• 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.

• 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.

• 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.

• Journal of Korean Association for Spatial Structures
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• v.2 no.1 s.3
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• pp.75-84
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• 2002

In this study, the 'force density method' for shape finding of cable net structures is presented. This concept is based on the force-length ratios or force densities which are defined for each branch of the net structures. This method renders a simple linear 'analytical form finding' possible. If the free choice of the force densities is restricted by further condition, the linear method is extended to a nonlinear one. The nonlinear one can be applied to the detailed computation of networks. In this paper, the general inverse matrix is introduced to solve the nonlinear equilibrium equation including Jacobian matrix which is rectangular matrix. Several examples for linear and nonlinear analysis applied additional constraints are presented. It is shown that the force density method is suitable for form finding of cable net and the general inverse matrix can be applied to solve the nonlinear equation without Lagrangian factors.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.50 no.9
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• pp.609-616
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• 2022

The performance of antenna reflectors crucially depends on the faceting error of the surface. The force density method (FDM) has been widely used for the form-finding analysis of the cable nets of reflectors. However, after performing form-finding of some cable nets, the effective reflective area will decrease. In addition, nonlinear deformations of the cable can not be achieved by using the FDM. Thus, an effective form-find methodology is proposed in this research. The whole parts of the cable networks are described by the absolute nodal coordinate formulation. The form-finding analysis of the reflector with standard configuration is performed to validate the proposed methodology. The influence of boundary condition changes on the configuration accuracy of the cable net is investigated.

• Journal of Aerospace System Engineering
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• v.16 no.4
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• pp.68-76
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• 2022

The purpose of this paper was to design the cable networks for mesh reflector antennas, considering the flexibility of structures. An effective form-find methodology is proposed. The whole parts of the cable networks are described by the absolute nodal coordinate formulation. Additionally, nonlinear deformation of the cable can be obtained. The form-finding analysis of the reflector with standard configuration is performed, to validate the proposed methodology. The truss ring structure is numerically modeled using the frame elements. To consider the flexibility of the truss ring as well as the cable net structure, an iteration analysis between the truss ring and the cable net under tensional forces is also performed in the form-finding process. The finial configuration of the reflector with tensioned cable networks is demonstrated.

• Journal of Korean Association for Spatial Structures
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• v.12 no.1
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• pp.77-85
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• 2012

The membrane structure maintains stable form by giving initial tension to ductile membrane and increasing the stiffness of exterior that is much adopted in the large span spatial structure by making its thickness thin. This kind of membrane structure has characteristic that can express free-form curve, so the selection of structural form is very important. So, this paper proposes the expression of free-form surface based on NURBS basis function and the finite element method considering geometrical nonlinearity for the deduction of large deformation result. Also, for minimizing the approximation of the surface that is derived from the form-finding result, the interface method that change finite element mesh to NURBS is proposed. So, the optimum surface of free-form membrane is derived.

• Journal of Korean Association for Spatial Structures
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• v.17 no.4
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• pp.141-148
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• 2017

In this study, an advanced form-finding method of tensegrity unit modules is presented to apply on renovation building. Here a fitness function of maximum natural frequency which can lead to a maximum stiffness status was used for a genetic algorithm. To apply the lightweight pin-jointed structure to the renovation project is more economical over to build new structures. In this paper, two types of tensegrity unit are presented to build expanded structures, and their force densities are shown using the proposed form-finding method. The expanded structures which may influence renovation projects are presented by using the tensegrity units.

• Journal of Korean Association for Spatial Structures
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• v.10 no.2
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• pp.87-94
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• 2010

Form-Finding of tensegrity structures by eigenvalue problem is presented, In ardor to maintain the structures stable, "Form-Finding" should be performed. The types of analytical methods are known to solve this phenomenon: One is to use force density method, and the other is to apply so called, generalized inverse method. In this paper, new form finding methods are presented to obtain the self-equilibrium stress of the tensegrity structures. This method is based on the equilibrium equation of the all of the joint and the governing equation is formulated as eigonvalue problem. In order to verify this approach, numerical example(tensegrity structures) are compared with others calculated by previous methods. The solution by present method is shown identical results. Furthermore, the developed process to find the results is more efficient than previous approaches.

• International Journal of High-Rise Buildings
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• v.7 no.2
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• pp.145-151
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• 2018

Newly-designed high-rise buildings, both in China and abroad, have demonstrated new innovations from the creative concept to the creative method. from the creative concept to the creative method. At the same time, digital technology has enabled more design freedom in the vertical dimension. "Twisting" has gradually become the morphological choice of many city landmark buildings in recent years. The form seems more likely to be driven by the interaction of aesthetics and structural engineering. Environmental performance is often a secondary consideration; it is typically not simulated until the evaluation phase. Based on the research results of "DigitalFUTURE Shanghai 2017 Workshop - Wind Tunnel Visualization", an approach that can be employed by architects to design environmental-performance buildings during the early stages has been explored. The integration of a dynamic form-finding approach (DFFA) and programming transforms the complex relationship between architecture and environment into a dialogue of computer language and dynamic models. It allows the design to focus on the relationship between morphology and the surrounding environment, and is not limited to the envelope form itself. This new concept of DFFA in this research consists of three elements: 1) architectural form; 2) integration of wind tunnel and dynamic models; and 3) environmental response. The concept of wind tunnel testing integrated with a dynamic model fundamentally abandons the functional definition of the traditional static environment simulation analysis. Instead it is driven by integral environmental performance as the basic starting point of morphological generation.