Self-adaptive predictor-corrector algorithms for static nonlinear structural analysis

Abstract This paper develops a multi phase self-adaptive predictor corrector type algorithm to enable the solution of highly nonlinear structural responses including kinematic, kinetic and material effects as well as potential pre/postbuckling behavior. The hierarchy of the strategy is such that three main phases are involved. The first features the use of a warpable hyperelliptic constraint surface which serves to upperbound dependent iterate excursions during successive INR type iterations. The second corrector phase uses an energy constraint to scale the generation of successive iterates so as to maintain the appropriate form of local convergence behavior. The third involves the use of quality of convergence checks which enable various self-adaptive modifications of the algorithmic structure when necessary. Such restructuring is achieved by tightening various conditioning parameters as well as switch to different algorithmic levels so as to improve the convergence process. Included in the paper are several numerical experiments which illustrate the capabilities of the procedure to handle varying types of nonlinear structural behavior.

[1]  J. A. Stricklin,et al.  Evaluation of Solution Procedures for Material and/or Geometrically Nonlinear Structural Analysis , 1973 .

[2]  F. B. Hildebrand.  Finite-difference equations and simulations , 1968 .

[3]  Klaus-Jürgen Bathe,et al.  Some practical procedures for the solution of nonlinear finite element equations , 1980 .

[4]  G. Strang,et al.  The solution of nonlinear finite element equations , 1979 .

[5]  M. Crisfield.  A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES "SNAP-THROUGH" , 1981 .

[6]  J. J. Moré,et al.  Quasi-Newton Methods, Motivation and Theory , 1974 .

[7]  P. Bergan,et al.  Solution techniques for non−linear finite element problems , 1978 .

[8]  J. Z. Zhu,et al.  The finite element method , 1977 .

[9]  E. Riks.  An incremental approach to the solution of snapping and buckling problems , 1979 .

[10]  J. Oden.  Finite Elements of Nonlinear Continua , 1971 .

[11]  Carlos A. Felippa,et al.  PROCEDURES FOR COMPUTER ANALYSIS OF LARGE NONLINEAR STRUCTURAL SYSTEMS , 1977 .

[12]  J. A. Stricklin,et al.  Displacement incrementation in non-linear structural analysis by the self-correcting method , 1977 .

[13]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[14]  Ahmed K. Noor,et al.  SURVEY OF COMPUTER PROGRAMS FOR SOLUTION OF NONLINEAR STRUCTURAL AND SOLID MECHANICS PROBLEMS , 1981 .

[15]  L. Berke,et al.  AUTOMATED METHOD FOR THE LARGE DEFLECTION AND INSTABILITY ANALYSIS OF THREE-DIMENSIONAL TRUSS AND FRAME ASSEMBLIES. , 1966 .

[16]  P. Bergan,et al.  A comparative study of different numerical solution techniques as applied to a nonlinear structural problem , 1973 .

[17]  C. G. Broyden.  A Class of Methods for Solving Nonlinear Simultaneous Equations , 1965 .

[18]  Y. C. Fung,et al.  Foundation of Solid Mechanics , 1966 .

[19]  J. Padovan.  Self-adaptive incremental Newton-Raphson algorithms , 1980 .

[20]  H. Y. Huang.  Unified approach to quadratically convergent algorithms for function minimization , 1970 .

[21]  Gouri Dhatt,et al.  Incremental displacement algorithms for nonlinear problems , 1979 .

[22]  Egor P. Popov,et al.  Nonlinear Buckling Analysis of Sandwich Arches , 1971 .