Mixed time integration for the transient analysis of jointed media

1986 ◽  
Vol 23 (4) ◽  
pp. 144
Keyword(s):  
Transient Analysis ◽  
Time Integration

scholarly journals A time variational method to couple heterogeneous time integrators

2010 ◽  
pp. 11-24
Author(s):  
Alain Combescure ◽  
Najib Mahjoubi ◽  
Anthony Gravouil ◽  
Nicolas Greffet
Keyword(s):  
Transient Analysis ◽  
Dynamic Equilibrium ◽  
Time Integration ◽  
Integration Scheme ◽  
Time Integrators ◽  
Coupling Strategy ◽  
Time Integration Scheme ◽  
New Vision ◽  
General Method

This paper is devoted to a brief presentation of recent research results upon structural mechanics code coupling in transient analysis. The domain is supposed to be decomposed into a series of sub domains which are treated independently with their own time integration scheme and or their own code. The paper gives a general method which allows to couple these subdomains. The proposed method is rather general and based upon a weak vision of dynamic equilibrium equation. This new vision allows to design a coupling strategy which ensure by design that no energy is introduced or dissipated in the interfaces between the sub domains. The proposed coupling method hence does not perturb the quality of the time integrators of each sub domain. This also allows to develop a general code coupler for transient dynamics. Two examples are given to illustrate the paper.

scholarly journals Adaptivity in Crashworthiness Calculations

1993 ◽  
Vol 1 (2) ◽  
pp. 97-106 ◽  
Author(s):  
Ted Belytschko ◽  
Sang-Ho Lee ◽  
I-Sheng Yeh ◽  
Jerry I. Lin ◽  
Chen-Shyh Tsay ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Transient Analysis ◽  
Time Integration ◽  
Adaptive Finite Element ◽  
Data Preparation ◽  
Adaptive Finite Element Methods ◽  
Explicit Time Integration ◽  
Car Model ◽  
Nonlinear Transient

h-Adaptive finite element methods for nonlinear transient analysis by explicit time integration are described. Examples are given of adaptive calculations for simple components and prototype calculations for a full car model. h-Adaptivity offers substantial reductions in data preparation costs and improvements in accuracy.

Superconvergent Isogeometric Transient Analysis of Wave Equations

2020 ◽  
Vol 20 (08) ◽  
pp. 2050083
Author(s):  
Xiwei Li ◽  
Dongdong Wang ◽  
Xiaolan Xu ◽  
Zhuangjing Sun
Keyword(s):  
Transient Analysis ◽  
Wave Equations ◽  
Time Integration ◽  
Quadrature Rule ◽  
Sixth Order ◽  
Step Size ◽  
Order Accuracy ◽  
Integration Schemes ◽  
Quadratic Splines ◽  
Time Integration Schemes

A superconvergent isogeometric formulation is presented for the transient analysis of wave equations with particular reference to quadratic splines. This formulation is developed in the context of Newmark time integration schemes and superconvergent quadrature rules for isogeometric mass and stiffness matrices. A detailed analysis is carried out for the full-discrete isogeometric formulation of wave equations and an error measure for the full-discrete algorithm is established. It is shown that a desirable superconvergence regarding the isogeometric transient analysis of wave equations can be achieved by two ingredients, namely, the design of a superconvergent quadrature rule and the criteria to properly define the step size for temporal integration. It turns out that the semi-discrete and full-discrete isogeometric formulations of wave equations with quadratic splines share an identical quadrature rule for a sixth-order accurate superconvergent analysis. Meanwhile, the relationships between the time step size and the element size are presented for various typical Newmark time integration schemes, in order to ensure the sixth-order accuracy in transient analysis. Numerical results of the transient analysis of wave equations consistently reveal that the proposed superconvergent isogeometric formulation is sixth-order accurate with respect to spatial discretizations, in contrast to the fourth-order accuracy produced by the standard isogeometric approach with quadratic splines.

Finite Cell Method: High-Order Structural Dynamics for Complex Geometries

2015 ◽  
Vol 15 (07) ◽  
pp. 1540018 ◽  
Author(s):  
M. Elhaddad ◽  
N. Zander ◽  
S. Kollmannsberger ◽  
A. Shadavakhsh ◽  
V. Nübel ◽  
...  
Keyword(s):  
Transient Analysis ◽  
Mathematical Formulation ◽  
Time Integration ◽  
Implicit Time ◽  
Weak Formulation ◽  
Finite Cell Method ◽  
Cell Method ◽  
Integration Schemes ◽  
Linear Elastodynamics ◽  
Finite Cell

In this contribution, the finite cell method (FCM) is applied to solve transient problems of linear elastodynamics. The mathematical formulation of FCM for linear elastodynamics is presented, following from the weak formulation of the initial/boundary-value problem. Semi-discrete time integration schemes are briefly discussed, and the choice of implicit time integration is justified. A 1D benchmark problem is solved using FCM, illustrating the method's ability to solve problems of linear elastodynamics obtaining high rates of convergence. Furthermore, a numerical example of transient analysis from an industrial application is solved using FCM. The numerical results are compared to the results obtained using state-of-the-art commercial software, employing linear finite elements, in conjunction with explicit time integration. The results illustrate the potential of FCM as a powerful tool for transient analysis in elastodynamics, offering a high degree of accuracy at a moderate computational effort.

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