Improved time integration of nonlinear dynamic problems

1987 ◽  
Vol 62 (2) ◽  
pp. 155-168 ◽  
Author(s):  
C.S. Desai ◽  
J. Kujawski ◽  
C. Miedzialowski ◽  
W. Ryzynski
Keyword(s):  
Nonlinear Dynamic ◽  
Time Integration ◽  
Dynamic Problems

scholarly journals Performance of a Three-Substep Time Integration Method on Structural Nonlinear Seismic Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Jinyue Zhang ◽  
Lei Shi ◽  
Tianhao Liu ◽  
De Zhou ◽  
Weibin Wen
Keyword(s):  
Nonlinear Dynamic ◽  
Integration Method ◽  
Seismic Analysis ◽  
Time Integration ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Dynamic Problems ◽  
Element Analysis ◽  
Time Integration Method ◽  
Period Elongation

In this work, a study of a three substeps’ implicit time integration method called the Wen method for nonlinear finite element analysis is conducted. The calculation procedure of the Wen method for nonlinear analysis is proposed. The basic algorithmic property analysis shows that the Wen method has good performance on numerical dissipation, amplitude decay, and period elongation. Three nonlinear dynamic problems are analyzed by the Wen method and other competitive methods. The result comparison indicates that the Wen method is feasible and efficient in the calculation of nonlinear dynamic problems. Theoretical analysis and numerical simulation illustrate that the Wen method has desirable solution accuracy and can be a good candidate for nonlinear dynamic problems.

A Comparative Study of Two Families of Higher-Order Accurate Time Integration Algorithms

2019 ◽  
Vol 17 (08) ◽  
pp. 1950048 ◽  
Author(s):  
Wooram Kim ◽  
Jin Ho Lee
Keyword(s):  
Structural Dynamics ◽  
Nonlinear Dynamic ◽  
Time Integration ◽  
Nonlinear Problems ◽  
Higher Order ◽  
Dynamic Problems ◽  
The Past ◽  
Numerical Tests ◽  
Integration Algorithms ◽  
Computational Structures

Two families of higher-order accurate time integration algorithms are numerically tested by using various nonlinear problems of structural dynamics, and the numerical results obtained from them are compared. To be specific, the higher-order algorithms of Kim and Reddy and the higher-order algorithms of Fung are used for this study. In linear analyses, these two different families of higher-order algorithms do not present noticeable differences. However, performances of these algorithms are quite different when they are applied to various nonlinear dynamic problems. For the numerical tests, well-known nonlinear problems are selected from the past studies. For the completeness, the two families of algorithms are briefly reviewed, and their advantageous computational structures are also explained.

A ROBUST TIME-INTEGRATION ALGORITHM FOR SOLVING NONLINEAR DYNAMIC PROBLEMS WITH LARGE ROTATIONS AND DISPLACEMENTS

2012 ◽  
Vol 12 (06) ◽  
pp. 1250051 ◽  
Author(s):  
SHYH-RONG KUO ◽  
J. D. YAU ◽  
Y. B. YANG
Keyword(s):  
Nonlinear Dynamic ◽  
Finite Difference Methods ◽  
Time Integration ◽  
Nonlinear Dynamic Analysis ◽  
Element Approximation ◽  
Dynamic Problems ◽  
Time Step ◽  
Integration Algorithm ◽  
Current Time ◽  
Time Integration Algorithm

An efficient time-integration algorithm for nonlinear dynamic analysis of structures is presented. By adopting the temporal discretization for time finite element approximation, very large time steps can be used by the algorithm. With an accuracy of fourth order, this technique requires only displacements and velocities to be made available at the start of the current time step for integration in state space. Using the weighted momentum principle, the problem of discontinuity caused by impulsive loads is resolved after time-integration of the applied load in external momentum. Since no knowledge is required of acceleration at the current time step, the errors caused by estimation of acceleration by previous finite-difference methods are circumvented. Moreover, an iterative procedure is included for each time step, involving the three phases of predictor, corrector, and error-checking. The effectiveness and robustness of the proposed algorithm in solving nonlinear dynamic problems is demonstrated in the numerical examples.

Finite Elements in Time and Space

1969 ◽  
Vol 73 (708) ◽  
pp. 1041-1044 ◽  
Author(s):  
J. H. Argyris ◽  
D. W. Scharpf
Keyword(s):  
Finite Elements ◽  
Linear Equations ◽  
Time Integration ◽  
Fixed Time ◽  
Time Interval ◽  
Structural Elements ◽  
Dynamic Problems ◽  
System Of Linear Equations ◽  
Interpolation Procedure ◽  
Variational Statement

The present paper seeks to apply the ideas of discretisation to time dependent phenomena. As a suitable variational statement we may use Hamilton's principle. In practise this means that the time is discretised into a set of finite elements which are taken to be the same for all structural elements. A finite element in time consists simply of a fixed time interval. In our present discussion we detail in particular the case when at the beginning and end of the time interval the generalised displacements and velocities are given. For dynamic problems this is the minimum of information required, but the technique may easily be extended to account for additional “timewise degrees of freedoms”. Introducing an appropriate interpolation procedure we may obtain the displacement and velocity at any instant of time. It is then possible to carry out in the variational statement the time integration explicitly and to obtain hence a system of linear equations. The method is extremely simple, since the time interpolation of all structural freedoms of an element in space is the same. We also demonstrate that the general case of a multi-degree of freedoms system can be made to depend on the matrices which describe the unidimensional motion of a mass point.

Sign in / Sign up

Export Citation Format

Share Document