Improved numerical dissipation for time integration algorithms in structural dynamics

  title={Improved numerical dissipation for time integration algorithms in structural dynamics},
  author={Hans M. Hilber and Thomas J. R. Hughes and Robert Taylor},
  journal={Earthquake Engineering \& Structural Dynamics},
A new family of unconditionally stable one-step methods for the direct integration of the equations of structural dynamics is introduced and is shown to possess improved algorithmic damping properties which can be continuously controlled. The new methods are compared with members of the Newmark family, and the Houbolt and Wilson methods. 
A simple explicit single step time integration algorithm for structural dynamics
  • Wooram Kim
  • Mathematics, Engineering
    International Journal for Numerical Methods in Engineering
  • 2019
In this article, a new single‐step explicit time integration method is developed based on the Newmark approximations for the analysis of various dynamic problems. The newly proposed method is
New Family of Explicit Structure-Dependent Integration Algorithms with Controllable Numerical Dispersion
This paper presents direct integration algorithms, which are effective methods to solve the temporally discretized differential equations of motion for structural dynamics with real-time requirements.
There are several known algorithms for the numerical integration of the equation of motions in structural dynamics. However, efforts have been made recently to obtain more efficient and accurate
Modified Rosenbrock Method for Computing the Transient Response of Nonlinear Structures
A desirable feature of implicit integration methods for structural dynamics problems is the numerical damping of spurious high-frequency oscillations in the solution. For example, the method of
Numerical Integration of Second Order Differential—Algebraic Systems in Flexible Mechanism Dynamics
This paper studies second order accurate methods to numerically time-integrate the equations of motion for flexible mechanism dynamics. The aspects of stability, accuracy, conditioning of equations
New Unconditionally Stable Explicit Integration Algorithm for Real-Time Hybrid Testing
This work presents a new approach to integrate discrete equations of motion in a real-time environment and demonstrates the ability of this approach to solve discrete-time discrete-partitioning problems.
Parabolic and cubic acceleration time integration schemes for nonlinear structural dynamics problems using the method of weighted residuals
ABSTRACT Two algorithms are proposed for direct time integration of an equation of motion of structural dynamics problems. The performance of the proposed methods is examined by evaluating stability,


Stability and accuracy analysis of direct integration methods
A systematic procedure is presented for the stability and accuracy analysis of direct integration methods in structural dynamics. Amplitude decay and period elongation are used as the basic
Transient shell response by numerical time integration
In using the finite element method to compute a transient response, two choices must be made. First, some form of mass matrix must be decided upon. Either the consistent mass matrix prescribed by the
A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft
A systematic procedure is developed for the calculation of the structural response of an airplane subject to dynamic loads. Particular attention is given the problem of determining the stresses