Padovan, Joe; Moscarello, Ralph Locally bound constrained Newton-Raphson solution algorithms. (English) Zbl 0582.73076 Comput. Struct. 23, 181-197 (1986). This paper develops strategies which enable the automatic adjustment of the constraint surfaces recently used to extend the range and numerical stability/efficiency of nonlinear finite-element equation solvers. In addition to handling kinematic and material induced nonlinearity, both pre- and postbuckling behavior can be treated. The scheme developed employs localized bounds on various hierarchical partitions of the field variables. These are used to resize, shape, and orient the global constraint surface, thereby enabling essentially automatic load/deflection incrementation. Due to the generality of the approach taken, it can be implemented in conjunction with constraints of arbitrary functional type. To benchmark the method, several numerical experiments are presented. These include problems involving kinematic and material nonlinearity, as well as, pre- and postbuckling characteristics. Cited in 2 Documents MSC: 74S30 Other numerical methods in solid mechanics (MSC2010) 65K10 Numerical optimization and variational techniques 74S99 Numerical and other methods in solid mechanics 74G60 Bifurcation and buckling 74H45 Vibrations in dynamical problems in solid mechanics 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 49M15 Newton-type methods Keywords:closed form Fourier series solutions; boundary value problems with variable coefficients; arbitrary boundaries; steady state; free vibration; variable properties; two dimensional problems; potential flow problem; summation equation of fast convergence; automatic adjustment; constraint surfaces; kinematic and material induced nonlinearity; pre- and postbuckling behavior; localized bounds on various hierarchical partitions of the field variables; resize, shape, and orient the global constraint surface; automatic load/deflection incrementation PDFBibTeX XMLCite \textit{J. Padovan} and \textit{R. Moscarello}, Comput. Struct. 23, 181--197 (1986; Zbl 0582.73076) Full Text: DOI