JZUS - Journal of Zhejiang University SCIENCE

Journal of Zhejiang University SCIENCE A 2014 Vol.15 No.4 P.255-271

An efficient numerical shape analysis for light weight membrane structures*

Author(s): Chao Yang, Yan-bin Shen, Yao-zhi Luo
Affiliation(s): . Space Structures Research Center, Zhejiang University, Hangzhou 310058, China
Corresponding email(s): benjamin127@163.com
Key Words: Tension membranes, Finite particle method (FPM), Shape analysis, Explicit time integration, Initial equilibrium shape

Share this article to： More <<< Previous Article \|Next Article >>>

Chao Yang, Yan-bin Shen, Yao-zhi Luo. An efficient numerical shape analysis for light weight membrane structures[J]. Journal of Zhejiang University Science A, 2014, 15(4): 255-271.

@article{title="An efficient numerical shape analysis for light weight membrane structures",
author="Chao Yang, Yan-bin Shen, Yao-zhi Luo",
journal="Journal of Zhejiang University Science A",
volume="15",
number="4",
pages="255-271",
year="2014",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1300245"
}

%0 Journal Article
%T An efficient numerical shape analysis for light weight membrane structures
%A Chao Yang
%A Yan-bin Shen
%A Yao-zhi Luo
%J Journal of Zhejiang University SCIENCE A
%V 15
%N 4
%P 255-271
%@ 1673-565X
%D 2014
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1300245

TY - JOUR
T1 - An efficient numerical shape analysis for light weight membrane structures
A1 - Chao Yang
A1 - Yan-bin Shen
A1 - Yao-zhi Luo
J0 - Journal of Zhejiang University Science A
VL - 15
IS - 4
SP - 255
EP - 271
%@ 1673-565X
Y1 - 2014
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1300245

Abstract
Chinese Summary
Academic Network
Reviewer Comment

Abstract: The determination of initial equilibrium shapes is a common problem in research work and engineering applications related to membrane structures. Using a general structural analysis framework of the finite particle method (FPM), this paper presents the first application of the FPM and a recently-developed membrane model to the shape analysis of light weight membranes. The FPM is rooted in vector mechanics and physical viewpoints. It discretizes the analyzed domain into a group of particles linked by elements, and the motion of the free particles is directly described by Newton’s second law while the constrained ones follow the prescribed paths. An efficient physical modeling procedure of handling geometric nonlinearity has been developed to evaluate the particle interaction forces. To achieve the equilibrium shape as fast as possible, an integral-form, explicit time integration scheme has been proposed for solving the equation of motion. The equilibrium shape can be obtained naturally without nonlinear iterative correction and global stiffness matrix integration. Two classical curved surfaces of tension membranes produced under the uniform-stress condition are presented to verify the accuracy and efficiency of the proposed method.

一种用于薄膜结构形态分析的新型数值计算方法

研究目的：为轻质柔性薄膜结构初始形态的确定提供一种准确、高效的新型数值模拟方法。
创新要点：1.建立基于有限质点法（FPM）的柔性薄膜非线性计算理论，并将其首次应用于膜结构的形态问题分析之中；2.提出一种将动力控制方程通过积分转化为动量方程，并利用加速静力收敛策略，快速获得初始平衡状态的方法。
研究方法：1.基于向量式固体力学的基本概念，将分析域离散为一系列质点，建立有限质点法柔性膜结构计算模型，并用牛顿第二定律描述质点运动（图1~图3）；2.采用一套基于物理模式的分析步骤来描述分析对象的几何非线性变形，有效扣除刚体运动的影响以准确获得质点间的相互作用内力（图4~图7）；3.根据膜内给定的预应力分布，按照膜结构初始形态分析步骤进行循环迭代求解（图9）。
重要结论：利用本文算法确定膜结构初始形态，计算速度快、准确性高，并且求解过程中不会因非线性变形而引起数值计算方面的困难。

关键词：膜结构；有限质点法；形态分析；显式时间积分；初始平衡态

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

References

[1] Argyris, J.H., Angelopoulos, T., Bichat, B., 1974. A general method for the shape finding of lightweight tension structures. Computer Methods in Applied Mechanics and Engineering, 3(1):135-149.

[2] Barnes, M., 1999. Form finding and analysis of tension structures by dynamic relaxation. International Journal of Space Structures, 14(2):89-104.

[3] Belytschko, T., Liu, W.K., Moran, B., 2000. Nonlinear Finite Elements for Continua and Structures. Wiley,New York :544-549.

[4] Bonet, J., Wood, R.D., 1997. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press,Cambridge, UK :57-113.

[5] Brew, J.S., Lewis, W.J., 2003. Computational form-finding of tension membrane structures: non-finite element approaches: Part 1. Use of cubic splines in finding minimal surface membranes. International Journal for Numerical Methods in Engineering, 56(5):651-668.

[6] Brew, J.S., Lewis, W.J., 2007. Free hanging membrane model for shell structures. International Journal for Numerical Methods in Engineering, 71(13):1513-1533.

[7] Chang, S., Tsai, K., Chen, K., 1998. Improved time integration for pseudodynamic tests. Earthquake Engineering & Structural Dynamics, 27(7):711-730.

[8] Gosling, P.D., Lewis, W.J., 1996. Optimal structural membranes-I. Form-finding of prestressed membranes using a curved quadrilateral finite element for surface definition. Computers & Structures, 61(5):885-895.

[9] Haug, E., Powell, G.H., 1972. Finite element analysis of nonlinear membrane structures. , IASS Pacific Symposium Part II: on Tension Structures and Space Frames, Tokyo and Kyoto, Japan, 93-102. :93-102.

[10] Jenkins, C.H.M., 2001. Gossamer spacecraft: membrane and inflatable structures technology for space applications. Progress in Astronautics and Aeronautics. AIAA,Reston, VA 191:

[11] Kilian, A., Ochsendorf, J., 2005. Particle-spring systems for structural form finding. Journal of the International Association for Shell and Spatial Structures, 46(2):77-84.

[12] Lewis, W.J., 2003. Tension Structures: Form and Behaviour. Thomas Telford,London :

[13] Lewis, W.J., Lewis, T.S., 1996. Application of formian and dynamic relaxation to the form-finding of minimal surfaces. Journal of the International Association for Shell and Spatial Structures, 37(3):165-186.

[14] Maurin, B., Motro, R., 1998. The surface stress density method as a form-finding tool for tensile membranes. Engineering Structures, 20(8):712-719.

[15] Otto, F., Rasch, B., 1995. Finding Form: Towards an Architecture of the Minimal. Edition Axel Menges,Fellbach, Deutschland :

[16] Pauletti, R.M.O., Pimenta, P.M., 2008. The natural force density method for the shape finding of taut structures. Computer Methods in Applied Mechanics and Engineering, 197(49-50):4419-4428.

[17] Schek, H.J., 1974. The force density method for form finding and computation of general networks. Computer Methods in Applied Mechanics and Engineering, 3(1):115-134.

[18] Shih, C., Wang, Y.K., Ting, E.C., 2004. Fundamentals of a vector form intrinsic finite element: Part III. Convected material frame and example. Journal of Mechanics, 20(2):133-143.

[19] Ting, E.C., Shih, C., Wang, Y.K., 2004. Fundamentals of a vector form intrinsic finite element: Part I. Basic procedure and a plane frame element. Journal of Mechanics, 20(2):113-122.

[20] Veenendaal, D., Block, P., 2012. An overview and comparison of structural form finding methods for general networks. International Journal of Solids and Structures, 49(26):3741-3753.

[21] Wood, R.D., 2002. A simple technique for controlling element distortion in dynamic relaxation form-finding of tension membranes. Computers & Structures, 80(27-30):2115-2120.

[22] Wchner, R., Bletzinger, K.U., 2005. Stress-adapted numerical form finding of pre-stressed surfaces by the updated reference strategy. International Journal for Numerical Methods in Engineering, 64(2):143-166.

[23] Ye, J., Feng, R., Zhou, S., 2011. The modified dynamic relaxation method for the form-finding of membrane structures. Advanced Science Letters, 4(8-10):2845-2853.

[24] Yu, Y., 2010. Progressive Collapse of Space Steel Structures based on the Finite Particle Method. PhD Thesis, (in Chinese), Zhejiang University,Hangzhou, China :

[25] Yu, Y., Luo, Y.Z., 2009. Finite particle method for kinematically indeterminate bar assemblies. Journal of Zhejiang University-SCIENCE A, 10(5):667-676.

[26] Yu, Y., Luo, Y.Z., 2009. Motion analysis of deployable structures based on the rod hinge element by the finite particle method. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 223:156-171.

[27] Yu, Y., Luo, Y.Z., Paulino, G.H., 2011. Finite particle method for progressive failure simulation of truss structures. ASCE Journal of Structural Engineering, 137(10):1168-1181.

[28] Yuan, S., Liu, X., Ye, K., 2010. FEMOL solution for minimal surface form finding of tensile membrane structures. China Civil Engineering Journal, (in Chinese),43(11):1-7.

Similar articles

- Go to

一种用于薄膜结构形态分析的新型数值计算方法

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

References