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A finite volume method for deformation analysis of woven fabrics. (English) Zbl 0977.74071
From the summary: This paper presents a finite volume method for the simulation of complex deformations of initially flat woven fabric sheets under self-weight or externally applied loading. The fabric sheet is assumed to undergo large displacements and rotations, but small strains during the deformation. The fabric material is assumed to be linear elastic and orthotropic. The fabric sheet is discretized into many small structured patches called finite volumes (or control volumes), each containing one grid node and several face nodes. The bending and membrane deformations of a typical volume can be defined using the global coordinates of its grid node and surrounding face nodes. The equilibrium equations governing the complex deformations are derived employing the principle of stationary total potential energy. These equations are solved using a single-step full Newton-Raphson method which is found to be capable of predicting the final deformed shape, the only result of interest in a fabric drape analysis.

##### MSC:
 74S10 Finite volume methods applied to problems in solid mechanics 74E30 Composite and mixture properties
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##### References:
 [1] Hu, Finite Element in Analysis and Design 21 pp 225– (1996) · Zbl 0875.73383 [2] Ng, IEEE Computer Graphics and Applications 16 pp 28– (1996) · Zbl 05086639 [3] Weil, Computer Graphics (Proc. Siggraph) 20 pp 49– (1986) [4] Geometric modeling of draped fabric surfaces. In Graphics, Design and Visualization (Proceedings of International Conference On Computer Graphics), (eds). Jaico Publishing House: Bombay, 1993; 173-180. [5] Modeling the appearance of cloth. Master’s Dissertation, Massachusetts Institute of Technology, Cambridge, 1986. [6] Terzopoulos, Computer Graphics 21 pp 205– (1987) [7] Techniques for cloth animation. In New Trends in Animation and Visualization, (eds). Wiley: Chichester, 1991; 243-256. [8] Cloth animation with self-collision detection. In Modeling in Computer Graphics, (ed.). Springer: Berlin, 1991; 179-187. [9] Carignan, Computer Graphics (Proc. Siggraph) 26 pp 99– (1992) [10] A particle-based computational model of cloth draping Behavior. In Scientific Visualization of Physical Phenomena (Proceedings of CG International), (ed.). Tokyo, 1991; 113-134. [11] Breen, The Visual Computer 8 pp 264– (1992) [12] A Particle-based model for simulating the draping behavior of woven cloth. Doctoral Dissertation, Rensselaer Polytechnic Institute, New York, 1993. [13] Breen, Textile Research Journal 64 pp 663– (1994) [14] The Standardization and Analysis of Hand Evaluation. Hand Evaluation and Standardization Committee of the Textile Machinery Society of Japan: Osaka, Japan, 1975. [15] Eberhardt, IEEE Computer Graphics and Applications 16 pp 51– (1996) · Zbl 05086641 [16] Stylios, International Journal of Clothing Science and Technology 7 pp 10– (1995) [17] Stylios, International Journal of Clothing Science and Technology 8 pp 95– (1996) [18] The lumped-parameter or bar-node model approach to thin shell analysis. In Numerical and Computer Methods in Structural Mechanics, (eds). Academic Press: London, 1973; 337-402. [19] The analysis of complex fabric deformations. In Mechanics of Flexible Fiber Assemblies, (eds). Sijthoff & Noordhoff, Alpen aan den Rijn: Netherlands, 1980; 311-342. [20] Collier, Journal of Textile Institute 82 pp 96– (1991) [21] Gan, Textile Research Journal 65 pp 660– (1995) [22] Fabric mechanics analysis using large deformation orthotropic shell theory. Doctoral Dissertation, North Carolina State University, Rayleigh, NC, 1991. [23] Simo, Computer Methods in Applied Mechanics and Engineering 72 pp 267– (1989) · Zbl 0692.73062 [24] Simo, Computer Methods in Applied Mechanics and Engineering 73 pp 53– (1989) · Zbl 0724.73138 [25] Simo, Computer Methods in Applied Mechanics and Engineering 79 pp 21– (1990) · Zbl 0746.73015 [26] Nonlinear fabric mechanics including material nonlinearity, contact, and an adaptive global solution algorithm. Doctoral Dissertation, North Carolina State University, Rayleigh, NC, 1994. [27] Eischen, IEEE Computer Graphics and Applications 16 pp 71– (1996) · Zbl 05086643 [28] Chen, Textile Research Journal 65 pp 324– (1995) [29] Drape properties of woven fabrics. Proceedings of 2nd Asian Textile Conference, vol. 1, 1993; 455-459. [30] Kang, Journal of Textile Institute 86 pp 635– (1995) [31] Finite Element Procedures in Engineering Analysis. Prentice-Hall: New Jersey, 1982. [32] Ascough, International Journal of Clothing Science and Technology 8 pp 59– (1996) [33] Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corporation: New York, 1980. · Zbl 0521.76003 [34] A Introduction to Computational Fluid Dynamics, The Finite Volume Method. Longman Scientific and Technical: Burnt Mill, Harlow, 1995. [35] Fryer, Applied Mathematical Modelling 15 pp 639– (1991) · Zbl 0833.73074 [36] Bailey, International Journal for Numerical Methods in Engineering 38 pp 1757– (1995) · Zbl 0822.73079 [37] Demirdzic, Computer Methods in Applied Mechanics and Engineering 109 pp 331– (1993) · Zbl 0846.73076 [38] Demirdzic, International Journal for Numerical Methods in Engineering 37 pp 3751– (1994) · Zbl 0814.73075 [39] Onate, International Journal for Numerical Methods in Engineering 37 pp 181– (1994) · Zbl 0795.73079 [40] Wheel, International Journal of Pressure Vessels Piping 68 pp 311– (1996) [41] Wheel, Computer Methods in Applied Mechanics and Engineering 147 pp 199– (1997) · Zbl 0887.73079 [42] Numerical Recipes in C: The Art of Scientific Computing (2nd edn). Cambridge University Press: New York, 1992. · Zbl 0845.65001 [43] Finite Element Procedures. Prentice Hall: Englewood cliffs, New Jersey, 1996. [44] Non-linear Finite Element Analysis of Solids and Structures, vol. 1: Essentials. Wiley: Chichester, 1991. [45] Chen, Textile Research Journal 66 pp 17– (1996) [46] Riks, International Journal of Solids and Structures 15 pp 524– (1979) · Zbl 0408.73040 [47] Schweizerhof, Computer Methods in Applied Mechanics and Engineering 72 pp 267– (1986)
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