Mesh-free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in-plane point loads

International Journal for Numerical Methods in Engineering

Volumn 60, Issue 11, 2004, Pages 1861-1877

  Liew, K M ^a,b   Chen, X L ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Buckling analysis; In plane point load; Initial stress; Mesh free method; Mindlin plate; Radial basis function; RPIM

Indexed keywords

BUCKLING; ELASTICITY; INTERPOLATION; LOADS (FORCES); NUMERICAL METHODS; STRESS CONCENTRATION;

MINDLIN PLATES; POINT LOADS;

PLATES (STRUCTURAL COMPONENTS);

BUCKLING;

EID: 3242762386     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1027     Document Type: Article

References (19)

1. Timoshenko S. Stabilität einer rechteckigen platte, die durch einzelne kräste gedrückt wird. Zeitschrift für Mathematik und Physik 1910; 58:357-360.
2. Leggett DMA. The effect of two isolated forces. In Proceedings of the Cambridge Philosophical Society, vol. 33, 1937; 325-329.
3. Alfutov NA, Balabukh LI. Energy criterion of the stability of elastic bodies which does not require the determination of the initial stress-strain state. Prikladnaya Matematika i Mekhanika 1968; 32:703-707.
4. Leissa AW, Ayoub EF. Vibration and buckling of a simply supported rectangular plate subjected to a pair of in-plane concentrated forces. Journal of Sound and Vibration 1988; 127:155-171.
5. Kansa EJ. Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamics. I: Surface approximations and partial derivative estimates. Computers and Mathematics with Applications 1990; 19:127-145.
6. Kansa EJ. Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations. Computers and Mathematics with Applications 1990; 19:147-161.
7. Zhang X, Song KZ, Lu MW. Meshless methods based on collocation with radial basis functions. Computational Mechanics 2000; 26:333-343.
8. Hon YC, Wu ZM. A quasi-interpolation method for solving stiff ordinary differential equations. International Journal for Numerical Methods in Engineering 2000; 48:1187-1197.
9. Hon YC, Lu MW, Xue WM, Zhu YM. Multiquadric method for the numerical solution of a biphasic model. Applied Mathematics and Computation 1997; 88:153-175.
10. Hon YC, Lu MW, Xue WM, Zhou X. Numerical algorithm for triphasic model of charged and hydrated soft tissues. Computational Mechanics 2002; 29:1-15.
11. Liu GR, Gu YT. A point interpolation method for two-dimensional solids. International Journal for Numerical Methods in Engineering 2001; 50:937-951.
12. Wang JG, Liu GR. A point interpolation meshless method based on radial basis functions. International Journal for Numerical Methods in Engineering 2002; 54:1623-1648.
13. Wang JG, Liu GR. On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Computer Methods in Applied Mechanics and Engineering 2002; 191:2611-2630.
14. Mindlin RD. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. Transactions of the Journal of Applied Mechanics (ASME) 1951; 18:31-38.
15. Wang CM, Liew KM, Xiang Y, Kitipornchai S. Buckling of rectangular Mindlin plates with internal line supports. International Journal of Solids and Structures 1993; 30:1-17.
16. Kitipornchai S, Xiang Y, Wang CM, Liew KM. Buckling of thick skew plates. International Journal for Numerical Methods in Engineering 1993; 36:1299-1310.
17. Timoshenko SP, James MG. Theory of Elastic Stability. McGraw-Hill: Singapore, 1985.
18. Azhari M, Hoshdar S, Bradford MA. On the use of bubble functions in the local buckling analysis of plate structures by the spline finite strip method. International Journal for Numerical Methods in Engineering 2000; 48:583-593.
19. Ayoub EF, Leissa AW. Free vibration and tension buckling of circular plates with diametrical point forces. Journal of Applied Mechanics 1990; 57:995-999.