with those reported approaches or the fundamental criterions in suspension bridge structural analysis, which eventually confirms the accuracy and efficiency of the proposed approach.

A Study on the Form Finding and Optimal Cutting Pattern Analysis Technique of Membrane Structures (막구조물의 형상탐색 및 최적재단도 해석기법에 관한 연구)

  • 서삼열
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.12 no.3
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    • pp.457-464
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    • 1999
  • The object of this study is form finding, stress-strain analysis and cutting pattern analysis of membrane structures under the following assumptions : (1) material is linearly elastic (2) stress state is plane stress. The cable and membrane structures undergo large deformation because of its highly flexibility, therefore, we must take account of its geometric nonlinearity. The analysis procedure is consisted of three steps considering geometric nonlinearity unlike any other structures. First step is the form finding analysis to determine the initial equilibrium shape. Second step is the stress-strain analysis to investigate the behaviors of structures under various external loads. Once a stationary shape has been fount a cutting pattern based on the form finding analysis may be generated for manufacturing procedure. In this paper, form finding, stress-strain analysis and cutting pattern analysis is carried out for applying to Seoguipo worldcup soccer stadium roof structures and optimal cutting pattern analysis technique is proposed.

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An Extended Force Density Method for the form finding of cable systems with new forms

  • Malerba, P.G.;Patelli, M.;Quagliaroli, M.
    • Structural Engineering and Mechanics
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    • v.42 no.2
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    • pp.191-210
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    • 2012
  • The Force Density Method (FDM) is a well known and extremely versatile tool in form finding of cable nets. In its linear formulation such method makes it possible to find all the possible equilibrium configurations of a net of cables having a certain given connectivity and given boundary conditions on the nodes. Each singular configuration corresponds to an assumed force density distribution. Its improvement as Non-Linear Force Density Method (NLFDM) introduces the possibility of imposing assigned relative distances among the nodes, the tensile level in the elements and/or their initial undeformed length. In this paper an Extended Force Density Method (EFDM) is proposed, which makes it possible to set conditions in terms of given fixed nodal reactions or, in other words, to fix the positions of a certain number of nodes and, at the same time, to impose the intensity of the reaction force. Through such extension, the (EFDM) enables us to deal with form findings problems of cable nets subjected to given constraints and, in particular, with mixed structures, made of cables and struts. The efficiency and the robustness of method are assessed through comparisons with other form finding techniques in dealing with characteristic applications to the prestress design of cable systems. As a further extension, the EFDM is applied to structures having some parts not yet geometrically defined, as can happen in designing new creative forms.

Form Finding of a Single-layered Pneumatic Membrane Structures by Using Nonlinear Force Method (비선형 내력법을 이용한 단일 공기막의 형상 탐색)

  • Shon, Sudeok;Ha, Junhong;Lee, Seungjae
    • Journal of Korean Association for Spatial Structures
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    • v.21 no.4
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    • pp.49-56
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    • 2021
  • This study aims to develop a form-finding algorithm for a single-layered pneumatic membrane. The initial shape of this pneumatic membrane, which is an air-supported type pneumatic membrane, is to find a state in which a given initial tension and internal pneumatic pressure are in equilibrium. The algorithm developed to satisfy these conditions is that a nonlinear optimization problem based on the force method considering the deformed shape is formulated, and, it's able to find the shape by iteratively repeating the process of obtaining a solution of the governing equations. An computational technique based on the Gauss-Newton method was used as a method for obtaining solutions of nonlinear equations. In order to verify the validity of the proposed form-finding algorithm, a single-curvature pneumatic membrane example and a double-curvature air pneumatic membrane example were adopted, respectively. In the results of these examples, it was possible to well observe the step-by-step convergence process of the shape of the pneumatic membrane, and it was also possible to confirm the change in shape according to the air pressure. In addition, the calculation results of the shape and internal force after deformation due to initial tension, air pressure, and self-weight were obtained.