Abstract
In this work, a new vertex-based finite volume method (FVM) using unstructured grids and cell-based data structure is proposed for computational analysis of two-and three-dimensional (2D/3D) general structural dynamic problems. The governing equations are spatially discretized by the FVM and an implicit dual time stepping scheme is employed to integrate the equations in time. The proposed method is applied to calculate deformations and dynamics of 2D and 3D cantilevers, as well as simply supported and clamped square plates. Computational results obtained are found to agree well with analytical solutions. It can be a viable alternative to the traditional finite element method (FEM) for structural dynamic calculations. And it can be seamlessly integrated into FVM-based Computational Fluid Dynamics (CFD) solver for simulating fluid-structure interaction (FSI).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Onate E, Cevera M, Zienkiewicz OC (1994) A finite volume method format for structural mechanics. Int J Numerical Methods Eng 37:181–201
Idelsohn SR, Onate E (1994) Finite volumes and finite elements: two ‘Good Friends’. Int J Numerical Methods Eng 37:3323–3341
Demirdzic I, Muzaferija S, Peric M (1997) Benchmark solutions of some structural analysis problems using finite volume method and multigrid acceleration. Int J Numerical Methods Eng 40:1893–1908
Wheel MA (1997) A finite volume method for analysing the bending deformation of thick and thin plates. Comput Methods Appl Mech Eng 147:199–208
Fallah N (2004) A cell vertex and cell centered finite volume method for plate bending analysis. Comput Methods Appl Mech Eng 193:3457–3470
Demirdzic I, Muzaferija S, Peric M (1994) Finite volume method for stress analysis in complex domains. Int J Numerical Methods Eng 37:3751–3766
Bailey C, Cross M (1995) A finite volume procedure to solve elastic solid mechanics problems in three dimensions on an unstructured mesh. Int J Numerical Methods Eng 38:1756–1776
Demirdzic I, Martinovic D (1993) Finite volume method for thermo-elasto plastic stress analysis. Comput Methods Appl Mech Eng 109:331–349
Slone AK, Bailey C, Cross M (2003) Dynamic solid mechanics using finite volume methods. Appl Math Model 27:69–87
Slone AK, Pericleous K, Bailey C, Cross M, Bennet C (2004) A finite volume unstructured mesh approach to dynamic fluid-structure interaction: an assessment of the challenge of predicting the onset of flutter. Appl Math Model 28:211–239
Wheel MA (1996) Geometrically versatile finite volume formulation for plane strain elastostatic stress analysis. J Strain Anal Eng Des 31:111–116
Taylor GA, Bailey C, Cross M (2003) A vertex-based finite volume method applied to non-linear material problems in computational solid mechanics. Int J Numerical Methods Eng 56:507–529
Xia GH, Zhao Y, Yeo JH (2005) Numerical simulation of 3D fluid-structure interaction using an immersed membrane method. Mod Phys Lett 19:28–29
Zhao Y, Tai CH (2001) Higher-order characteristics-based methods for incompressible flow computation on unstructured grids. AIAA J 39(7):1280–1287
Zhao Y, Zhang BL, Tan CH (2002) A high-resolution characteristics-based implicit dual time stepping VOF method for free surface flow simulation on unstructured grids. J Comput Phys 183
Tai CH, Zhao Y, Liew KM (2005) An unstructured parallel-multigrid matrix-free implicit method for computation of unsteady incompressible viscous flows using a high-resolution characteristics-based scheme. Comput Methods Appl Mech Eng 194:36–38
Jameson A (1991) Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings. AIAA Paper 91–1596, June 1991
Rogers SE, Kwak D, Kiris C (1991) Steady and unsteady solutions of the incompressible Navier-Stokes equations. AIAA J 29(4):603–610
Pedley TJ, Stephanoff KD (1985) Flow along a channel with a time-dependent indentation in one wall: the generation of vorticity waves. J Fluid Mech 160:337–367
Schiff D (1990) Dynamic analysis and failure modes of simple structure. Wiley, New York
Timoshenko SP, Goodier JN (1982) Theory of Elasticity. McGraw-Hill, New York
Fenner RT (1986) Engineering elasticity: applications of numerical and analytical techniques. Ellis Horwood, New York
Timoshenko SP (1972) Mechanics of materials. Brooks/Cole Engineering Division, Monterey
Hart GC, Wong K (1999) Structural dynamics for structural engineers. Wiley, New York
Timoshenko SP, Wienowsky-Kreiger S (1959) Theory of plates and shells, 2nd edn. McGraw-Hill, New York
Leissa AW (1973) The free vibration of rectangular plates. J Sound Vib 31(3):257–293
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xia, G.H., Zhao, Y., Yeo, J.H. et al. A 3D implicit unstructured-grid finite volume method for structural dynamics. Comput Mech 40, 299–312 (2007). https://doi.org/10.1007/s00466-006-0100-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-006-0100-7