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**A survey of direct time-integration methods in computational structural dynamics. I: Explicit methods.**
*(English)*
Zbl 0702.73072

Summary: A comprehensive survey of direct time-integration methods and computational solution procedures for easier computer implementation is given in four parts for dynamic analysis of linear and nonlinear structures.

Part I is exclusively devoted to explicit methods. Popular second order central difference methods (formulation, step-by-step solution procedures, recent developments, computational and stability aspects) are described in detail. Other explicit methods, viz. Runge-Kutta methods, stiffly stable methods, predictor-corrector methods and Taylor series schemes are also presented. Techniques for stabilizing numerical computations are given. In Part II, conventional implicit methods, viz. the Newmark, Wilson-Theta and Houbolt methods and their step-by-step solution procedures are given with reference to solution of linear and nonlinear structural dynamics problems. Also presented are Trujillo’s modified Newmark-beta method and implicit formula via weighted residual approach. Computational and stability aspects, desirable characteristics of an ideal solution procedure and salient features of conventional implicit algorithms are discussed. Part III reviews further developments in implicit methods. In Part IV, mixed implicit-explicit finite element methods and operator-splitting methods are described. Numerical solution methods surveyed here will be of much use to practicing computational/finite element/structural engineers working in the area of dynamics of structures.

Part I is exclusively devoted to explicit methods. Popular second order central difference methods (formulation, step-by-step solution procedures, recent developments, computational and stability aspects) are described in detail. Other explicit methods, viz. Runge-Kutta methods, stiffly stable methods, predictor-corrector methods and Taylor series schemes are also presented. Techniques for stabilizing numerical computations are given. In Part II, conventional implicit methods, viz. the Newmark, Wilson-Theta and Houbolt methods and their step-by-step solution procedures are given with reference to solution of linear and nonlinear structural dynamics problems. Also presented are Trujillo’s modified Newmark-beta method and implicit formula via weighted residual approach. Computational and stability aspects, desirable characteristics of an ideal solution procedure and salient features of conventional implicit algorithms are discussed. Part III reviews further developments in implicit methods. In Part IV, mixed implicit-explicit finite element methods and operator-splitting methods are described. Numerical solution methods surveyed here will be of much use to practicing computational/finite element/structural engineers working in the area of dynamics of structures.

### MSC:

74S20 | Finite difference methods applied to problems in solid mechanics |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74S05 | Finite element methods applied to problems in solid mechanics |

74H45 | Vibrations in dynamical problems in solid mechanics |