### Analysis of Rectangular Stiffened Plates Based on FSDT and Meshless Collocation Method

Document Type: Research Paper

Authors

1 Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

2 Faculty of Mechanical Engineering, University of Kashan,Kashan,Iran

Abstract

In this paper, bending analysis of concentric and eccentric beam stiffened square and rectangular plate using the meshless collocation method has been investigated. For detecting the governing equations of plate and beams, Mindlin plate theory and Timoshenko beam theory have been used, respectively, with the stiffness matrices of the plate and the beams obtained separately. The stiffness matrices of the plate and the beams were combined together using transformation equations to obtain a total stiffness matrix. Being independent of the mesh along with its simpler implementation process, compared to the other numerical methods, the meshless collocation method was used for analyzing the beam stiffened plate. In order to produce meshless shape functions, radial point interpolation method was used where moment matrix singularity problem of the polynomial interpolation method was fixed. Also, the Multiquadric radial basis function was used for point interpolations. Used to have solutions of increased accuracy and stability were polynomials with the radial basis functions. Several examples are presented to demonstrate the accuracy of the method used to analyze stiffened plates with the accuracy of the results showing acceptable accuracy that the employed method in analyzing concentric and eccentric beam stiffened square and rectangular plates.

Keywords

[1] Kendrick S., 1995, The analysis of a flat plated grillage, European Shipbuilding 5: 4-10.
[2] Schade H., 1940, The orthogonally stiffened plate under uniform lateral load, Journal of Applied Mechanics ASME 62: 143-146.
[3] Peng L., Kitipornchai S., Liew K., 2005, Analysis of rectangular stiffened plates under uniform lateral load based on FSDT and element-free Galerkin method, International Journal of Mechanical Sciences 47(2): 251-276.
[4] Rossow M., Ibrahimkhail A., 1978, Constraint method analysis of stiffened plates, Computers and Structures 8(1): 51-60.
[5] Sadek E. A., Tawfik S. A., 2000, A finite element model for the analysis of stiffened laminated plates, Computers and Structures 75(4): 369-383.
[6] Liew K. M., Lam K. Y., Chow S. T., 1990, Free vibration analysis of rectangular plates using orthogonal plate function, Computers and Structures 34(1): 79-85.
[7] Aksu G., Ali R., 1976, Free vibration analysis of stiffened plates using finite difference method, Journal of Sound and Vibration 48(1): 15-25.
[8] McBean R., 1968, Analysis of Stiffened Plates by the Finite Element Method, Thesis, Stanford University.
[9] Nguyen-Thoi T., Bui-Xuan T., Phung-Van P., Nguyen-Xuan H., Ngo-Thanh P., 2013, Static, free vibration and buckling analyses of stiffened plates by CS-FEM-DSG3 using triangular elements, Computers and Structures 125: 100-113.
[10] Azizian Z., Dawe D., 1985, The analytical strip method of solution for stiffened rectangular plates using finite strip method, Computers and structures 21(3): 423-436.
[11] Mukhopadhyay M., 1989, Vibration and stability of analysis of stiffened plates by semi-analytic finite difference method, Part II: Consideration of bending and axial displacements, Journal of Sound and Vibration 130: 41-53.
[12] Wen P., Aliabadi M., Young A., 2002, Boundary element analysis of shear deformable stiffened plates, Engineering Analysis with Boundary Elements 26(6): 511-520.
[13] Liu G., 2005, An Introduction to Meshfree Methods and Their Programming, Springer.
[14] Liu G., 2009, Mesh Free Methods: Moving Beyond the Finite Element Method, CRC Press.
[15] Ardestani M. M., Soltani B., Shams S., 2014, Analysis of functionally graded stiffened plates based on FSDT utilizing reproducing kernel particle method, Composite Structures 112: 231-240.
[16] Kansa E. J., 1990, Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics-I, Computers and Mathematics with Applications 19(8): 127-145.
[17] Hardy R. L., 1971, Multiquadric equations of topography and other irregular surfaces, Journal of Geophysical Research 78(8): 1905-1915.
[18] Franke R., 1982, Scattered data interpolation:tests of some methods, Mathematics of Computation 38(157): 181-200.
[19] Fasshauer G., 1997, Solving partial differential equations by collocation with radial basis functions, Proceedings of the 3rd International Conference on Curves and Surfaces, Surface Fitting and Multiresolution Methods.
[20] Ferreiraa A. J. M., Batrab R. C., Roquea C. M. C., Qianc L. F., Martins P. A. L. S., 2005, Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method, Composite Structures 69(4): 449-457.
[21] Chang S., 1973, Analysis of Eccentrically Stiffened Plates, Thesis, University of Missouri, Columbia.
[22] Deb A., Booton M., 1988, Finite element models for stiffened plates under transverse loading, Computers and Structures 28(3): 361-372.
[23] Biswal K. C., Ghosh A. K., 1994, Finite element analysis for stiffened laminated plates using higher order shear deformation theory, Computers and Structures 53(1): 161-171.