PSI - Issue 5

Behzad V. Farahani et al. / Procedia Structural Integrity 5 (2017) 584–591 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2017) 000 – 000

590

7

densities. The RBF results compared to the exact solution is shown in Fig. 4-a. To access the performance of the presented optimal shape parameter, the relative error was thereby evaluated for various mesh densities, see Fig. 4-b.

0,002

0,00428

0,0016

0,0012

0,00427

0,0008

Error

w max

Exact RBF

0,0004

0

0,00426

0

1000

2000

3000

0

1000

2000

3000

Number of nodes

Number of nodes

(a)

(b)

Fig. 4. RBF analysis if k = 1.75 for several mesh densities (a) the maximum transverse displacement results and (b) the relative error.

5. Conclusion In the present study, a single-layered isotropic plate under a uniform distributed load was numerically analyzed. The Reissner-Mindlin plate deformation theory combined with a Wendland’s Radial Basis Function meshless formulation was considered. The supporting method revealed to be adequate to analyse any geometry with the same governing equations, providing suitable boundary conditions were assumed and imposed. The equations of motion in terms of displacement based on the first-order shear deformation theory were developed in which nonzero laminate stiffnesses were defined for single layer isotopic plates. Regarding RBF definition, a piecewise smooth, compact radial functions ( ) , Wendland type order 6 (W6) was used in which the shape parameter equation ( ) was optimized based on the convergence studies using several mesh densities. Concluding the results, the maximum transverse displacement was determined through RBF formulations and the obtained results were thereby compared to exact solution (Timoshenko & Woinowsky-Krieger 1959). Consequently, the shape parameter equation was optimized. To assess functionalities of the proposed shape parameter, the relative error was thus calculated where the results demonstrated small and acceptable error values, hence the success of the present methodology was achieved. This study precisely emphasized that the RBF accuracy on displacement field mainly depends on the shape parameter equation.

Acknowledgements

The first author truly acknowledges the funding provided by Ministério da Educação e Ciência, Fundação para a Ciência e a Tecnologia (Portugal), under grants PD/BD/114095/2015 and SFRH/BPD/111020/2015. Dr. Moreira acknowledges POPH - QREN-Tipologia 4.2 - Promotion of scientific employment funded by the ESF and MCTES. Authors gratefully acknowledge the funding of Project NORTE-01-0145-FEDER-000022 - SciTech - Science and Technology for Competitive and Sustainable Industries, cofinanced by Programa Operacional Regional do Norte (NORTE2020), through Fundo Europeu de Desenvolvimento Regional (FEDER).

Reference

Carrera, E., 1996. C0 Reissner – Mindlin Multilayered Plate Elements Including Zig-Zag and Interlaminar Stress Continuity. International Journal of Numerical Methods in Engineering , 39(11), pp.1797 – 1820.