Skip to main content
SpringerLink
Log in

A novel meshfree radial point interpolation method with discrete shear gap for nonlinear static analysis of functionally graded plates

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

In this paper, the discrete shear gap (DSG) is for the first time incorporated into the meshfree radial point interpolation method (RPIM) for nonlinear static analysis of functionally graded plates based on Reissner–Mindlin theory. The technique of DSG, originally developed for finite element analysis during the last decades, is re-formulated to be adopted into a meshfree analysis to treat the well-known shear locking issue and to improve accuracy. As one of the rare meshfree scheme that possesses Kronecker delta property, the RPIM allows direct imposition of boundary conditions. Numerical integration is conducted by the Cartesian transformation method (CTM), which enables the possibility to avoid the creation of background cells during numerical integration, making one step further towards a truly meshfree approach, in the sense that there is no discretization of problem domain into sub-domains either in the form of elements or integration cells. For non-linear analysis, the iterative Newton-Raphson scheme is employed. Via various numerical examples, the accuracy and efficiency of the proposed approach (i.e. RPIM with DSG) is demonstrated and discussed. It is found that the DSG has better performance than other existing techniques used in meshfree RPIM analysis of Reissner–Mindlin plates.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27

Similar content being viewed by others

References

  1. Liu G-R, Tani J, Ohyoshi T (1991) Lamb waves in a functionally gradient material plate and its transient response (part 1 theory). Trans Japan Soc Mech Eng Ser A 57(535):603–608. https://doi.org/10.1299/kikaia.57.603

    Article  Google Scholar 

  2. Liu G-R, Tani J, Ohyoshi T (1991) Lamb waves in a functionally gradient material plate and its transient responses. Part 2 calculation results. Trans Japan Soc Mech Eng Ser A 57(535):609–614. https://doi.org/10.1299/kikaia.57.609

    Article  Google Scholar 

  3. Ferreira AJM, Batra RC, Roque CMC, Qian LF, Martins PALS (2005) Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method. Compos Struct 69(4):449–457. https://doi.org/10.1016/j.compstruct.2004.08.003

    Article  Google Scholar 

  4. Fares ME, Elmarghany MK, Atta D (2009) An efficient and simple refined theory for bending and vibration of functionally graded plates. Compos Struct 91(3):296–305. https://doi.org/10.1016/j.compstruct.2009.05.008

    Article  Google Scholar 

  5. Jha DK, Kant T, Singh RK (2013) A critical review of recent research on functionally graded plates. Compos Struct 96:833–849. https://doi.org/10.1016/j.compstruct.2012.09.001

    Article  Google Scholar 

  6. Nguyen-Xuan H, Tran LV, Thai CT, Kulasegaram S, Bordas SPA (2014) Isogeometric analysis of functionally graded plates using a refined plate theory. Compos B Eng 64:222–234

    Article  Google Scholar 

  7. Do VNV, Thai CH (2017) A modified Kirchhoff plate theory for analyzing thermo-mechanical static and buckling responses of functionally graded material plates. Thin-Walled Struct 117:113–126. https://doi.org/10.1016/j.tws.2017.04.005

    Article  Google Scholar 

  8. Vu T-V, Nguyen N-H, Khosravifard A, Hematiyan MR, Tanaka S, Bui TQ (2017) A simple FSDT-based meshfree method for analysis of functionally graded plates. Eng Anal Bound Elem 79:1–12

    Article  MathSciNet  MATH  Google Scholar 

  9. Thai CH, Do VNV, Nguyen-Xuan H (2016) An improved moving kriging-based meshfree method for static, dynamic and buckling analyses of functionally graded isotropic and sandwich plates. Eng Anal Bound Elem 64:122–136

    Article  MathSciNet  MATH  Google Scholar 

  10. Tessler A, Hughes TJR (1985) A three-node Mindlin plate element with improved transverse shear. Comput Methods Appl Mech Eng 50(1):71–101. https://doi.org/10.1016/0045-7825(85)90114-8

    Article  MATH  Google Scholar 

  11. Hughes TJR, Tezduyar TE (1981) Finite elements based upon Mindlin plate theory with particular reference to four-node bilinear isoparametric element. J Appl Mech 48(3):587–596. https://doi.org/10.1115/1.3157679

    Article  MATH  Google Scholar 

  12. Briassoulis D (1993) The four node C0 Mindlin plate bending element reformulated, part I: Formulation. Comput Methods Appl Mech Eng 107(1–2):23–43. https://doi.org/10.1016/0045-7825(93)90167-V

    Article  MATH  Google Scholar 

  13. Briassoulis D (1993) The four node C0 Mindlin plate bending element reformulated, part II: verification. Comput Methods Appl Mech Eng 107(1–2):45–100. https://doi.org/10.1016/0045-7825(93)90168-W

    Article  MATH  Google Scholar 

  14. Zienkiewicz OC, Taylor RL, Too JM (1971) Reduced integration technique in general analysis of plates and shells. Int J Numer Meth Eng 3(2):275–290. https://doi.org/10.1002/nme.1620030211

    Article  MATH  Google Scholar 

  15. Hughes TJR, Cohen M, Haroun M (1978) Reduced and selective integration techniques in finite element analysis of plates. Nucl Eng Des 46(1):203–222. https://doi.org/10.1016/0029-5493(78)90184-X

    Article  Google Scholar 

  16. Bathe K-J, Dvorkin E (1985) A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation. Int J Numer Meth Eng 21(2):367–383. https://doi.org/10.1002/nme.1620210213

    Article  MATH  Google Scholar 

  17. Bathe K-J, Brezzi F, Cho SW (1989) The MITC7 and MITC9 plate bending elements. Comput Struct 32(3–4):797–814. https://doi.org/10.1016/0045-7949(89)90365-9

    Article  MATH  Google Scholar 

  18. Lyly M, Stenberg R, Vihinen T (1993) A stable bilinear element for the Reissner–Mindlin plate model. Comput Methods Appl Mech Eng 110(3–4):343–357. https://doi.org/10.1016/0045-7825(93)90214-I

    Article  MathSciNet  MATH  Google Scholar 

  19. Lee PS, Bathe K-J (2004) Development of MITC isotropic triangular shell finite elements. Comput Struct 82(11–12):945–962. https://doi.org/10.1016/j.compstruc.2004.02.004

    Article  Google Scholar 

  20. Andelfinger U, Ramm E (1993) EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements. Int J Numer Meth Eng 36(8):1311–1337. https://doi.org/10.1002/nme.1620360805

    Article  MATH  Google Scholar 

  21. Li LM, Peng YH, Li DY (2011) A stabilized underintegrated enhanced assumed strain solid-shell element for geometrically nonlinear plate/shell analysis. Finite Element Anal Des 47(5):511–518. https://doi.org/10.1016/j.finel.2011.01.001

    Article  Google Scholar 

  22. Cardoso RPR, Yoon JW, Mahardika M, Choudry S, de Sousa RJA, Valente RAF (2007) Enhanced assumed strain (EAS) and assumed natural strain (ANS) methods for one-point quadrature solid-shell elements. Int J Numer Meth Eng 75(2):156–187. https://doi.org/10.1002/nme.2250

    Article  MathSciNet  MATH  Google Scholar 

  23. Bletzinger K-U, Bischoff M, Ramm E (2000) A unified approach for shear-locking-free triangular and rectangular shell finite elements. Comput Struct 75(3):321–334. https://doi.org/10.1016/S0045-7949(99)00140-6

    Article  Google Scholar 

  24. Nguyen-Thoi T, Phung-Van P, Nguyen-Xuan H, Thai-Hoang C (2012) A cell-based smoothed discrete shear gap method using triangular elements for static and free vibration analyses of Reissner–Mindlin plates. Int J Numer Methods Eng 91(7):705–741. https://doi.org/10.1002/nme.4289

    Article  MathSciNet  MATH  Google Scholar 

  25. Nguyen-Xuan H, Rabczuk T, Nguyen-Thanh N, Nguyen-Thoi T, Bordas SPA (2010) A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates. Comput Mech 46:679–701. https://doi.org/10.1007/s00466-010-0509-x

    Article  MathSciNet  MATH  Google Scholar 

  26. Nguyen-Thoi T, Nguyen-Thoi MH, Vo-Duy T, Nguyen-Minh N (2015) Development of the cell-based smoothed discrete shear gap plate element (CS-FEM-DSG3) using three-node triangles. Int J Comput Methods 12(04):1540015. https://doi.org/10.1142/s0219876215400150

    Article  MathSciNet  MATH  Google Scholar 

  27. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195. https://doi.org/10.1016/j.cma.2004.10.008

    Article  MathSciNet  MATH  Google Scholar 

  28. de Veiga LB, Buffa A, Lovadina C, Martinelli M, Sangalli G (2012) An isogeometric method for the Reissner–Mindlin plate bending problem. Comput Methods Appl Mech Eng 209–212:45–53. https://doi.org/10.1016/j.cma.2011.10.009

    Article  MathSciNet  MATH  Google Scholar 

  29. Yin S, Yu T, Bui TQ, Nguyen MN (2015) Geometrically nonlinear analysis of functionally graded plates using isogeometric analysis. Eng Comput 32(2):519–558. https://doi.org/10.1108/EC-09-2013-0220

    Article  Google Scholar 

  30. Gupta A, Ghosh A (2019) Static and transient analysis of sandwich composite plates using isogeometric analysis. Mech Adv Mater Struct 26(1):81–87. https://doi.org/10.1080/15376494.2018.1534169

    Article  Google Scholar 

  31. Zhong S, Zhang J, Jin G, Ye T, Song X (2021) Thermal bending and vibration of FGM plates with various cutouts and complex shapes using isogeometric method. Compos Struct 260:113518. https://doi.org/10.1016/j.compstruct.2020.113518

    Article  Google Scholar 

  32. Wang J, Liew KM, Tan MJ, Rajendra S (2002) Analysis of rectangular laminated composite plates via FSDT meshless method. Int J Mech Sci 44(7):1275–1293. https://doi.org/10.1016/S0020-7403(02)00057-7

    Article  MATH  Google Scholar 

  33. Tanaka S, Suzuki H, Sadamoto S, Imachi M, Bui TQ (2015) Analysis of cracked shear deformable plates by an effective meshfree plate formulation. Eng Fract Mech 144:142–157. https://doi.org/10.1016/j.engfracmech.2015.06.084

    Article  Google Scholar 

  34. Wang D, Chen JS (2004) Locking-free stabilized conforming nodal integration for meshfree Mindlin–Reissner plate formulation. Eng Fract Mech 193(12–14):1065–1083. https://doi.org/10.1016/j.cma.2003.12.006

    Article  MATH  Google Scholar 

  35. Liu GR, Zhao X, Dai KY, Zhong ZH, Li GY, Han X (2008) Static and free vibration analysis of laminated composite plates using the conforming radial point interpolation method. Compos Sci Technol 68:354–366. https://doi.org/10.1016/j.compscitech.2007.07.014

    Article  Google Scholar 

  36. Thai CH, Nguyen-Xuan H (2018) A Moving Kriging interpolation meshfree method based on naturally stabilized nodal integration scheme for plate analysis. Int J Comput Methods 15(3):1850100. https://doi.org/10.1142/S0219876218501001

    Article  MathSciNet  MATH  Google Scholar 

  37. Belinha J, Dinis LMJS (2006) Analysis of plates and laminates using the element-free Galerkin method. Comput Struct 84(22–23):1549–1559. https://doi.org/10.1016/j.compstruc.2006.01.013

    Article  Google Scholar 

  38. Peng LX, Liew KM, Kitipornchai S (2007) Analysis of stiffened corrugated plates based on the FSDT via the mesh-free method. Int J Mech Sci 49(3):364–378. https://doi.org/10.1016/j.ijmecsci.2006.08.018

    Article  Google Scholar 

  39. Bui TQ, Nguyen MN, Zhang C (2011) Buckling analysis of Reissner–Mindlin plates subjected to in-plane edge loads using a shear-locking-free and meshfree method. Eng Anal Bound Elem 35(9):1038–1053. https://doi.org/10.1016/j.enganabound.2011.04.001

    Article  MathSciNet  MATH  Google Scholar 

  40. Bui TQ, Doan DH, Do TV, Hirose S, Nguyen DD (2016) High frequency modes meshfree analysis of Reissner–Mindlin plates. J Sci Adv Mater Dev 1(3):400–412. https://doi.org/10.1016/j.jsamd.2016.08.005

    Article  Google Scholar 

  41. Liew KM, Chen XL (2004) Mesh-free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in-plane point loads. Int J Numer Methods Eng 60(11):1861–1877. https://doi.org/10.1002/nme.1027

    Article  MATH  Google Scholar 

  42. Truong TT, Lo VS, Nguyen MN, Nguyen NT, Nguyen DK (2021) Evaluation of fracture parameters in cracked plates using an extended meshfree method. Eng Fract Mech 247:107–671. https://doi.org/10.1016/j.engfracmech.2021.107671

    Article  Google Scholar 

  43. Cui XY, Tian T (2010) A cell-based smoothed radial point interpolation method (CS-RPIM) for static and free vibration of solids. Eng Anal Bound Elem 34(2):144–157. https://doi.org/10.1016/j.enganabound.2009.07.011

    Article  MathSciNet  MATH  Google Scholar 

  44. Liu GR, Jiang Y, Chen L, Zhang GY, Zhang YW (2011) A singular cell-based smoothed radial point interpolation method for fracture problems. Comput Struct 89(13–14):1378–1396. https://doi.org/10.1016/j.compstruc.2011.03.009

    Article  Google Scholar 

  45. Wang JG, Liu GR (2002) A point interpolation meshless method based on radial basis functions. Int J Numer Methods Eng 54(11):1623–1648. https://doi.org/10.1002/nme.489

    Article  MATH  Google Scholar 

  46. Gu L (2003) Moving kriging interpolation and element-free Galerkin method. Int J Numer Methods Eng 56(1):1–11

    Article  MATH  Google Scholar 

  47. Dai KY, Liu GR, Lim KM, Gu YT (2003) Comparison between the radial point interolation and the Kriging interpolation used in meshfree methods. Comput Mech 32:60–70. https://doi.org/10.1007/s00466-003-0462-z

    Article  MATH  Google Scholar 

  48. Bui TQ, Nguyen NT, Le VL, Nguyen MN, Truong TT (2018) Analysis of transient dynamic fracture parameters of cracked functionally graded composites by improved meshfree methods. Theoret Appl Fract Mech 96:642–657. https://doi.org/10.1016/j.tafmec.2017.10.005

    Article  Google Scholar 

  49. Liu GR (2010) Meshfree methods : moving beyond the finite element method. CRC Press, Boca Raton. https://doi.org/10.1201/9781420082104

    Book  MATH  Google Scholar 

  50. Chen J-S, Wu C-T, Yoon SYY (2000) A stabilized conforming nodal integration for Galerkin mesh-free methods. Int J Numer Methods Eng 50(2):435–466

    Article  MATH  Google Scholar 

  51. Chen J-S, Wang D (2006) A constrained reproducing kernel particle formulation for shear deformable shell in cartesian coordinates. Int J Numer Meth Eng 68(2):151–172. https://doi.org/10.1002/nme.1701

    Article  MATH  Google Scholar 

  52. Hillman M, Chen J-S (2015) An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics. Int J Numer Methods Eng 107(7):603–630. https://doi.org/10.1002/nme.5183

    Article  MathSciNet  MATH  Google Scholar 

  53. Khosravifard A, Hematiyan MR (2010) A new method for meshless integration in 2d and 3d Galerkin meshfree methods. Eng Anal Bound Elem 34(1):30–40. https://doi.org/10.1016/j.enganabound.2009.07.008

    Article  MathSciNet  MATH  Google Scholar 

  54. Khosravifard A, Hematiyan MR, Marin L (2011) Nonlinear transient heat conduction analysis of functionally graded materials in the presence of heat sources using an improved meshless radial point interpolation method. Appl Math Model 35(9):4157–4174. https://doi.org/10.1016/j.apm.2011.02.039

    Article  MathSciNet  MATH  Google Scholar 

  55. Bui TQ, Khosravifard A, Zhang C, Hematiyan MR, Golub MV (2013) Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method. Eng Struct 47:90–104. https://doi.org/10.1016/j.engstruct.2012.03.041

    Article  Google Scholar 

  56. Nguyen NT, Bui TQ, Nguyen MN, Truong TT (2020) Meshfree thermomechanical crack growth simulations with new numerical integration scheme. Eng Fract Mech 235:107121. https://doi.org/10.1016/j.engfracmech.2020.107121

    Article  Google Scholar 

  57. Nguyen MN, Nguyen NT, Truong TT, Bui TQ (2021) An efficient reduced basis approach using enhanced meshfree and combined approximation for large deformation. Eng Anal Bound Elem 133:319–329. https://doi.org/10.1016/j.enganabound.2021.09.007

    Article  MathSciNet  MATH  Google Scholar 

  58. Nguyen NT, Nguyen MN, Vu TV, Truong TT, Bui TQ (2022) A meshfree model enhanced by NURBS-based cartesian transformation method for cracks at finite deformation in hyperelastic solids. Eng Fract Mech 261:108176. https://doi.org/10.1016/j.engfracmech.2021.108176

    Article  Google Scholar 

  59. Do VNV, Lee C-H (2018) Nonlinear analyses of FGM plates in bending by using a modified radial point interpolation mesh-free method. Appl Math Model 57:1–20. https://doi.org/10.1016/j.apm.2017.12.035

    Article  MathSciNet  MATH  Google Scholar 

  60. Nguyen TN, Thai CH, Nguyen-Xuan H, Lee J (2018) Geometrically nonlinear analysis of functionally graded material plates using an improved moving kriging meshfree method based on a refined plate theory. Compos Struct 193:268–280. https://doi.org/10.1016/j.compstruct.2018.03.036

    Article  Google Scholar 

  61. Nourmohammadi H, Behjat B (2019) Geometrically nonlinear analysis of functionally graded piezoelectric plate using mesh-free RPIM. Eng Anal Bound Elem 99:131–141. https://doi.org/10.1016/j.enganabound.2018.11.006

    Article  MathSciNet  MATH  Google Scholar 

  62. Reddy JN (2000) Analysis of functionally graded plates. Int J Numer Methods Eng 47(1–3):663–684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8

    Article  MATH  Google Scholar 

  63. Ferreira AJM, Fantuzzi N (2020) MATLAB codes for finite element analysis. Springer, Cham. https://doi.org/10.1007/978-3-030-47952-7

    Book  MATH  Google Scholar 

  64. Pham Q-H, Pham T-D, Trinh QV, Phan D-H (2019) Geometrically nonlinear analysis of functionally graded shells using an edge-based smoothed MITC3 (ES-MITC3) finite elements. Eng Comput 36(3):1069–1082. https://doi.org/10.1007/s00366-019-00750-z

    Article  Google Scholar 

  65. Dolbow J, Moes N, Belytschko T (2000) Modeling fracture in Mindlin–Reissner plates with the extended finite element method. Int J Solids Struct 37:7161–7183. https://doi.org/10.1016/S0020-7683(00)00194-3

    Article  MATH  Google Scholar 

  66. Yu TT, Yin S, Bui TQ, Hirose S (2015) A simple FSDT-based isogeometric analysis for geometrically nonlinear analysis of functionally graded plates. Finite Elem Anal Des 96:1–10. https://doi.org/10.1016/j.finel.2014.11.003

    Article  Google Scholar 

  67. Nguyen NT, Bui TQ, Truong TT (2017) Transient dynamic fracture analysis by an extended meshfree method with different crack-tip enrichments. Meccanica 52(10):2363–2390. https://doi.org/10.1007/s11012-016-0589-6

    Article  MathSciNet  MATH  Google Scholar 

  68. Tongsuk P, Kanok-Nukulchai W (2004) Further investigation of element-free Galerkin method using moving kriging interpolation. Int J Comput Methods 01(02):345–365. https://doi.org/10.1142/S0219876204000162

    Article  MATH  Google Scholar 

  69. Cui XY, Tian L (2017) A central point-based discrete shear gap method for plates and shells analysis using triangular elements. Int J Appl Mech 09(04):1750055. https://doi.org/10.1142/S1758825117500557

    Article  Google Scholar 

  70. Le CV (2013) A stabilized discrete shear gap finite element for adaptive limit analysis of Mindlin–Reissner plates. Int J Numer Methods Eng 96(4):231–246. https://doi.org/10.1002/nme.4560

    Article  MathSciNet  MATH  Google Scholar 

  71. Yu T, Bui TQ, Liu P, Hirose S (2014) A stabilized discrete shear gap extended finite element for the analysis of cracked Mindlin–Reissner plate vibration problems involving distorted meshes. Int J Mech Mater Des 12(1):85–107. https://doi.org/10.1007/s10999-014-9282-x

    Article  Google Scholar 

  72. Zhang C, Liu P, Zhu D, Lich LV, Bui TQ (2019) Analysis of natural frequency for bioinspired functional gradient plates. Int J Mech Mater Des 16:367–386. https://doi.org/10.1007/s10999-019-09466-w

    Article  Google Scholar 

  73. Nguyen-Thoi T, Phung-Van P, Luong-Van H, Nguyen-Van H, Nguyen-Xuan H (2012) A cell-based smoothed three-node Mindlin plate element (CS-MIN3) for static and free vibration analyses for plates. Comput Mech 51:65–81. https://doi.org/10.1007/s00466-012-0705-y

    Article  MathSciNet  MATH  Google Scholar 

  74. Lee PS, Noh H-C, Bathe K-J (2007) Insight into 3-node triangular shell finite elements: the effects of element isotropy and mesh patterns. Comput Struct 85(7–8):404–418. https://doi.org/10.1016/j.compstruc.2006.10.006

    Article  Google Scholar 

  75. Belounar A, Benmebarek S, Houhou MN, Belounar L (2019) Static, free vibration, and buckling analysis of plates using strain-based Reissner–Mindlin elements. Int J Adv Struct Eng 11(2):211–230. https://doi.org/10.1007/s40091-019-0226-4

    Article  Google Scholar 

  76. Taylor RL, Auricchio F (1993) Linked interpolation for Reissner–Mindlin plate elements: part II—a simple triangle. Int J Numer Methods Eng 36(18):3057–3066. https://doi.org/10.1002/nme.1620361803

    Article  MATH  Google Scholar 

  77. Urthaler Y, Reddy JN (2008) A mixed finite element for the nonlinear bending analysis of laminated composite plates based on FSDT. Mech Adv Mater Struct 15(5):335–354. https://doi.org/10.1080/15376490802045671

    Article  Google Scholar 

  78. Pica A, Wood RD, Hinton E (1980) Finite element analysis of geometrically nonlinear plate behaviour using a Mindlin formulation. Comput Struct 11(3):203–215. https://doi.org/10.1016/0045-7949(80)90160-1

    Article  MathSciNet  MATH  Google Scholar 

  79. Tanaka S, Dai MJ, Sadamoto S, Bui TQ (2019) Stress resultant intensity factors evaluation of cracked folded structures by 6 DOFs flat shell meshfree modeling. Thin-walled Struct 144:106285. https://doi.org/10.1016/j.tws.2019.106285

    Article  Google Scholar 

  80. Anaei MTM, Khosravifard A, Bui TQ (2021) Analysis of fracture mechanics and fatigue crack growth in moderately thick plates using an efficient meshfree approach. Theor Appl Fract Mech 113:102943. https://doi.org/10.1016/j.tafmec.2021.102943

    Article  Google Scholar 

  81. Peng LX, Tao Y, Liang N, Li L, Qin X, Zeng Z, Teng X (2017) Simulation of a crack in stiffened plates via a meshless formulation and FSDT. Int J Mech Sci 131–132:880–893. https://doi.org/10.1016/j.ijmecsci.2017.07.063

    Article  Google Scholar 

Download references

Acknowledgements

This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number C2020-20-13. We acknowledge the support of time and facilities from Ho Chi Minh City University of Technology (HCMUT), VNU-HCM for this study.

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Faculty of Applied Sciences, Ho Chi Minh City University of Technology, 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Vietnam

    Thien T. Truong, Vay S. Lo, Minh N. Nguyen & Nha T. Nguyen

  2. Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc City, Ho Chi Minh City, Vietnam

    Thien T. Truong, Vay S. Lo, Minh N. Nguyen & Nha T. Nguyen

  3. Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam

    Kien D. Nguyen

Authors
  1. Thien T. Truong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vay S. Lo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Minh N. Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nha T. Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kien D. Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Thien T. Truong or Kien D. Nguyen.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Truong, T.T., Lo, V.S., Nguyen, M.N. et al. A novel meshfree radial point interpolation method with discrete shear gap for nonlinear static analysis of functionally graded plates. Engineering with Computers 39, 2989–3009 (2023). https://doi.org/10.1007/s00366-022-01691-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-022-01691-w

Keywords

Search

Navigation