Three-dimensional Structural Dynamic Analysis using Parallel Direct Time Integration Methods

2009 ◽  
Author(s):  
J.M. Alonso ◽  
V. Hernández
Keyword(s):  
Dynamic Analysis ◽  
Time Integration ◽  
Three Dimensional ◽  
Structural Dynamic ◽  
Integration Methods ◽  
Time Integration Methods

A weak form temporal quadrature element formulation for linear structural dynamics

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Junning Qin ◽  
Hongzhi Zhong
Keyword(s):  
Structural Dynamics ◽  
Initial Conditions ◽  
Time Integration ◽  
Weak Form ◽  
Element Formulation ◽  
Dynamic Problems ◽  
Structural Dynamic ◽  
Integration Methods ◽  
Content Type ◽  
Time Integration Methods

PurposeVarious time integration methods and time finite element methods have been developed to obtain the responses of structural dynamic problems, but the accuracy and computational efficiency of them are sometimes not satisfactory. The purpose of this paper is to present a more accurate and efficient formulation on the basis of the weak form quadrature element method to solve linear structural dynamic problems.Design/methodology/approachA variational principle for linear structural dynamics, which is inspired by Noble's work, is proposed to develop the weak form temporal quadrature element formulation. With Lobatto quadrature rule and the differential quadrature analog, a system of linear equations is obtained to solve the responses at sampling time points simultaneously. Computation for multi-elements can be carried out by a time-marching technique, using the end point results of the last element as the initial conditions for the next.FindingsThe weak form temporal quadrature element formulation is conditionally stable. The relation between the normalized length of element and the suggested number of integration points in one element is given by a simple formula. Results show that the present formulation is much more accurate than other time integration methods and its dissipative property is also illustrated.Originality/valueThe weak form temporal quadrature element formulation provides a choice with high accuracy and efficiency for solution of linear structural dynamic problems.

Accuracy and efficiency of time integration methods for 1D diffusive wave equation

2014 ◽  
Vol 18 (5) ◽  
pp. 697-709 ◽  
Author(s):  
Sylvain Weill ◽  
Raphael di Chiara-Roupert ◽  
Philippe Ackerer
Keyword(s):  
Wave Equation ◽  
Time Integration ◽  
Integration Methods ◽  
Time Integration Methods

scholarly journals Efficient time integration methods for Gross-Pitaevskii equations with rotation term

2019 ◽  
Vol 6 (2) ◽  
pp. 147-169 ◽  
Author(s):  
Philipp Bader ◽  
◽  
Sergio Blanes ◽  
Fernando Casas ◽  
Mechthild Thalhammer ◽  
...  
Keyword(s):  
Time Integration ◽  
Integration Methods ◽  
Time Integration Methods

Development of Differential Quadrature Related Generalized Methods, Discrete Element Analysis Methods and EDQ Based Time Integration Methods

2005 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Time Integration ◽  
Numerical Algorithms ◽  
Discrete Element ◽  
Numerical Results ◽  
Differential Quadrature ◽  
Element Analysis ◽  
Integration Methods ◽  
Analysis Methods ◽  
Time Integration Methods

Development of differential quadrature related generalized methods, discrete element analysis methods and EDQ based time integration methods has been carried out the last few years. The related numerical algorithms are summarized and presented. Numerical results are also presented.

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