The global nonlinear galerkin method for the analysis of elastic large deflections of plates under combined loads: A scalar homotopy method for the direct solution of nonlinear algebraic equations

Computers, Materials and Continua

Volumn 23, Issue 1, 2011, Pages 69-99

  Dai, Hong Hua ^a,b   Paik, Jeom Kee ^c   Atluri, Satya N ^b  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c Pusan National University   (South Korea)

Author keywords

Combined loads; Exponentially convergent scalar homotopy algorithm (ECSHA); Initial guess; Large deflections; Nonlinear algebraic equations (NAEs); Nonlinear global Galerkin method

Indexed keywords

COMBINED LOADS; GALERKIN; HOMOTOPY ALGORITHMS; INITIAL GUESS; LARGE DEFLECTION; NONLINEAR ALGEBRAIC EQUATIONS;

ALGEBRA; ALGORITHMS; FINITE ELEMENT METHOD; GALERKIN METHODS; NEWTON-RAPHSON METHOD; PARTIAL DIFFERENTIAL EQUATIONS; STIFFNESS MATRIX;

NONLINEAR EQUATIONS;

EID: 79961072474     PISSN: 15462218     EISSN: 15462226     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. Atluri, S. N. (2002): Methods of Computer Modeling in Engineering and Science. Tech. Science Press, 1400 pages.
2. Atluri, S. N.; Shen, S. (2002): The meshless local Petrov-Galerkin (MLPG) method: a simple & less-costly alternative to finite element and boundary element methods. CMES: Computer Modeling in Engineering & Sciences, vol. 3, pp. 11-51. (Pubitemid 135695145)
3. Atluri, S. N.; Liu, H. T.; Han, Z. D. (2006): Meshless local Petrov-Galerkin (MLPG) mixed collocation method for elasticity problems. CMES: Computer Modeling in Engineering & Sciences, vol. 14, pp. 141-152. (Pubitemid 44562740)
4. Cai Y. C.; Paik J. K.; Atluri S. N. (2009): Large Deformation Analyses of Space- Frame Structures, with Members of arbitrary Cross-Section, Using Explicit Tangent Stiffness Matrices, Based on a von Karman Type Nonlinear Theory in Rotated Reference Frames. CMES: Computer Modeling in Engineering & Sciences, vol. 53, pp. 117-145.
5. Cai Y. C.; Paik J. K.; Atluri S. N. (2009): Large Deformation Analyses of Space- Frame Structures, Using Explicit Tangent Stiffness Matrices, Based on the Reissner variational principle and a von Karman Type Nonlinear Theory in Rotated Reference Frames. CMES: Computer Modeling in Engineering & Sciences, vol. 54, pp. 335-368.
6. Cai Y. C.; Paik J. K.; Atluri S. N. (2010): Locking-free Thick-Thin Rod/Beam Element for Large Deformation Analyses of Space-Frame Structures, Based on the Reissner variational Principle and A von Karman Type Nonlinear Theory. CMES: Computer Modeling in Engineering & Sciences, vol. 58, pp. 75-108.
7. Cai Y. C.; Paik J. K.; Atluri S. N. (2010): A Triangular Plate Element with Drilling Degrees of Freedom, for Large Rotation Analyses of Built-up Plate/Shell Structures, Based on the Reissner Variational Principle and the von Karman Nonlinear Theory in the Co-rotational Reference Frame. CMES: Computer Modeling in Engineering & Sciences, vol.61, pp.273-312.
8. Fan, C. M.; Liu, C. S.; Yeih, W. C.; Chan, H. F. (2010): The Scalar Homotopy Method for Solving Non-Linear Obstacle Problems. CMC: Computers, Materials & Continua, vol. 15, pp. 67-86.
9. Ku, C. Y.; Yeih, W. C.; Liu, C. S. (2010): Solving Non-Linear Algebraic Equations by a Scalar Newton-homotopy Continuation Method. International Journal of Nonlinear Science & Numerical Simulation, vol. 11, pp. 435-450.
10. Liu, C. S.; Atluri, S. N. (2009): A Novel Time Integration Method for Solving A Large System of Non-Linear Algebraic Equations. CMES: Computer Modeling in Engineering & Sciences, vol. 31, pp. 71-83.
11. Liu, C. S.; Atluri, S. N. (2008): A Fictitious Time Integration Method (FTIM) for Solving Mixed Complementarity Problems with Applications to Non-Linear Optimization. CMES: Computer Modeling in Engineering & Sciences, vol. 34, pp. 155-178.
12. Liu, C. S.; Atluri, S. N. (2009): A Fictitious Time Integration Method for the Numerical Solution of the Fredholm Integral Equation and for Numerical Differentiation of Noisy Data, and Its Relation to the Filter Theory. CMES: Computer Modeling in Engineering & Sciences, vol. 41, pp. 243-261.
13. Liu, C. S.; Ku, Y. C.; Yeih, W. C.; Fan, C. M.; Atluri, S. N. (2010): An Exponentially Convergent Scalar Homotopy Algorithm for Solving A Determinate/ Indeterminate System of Non-Linear Algebraic Equations. CMES: Computer Modeling in Engineering & Sciences
14. Liu, C. S.; Yeih, W. C.; Atluri, S. N. (2010): An Enhanced Fictitious Time Integration Method for Non-Linear Algebraic Equations with Multiple Solutions: Boundary Layer, Boundary Value and Eigenvalue Problems. CMES: Computer Modeling in Engineering & Sciences, vol. 59, pp. 301-323.
15. Liu, C. S.; Yeih, W. C.; Kuo, L. C.; Atluri, S. N. (2009): A Scalar Homotopy Method for Solving an Over/Under-determined System of Non-Linear Algebraic Equations. CMES: Computer Modeling in Engineering & Sciences, vol. 53, pp. 47-71.
16. Paik, J. K.; Thayamballi, A. K.; Lee, S. K.; Kang, S. J. (2001): A semianalytical method for the elastic-plastic large deflection analysis of welded steel or aluminum plating under combined in-plane and lateral pressure loads. Thin-Walled Structure, vol. 39, pp.125-152. (Pubitemid 32874449)
17. Paik, J. K.; Lee, M. S. (2005): A semi-analytical method for the elastic-plastic large deflection analysis of stiffened panels under combined biaxial compression/tension, biaxial in-plane bending, edge shear, and lateral pressure loads. Thin-Walled Structure, vol. 43, pp.375-410.
18. Timoshenko, S.; Krieger, S. W. (1959): Theory of Plates and Shells. McGraw- Hill Companies, 580 pages
19. Ueda, Y.; Rashed, S. M. H.; Paik, J. K. (1987): An Incremental Galerkin Method for Plates and Stiffened Plates. Computers & Structures, vol. 27, pp. 147-156.
20. Zhu H. H.; Cai Y. C.; Paik J. K.; Atluri S. N. (2010): Locking-free Thick-Thin Rod/Beam Element Based on a von Karman Type Nonlinear Theory in Rotated Reference Frames For Large Deformation Analyses of Space-Frame Structures. CMES: Computer Modeling in Engineering & Sciences, vol. 57, pp. 175-204.
21. Zhu, T.; Zhang, J.; Atluri, S. N. (1999): A meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and non-linear boundary value problems. Eng. Anal. Bound. Elem., vol. 23, pp. 375-389.