• Structural Engineering and Mechanics
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• v.84 no.5
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• pp.605-618
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• 2022

Glass fiber reinforced polymer (GFRP) elastic gridshells consist of long continuous GFRP tubes that form elastic deformations. In this paper, a method for the form-finding of gridshell structures is presented based on the interpretable machine learning (ML) approaches. A comparative study is conducted on several ML algorithms, including support vector regression (SVR), K-nearest neighbors (KNN), decision tree (DT), random forest (RF), AdaBoost, XGBoost, category boosting (CatBoost), and light gradient boosting machine (LightGBM). A numerical example is presented using a standard double-hump gridshell considering two characteristics of deformation as objective functions. The combination of the grid search approach and k-fold cross-validation (CV) is implemented for fine-tuning the parameters of ML models. The results of the comparative study indicate that the LightGBM model presents the highest prediction accuracy. Finally, interpretable ML approaches, including Shapely additive explanations (SHAP), partial dependence plot (PDP), and accumulated local effects (ALE), are applied to explain the predictions of the ML model since it is essential to understand the effect of various values of input parameters on objective functions. As a result of interpretability approaches, an optimum gridshell structure is obtained and new opportunities are verified for form-finding investigation of GFRP elastic gridshells during lifting construction.

• 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 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.

• 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.

• Architectural research
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• v.17 no.1
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• pp.31-40
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• 2015

A simple force-finding process based on an optimization technique is proposed for tensegrity structures. For this purpose, the inverse problem of form-finding process is formulated. Therefore, the position vector of nodes and element connectivity information are provided as priori. Several benchmark tests are carried out to demonstrate the performance of the present force-finding process. In particular, the force density distributions of simplex tensegrity are thoroughly investigated with the important parameters such as the radius, height and twisting angle of simplex tensegrity. Finally, the force density distribution of arch tensegrity is produced by using the present force-finding process for a future reference solution.

• Structural Engineering and Mechanics
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• v.67 no.6
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• pp.555-563
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• 2018

Architectural fabrics membranes have not only the structural performance but also act as an efficient cladding to cover large areas. Because of the direct relationship between form and force distribution in tension membrane structures, form-finding procedure is an important issue. Ideally, once the optimal form is found, a uniform pre-stressing is applied to the fabric which takes the form of a minimal surface. The force density method is one of the most efficient computational form-finding techniques to solve the initial equilibrium equations. In this method, the force density ratios of the borders to the membrane is the main parameter for shape-finding. In fact, the shape is evolved and improved with the help of the stress state that is combined with the desired boundary conditions. This paper is evaluated the optimum amount of this ratio considering the curvature of the flexible boarders for structural configurations, i.e., hypar and conic membranes. Results of this study can be used (in the absence of the guidelines) for the fast and optimal design of fabric structures.

• 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.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.147-151
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• 2003

In this study, we discussed the local buckling behavior of pultruded structural flexural members. Previous works were briefly reviewed and the local buckling behavior of orthotropic box-shape flexural members was discussed. The simplified form of equation for finding the width ratio of plate element of box-shape flexural members in which all plate components buckle simultaneously was proposed and the macro flow-chart for finding local buckling strength of pultruded flexural members was also suggested. To establish the design guide line for the local buckling of pultruded flexural members, further studies need to be performed as follows; the simplified form of solutions for finding the minimum buckling coefficient of orthotropic plate with various loading and boundary conditions including rotationally restrained boundary conditions, the simplified form of equation for calculating the coefficient of restraint provided by the adjacent plate elements.

• 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.11 no.4
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• pp.49-59
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• 2011

This paper presents a new numerical method by using Singular Value Decomposition force method for form-finding of tensegrity structures with constraints. In order to maintain the tensegrity structures stable, state of self-equilibrium stress should be introduced. The existing force method has some advantages about form-finding of tensegrity structures. However, this method has complex formulation. In force density method, dummy members are required for form -finding of tensegrity structures with constraints. Therefore this study proposes new force method using Singular value decomposition. The proposed method is both having easy basic consept and simple computation than existing force method. A numerical example is presented to demonstrate the efficiency and robustness in searching initial single integral feasible self-stress mode for tensegrity structures with constraints.