Optimization of geometric parameters of reinforced sheets based on a cell-based smoothed discrete shear gap (CS-FEM-DSG3) method

Abstract

Optimization of design features of reinforced sheet is investigated. Initially, equations governing composite structures are extracted based on Kirchhoff sheet model under bending using Hamilton’s principal. Then, design parameters for the composite structure are extracted with simple supportive boundary conditions from proposed solution. Next, optimization is achieved by determining dimensions of a reinforced sheet specimen. Weight optimization of reinforced sheet structure has been obtained based on variations in thickness and number of longitudinal and transverse reinforcements. Buckling static characteristic is utilized in optimization process. To solve the extracted equations, semi-analytical method of CS-DSG3 has been applied. Results are presented in graphs that show variation of design parameters by changing the geometric parameters. ABAQUS software has been used for design verification. The results show that an increase in thickness of 3 mm skip value tends to be zero. Also, there is a change in the amount of deflection for sheets with a minimum thickness of 3 mm by increasing the number of longitudinal and transverse reinforcement. There is a good agreement between the numerical method of finite elements and the method X-FEM-DSG3.

Keywords

optimization / reinforced sheet / design / CS-FEM-DSG3 method

References

[1] MouritzA P, GellertE, BurchillP, ChallisK. Review of advanced composite structures for naval ships and submarines [J].. Composite Structures, 2001, 53(1): 21-42

[2] AcevesC M, SkordosA A, SutcliffeM P. Design selection methodology for composite structures [J].. Materials & Design, 2008, 29(2): 418-426

[3] PalaniG S, IyerN R, RaoT A. An efficient finite element model for static and vibration analysis of eccentrically stiffened plates/shells [J].. Computers & Structures, 1992, 43(4): 651-661

[4] KangJ H, LeissaA W. Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges [J].. International Journal of Solids and Structures, 2005, 42(14): 4220-4238

[5] LuongN T, TriT H. Influence of variable thickness on stability of rectangular plate under compression [J].. Mechanics Research Communications, 2005, 32(2): 139-146

[6] CiancioP M, ReyesJ A. Buckling of circular, annular plates of continuously variable thickness used as internal bulkheads in submersibles [J].. Ocean Engineering, 2003, 30(11): 1323-1333

[7] TaysiN. Determination of thickness and stiffener locations for optimization of critical buckling load of stiffened plates [J].. Scientific Research and Essays, 2010, 5(9): 897-910

[8] OuD Y, MakC M, KongP R. Free flexural vibration analysis of stiffened plates with general elastic boundary supports [J].. World Journal of Modelling and Simulation, 2012, 8(2): 96-102

[9] LiuG R, Nguyen-ThoiTSmoothed finite element methods [M], 2010822-827

[10] LiuG R D K, NguyenT T. A smoothed finite element method for mechanics problems [J].. Computational Mechanics, 2007, 39(6): 859-877

[11] LiuG R, NguyenT T, DaiKY, LamK Y. Theoretical aspects of the smoothed finite element method (SFEM) [J].. International Journal for Numerical Methods in Engineering, 2007, 71(8): 902-930

[12] LiuG R, Nguyen-ThoiT, Nguyen-XuanH, DaiKY, LamK Y. On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM) [J].. International Journal for Numerical Methods in Engineering., 2009, 77(13): 1863-1869

[13] Nguyen-ThoiT, LiuG R, Nguyen-XuanH. Additional properties of the node-based smoothed finite element method (NS-FEM) for solid mechanics problems [J].. International Journal of Computational Methods., 2009, 6(4): 633-666

[14] Nguyen-XuanH, LiuG R, Nguyen-ThoiT, NguyentranC. An edge-based smoothed finite element method for analysis of two-dimensional piezoelectric structures [J].. Smart Materials and Structures, 2009, 18(6): 065015

[15] LiuG R, Nguyen-XuanH, Nguyen-ThoiT. A theoretical study on NS/ES-FEM: Properties, accuracy and convergence rates [J].. Int J Numer Methods Eng, 2010, 84: 1222-1256

[16] Nguyen-ThoiT, LiuG R, Nguyen-XuanH. An n-sided polygonal edge based smoothed finite element method (nES FEM) for solid mechanics [J].. International Journal for Numerical Methods in Biomedical Engineering, 2011, 27(9): 1446-1472

[17] Nguyen-ThoiT, LiuG R L K, ZhangG Y. A face-based smoothed finite element method (FS-FEM) for 3D linear and geometrically non-linear solid mechanics problems using 4-node tetrahedral elements [J].. International Journal for Numerical Methods in Engineering, 2009, 78(3): 324-353

[18] Nguyen-XuanH, LiuG R, Thai-HoangC, Nguyen-ThoiT. An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates [J].. Computer Methods in Applied Mechanics and Engineering, 2010, 199(9): 471-489

[19] Nguyen-XuanH, RabczukT, Nguyen-ThanhN, Nguyen-ThoiT, BordasS. A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates [J].. Computational Mechanics, 2010, 46(5): 679-701

[20] Nguyen-XuanH, TranL V, Nguyen-ThoiT, Vu-DoH C. Analysis of functionally graded plates using an edge-based smoothed finite element method [J].. Composite Structures, 2011, 93(11): 3019-3039

[21] ThaiC H, TranL V, TranD T, Nguyen-ThoiT, NguyenxuanH. Analysis of laminated composite plates using higher-order shear deformation plate theory and node-based smoothed discrete shear gap method [J].. Applied Mathematical Modelling, 2012, 36(11): 5657-5677

[22] Nguyen-XuanH, TranL V, ThaiC H, Nguyen-ThoiT. Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing [J].. Thin-Walled Structures, 2012, 54: 1-8

[23] Nguyen-ThoiT, Phung-VanP, Luong-VanH, NguyenvanH, Nguyen-XuanH. A cell-based smoothed three-node Mindlin plate element (CS-MIN3) for static and free vibration analyses of plates [J].. Computational Mechanics, 2013, 51(1): 65-81

[24] Phung-VanP, Nguyen-ThoiT, Luong-VanH, LieuxuanQ. Geometrically nonlinear analysis of functionally graded plates using a cell-based smoothed three-node plate element (CS-MIN3) based on the C 0-HSDT [J].. Computer Methods in Applied Mechanics and Engineering, 2014, 270: 15-36

[25] Luong-VanH, Nguyen-ThoiT, LiuGR, Phung-VanP. A cell-based smoothed finite element method using three-node shear-locking free Mindlin plate element (CS-FEM-MIN3) for dynamic response of laminated composite plates on viscoelastic foundation [J].. Engineering Analysis with Boundary Elements, 2014, 42: 8-19

[26] NatarajanS, KaleeswaranK, ManickamG. Functionally graded material panel flutter by cell-based smoothed finite elements [J].. Journal of Coupled Systems and Multiscale Dynamics, 2013, 1(2): 205-215

[27] Nguyen-ThoiT, Phung-VanP, Nguyen-XuanH, ThaihoangC. A cell based smoothed discrete shear gap method using triangular elements for static and free vibration analyses of Reissner–Mindlin plates [J].. International Journal for Numerical Methods in Engineering, 2012, 91(7): 705-741

[28] BletzingerK U, BischoffM, RammE. A unified approach for shear-locking-free triangular and rectangular shell finite elements [J].. Computers & Structures, 2000, 75(3): 321-334

[29] Nguyen-ThoiT, Bui-XuanT, Phung-VanP, NguyenxuanH, Ngo-ThanhP. Static, free vibration and buckling analyses of stiffened plates by CS-FEM-DSG3 using triangular elements [J].. Computers & Structures, 2013, 125: 100-113

[30] Phung-VanP, Nguyen-ThoiT, TranLV, Nguyen-XuanH. A cell-based smoothed discrete shear gap method (CS-DSG3) based on the C0-type higher-order shear deformation theory for static and free vibration analyses of functionally graded plates [J].. Computational Materials Science, 2013, 79: 857-872

[31] Phung-VanP, Nguyen-ThoiT, Le-DinhT, NguyenxuanH. Static and free vibration analyses and dynamic control of composite plates integrated with piezoelectric sensors and actuators by the cell-based smoothed discrete shear gap method (CS-FEMDSG3) [J].. Smart Materials and Structures, 2013, 22(9): 095026

[32] Nguyen-ThoiT, Luong-VanH, Phung-VanP, RabczukT, Tran-TrungD. Dynamic responses of composite plates on the Pasternak foundation subjected to a moving mass by a cell-based smoothed discrete shear gap (CS-FEM-DSG3) method [J]. International Journal of Composite Materials, 2013, 3A: 19-27

[33] Phung-VanP, Nguyen-ThoiT, Dang-TrungH, Nguyen-MinhN. A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using layerwise theory based on the C0-HSDT for analyses of composite plates [J].. Composite Structures, 2014, 111: 553-565

[34] Phung-VanP, Nguyen-ThoiT, Luong-Vanh Thai-HoangC, Nguyen-XuanH. A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using layerwise deformation theory for dynamic response of composite plates resting on viscoelastic foundation [J].. Computer Methods in Applied Mechanics and Engineering, 2014, 272: 138-159

[35] Nguyen-MinhN, Nguyen-ThoiT, Bui-XuanT, Vo-DuyT. Static and free vibration analyses of stiffened folded plates using a cell-based smoothed discrete shear gap method (CS-FEM-DSG3) [J].. Applied Mathematics and Computation, 2015, 266: 212-234

[36] WangD, AbdallaM M. Global and local buckling analysis of grid-stiffened composite panels [J].. Composite Structures, 2015, 119: 767-776

[37] ZhaoW, KapaniaR K. Buckling analysis of unitized curvilinearly stiffened composite panels [J].. Composite Structures, 2016, 135: 365-382

[38] GeD, MoY, HeB, WuY, DuX. Experimental and numerical investigation of stiffened composite curved panel under shear and in-plane bending [J].. Composite Structures, 2016, 137: 185-195