×

zbMATH — the first resource for mathematics

A note on the dynamic analysis using the generalized finite difference method. (English) Zbl 1290.74043
Summary: This paper shows the application of the generalized finite difference method (GFDM) to the problem of dynamic analysis of beams and plates. The stability conditions for a fully explicit algorithm are given for beams and plates. Measures of the irregularity of the clouds of points for beams and plates are given. Various cases of vibrations of beams and plates have been solved and the results show the accuracy of the method for irregular clouds of nodes.

MSC:
74S20 Finite difference methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K20 Plates
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Liszka, T.; Orkisz, J., The finite difference method at arbitrary irregular grids and its application in applied mechanics, Computer & Structures, 11, 83-95, (1980) · Zbl 0427.73077
[2] Orkisz, J., (Kleiber, M., Finite Difference Method (Part, III) in Handbook of Computational Solid Mechanics, (1998), Spriger-Verlag Berlin)
[3] Benito, J. J.; Ureña, F.; Gavete, L., Leading-edge applied mathematical modelling research, (2008), Nova Science Publishers New York, (Chapter 7)
[4] Benito, J. J.; Ureña, F.; Gavete, L., Influence several factors in the generalized finite difference method, Applied Mathematical Modeling, 25, 1039-1053, (2001) · Zbl 0994.65111
[5] Benito, J. J.; Ureña, F.; Gavete, L.; Alvarez, R., An \(h\)-adaptive method in the generalized finite difference, Computer Methods in Applied Mechanics and Engineering, 192, 735-759, (2003) · Zbl 1024.65099
[6] Benito, J. J.; Ureña, F.; Gavete, L.; Alonso, B., Application of the generalized finite difference method to improve the approximated solution of pdes, Computer Modelling in Engineering & Sciences, 38, 39-58, (2009) · Zbl 1357.74075
[7] Gavete, L.; Gavete, M. L.; Benito, J. J., Improvements of generalized finite difference method and comparison other meshless method, Applied Mathematical Modelling, 27, 831-847, (2003) · Zbl 1046.65085
[8] Ureña, F.; Benito, J. J.; Gavete, L., Application of the generalized finite difference method to solve the advection-diffusion equation, Journal of Computational and Applied Mathematics, 235, 1849-1855, (2011) · Zbl 1209.65088
[9] Benito, J. J.; Ureña, F.; Gavete, L.; Alonso, B., Solving parabolic and hyperbolic equations by generalized finite difference method, Journal of Computational and Applied Mathematics, 209, 2, 208-233, (2007) · Zbl 1139.35007
[10] Thomson, W. T., Vibration theory and applications, (1965), Prentice Hall Publishers
[11] Timoshenko, S. P.; Young, D. H., Theory of structures, (1965), McGraw-Hill
[12] Weaver, W.; Timoshenko, S. P.; Young, D. H., Vibration problems in engineering, (1990), John Wiley & Sons, Inc. New York
[13] Vinson, J. R., The behavoir or thin walled strutures: beams, plates ans shells, (1989), Kluwer Academic Publishers Boston
[14] Mitchell, A. R.; Griffiths, D. F., The finite difference method in partial differential equations, (1980), John Wiley & Sons New York · Zbl 0417.65048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.