scholarly journals Dynamic analysis of 2-D and 3-D quasi-brittle solids and structures by D/BEM

2002 ◽  
pp. 39-48 ◽  
Author(s):  
George Hatzigeorgiou ◽  
Beskos Dimitri
Keyword(s):  
Dynamic Analysis ◽  
Singular Integrals ◽  
Time Integration ◽  
The Body ◽  
Material Behavior ◽  
Integration Scheme ◽  
Brittle Solids ◽  
Integration Techniques ◽  
Time Integration Scheme ◽  
Loading Effects

A general boundary element methodology for the dynamic analysis of 2-D and 3-D solids and structures exhibiting quasi-brittle material behavior is presented. Inelasticity is modeled with the aid of the elastic damage theory. Strain rate and cyclic loading effects are also considered. The integral formulation of the problem employs the electrostatic fundamental solution and thus both surface and volume integrals due to inertia and inelasticity are created. Consequently the discrimination involves both the surface and the interior of the body. The singular integrals are evaluated by advanced numerical integration techniques, while Humboldt's step-by-step time integration scheme is used to obtain the dynamic response. Numerical examples are presented to illustrate the proposed method and demonstrate its accuracy and potential. .

Explicit Time Integration Algorithm for Fully Flexible Cell Molecular Dynamics

2006 ◽  
Vol 326-328 ◽  
pp. 337-340 ◽  
Author(s):  
Shi Dong Park ◽  
Maeng Hyo Cho
Keyword(s):  
Molecular Dynamics ◽  
Real Time ◽  
Time Domain ◽  
Time Integration ◽  
Unit Cell ◽  
Material Behavior ◽  
Integration Scheme ◽  
Time Reversibility ◽  
Time Integration Scheme ◽  
Splitting Time

Fully flexible cell with Nose-Poincare method preserves Hamiltonian in structure, so the extended Hamiltonian is preserved in the real time domain. In the previous development of Nose- Poincare method for NVT, NPT, and NT ensemble unit cell simulations, implicit algorithm such as generalized leapfrog integration scheme was used. The formulation and numerical implementatio n of the implicit formula is much more complicated because it includes nonlinear iteration procedur e. Furthermore, it is not easy to show time reversibility in implicit formula. Thus for these reasons, it is necessary to develop explicit formula in MD unit cell simulation. We develop fully flexible explicit Nσ T ensemble MD simulation algorithm. It guarantees the preservation of extended Hamil tonian in real time domain and time reversibility. The numerical implementation is easy and relative ly simple since it does not require iteration process. It is established by using the splitting time integ ration. It separates flexible cell Hamiltonian into several terms corresponding to each Hamiltonian part, so the simple and completely explicit recursion formula was obtained. Unit cell tension, shear test for bulk material tension and shear tests are performed to demonstrate the validity and performance of the present explicit molecular dynamics scheme formulated through the spitting method. We compare the results of the explicit splitting time integration scheme with those of the implicit generalized leapfrog time integration scheme. The proposed explicit NT unit cell simulati on method should serve as a powerful tool in the prediction of the material behavior.

scholarly journals Structural Reliability Sensitivities under Nonstationary Random Vibrations

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Rita Greco ◽  
Francesco Trentadue
Keyword(s):  
Structural Reliability ◽  
Structural Parameters ◽  
Time Integration ◽  
Structural Response ◽  
Integration Scheme ◽  
Structural Systems ◽  
Frame Building ◽  
Time Integration Scheme ◽  
Noise Input ◽  
The Time Domain

Response sensitivity evaluation is an important element in reliability evaluation and design optimization of structural systems. It has been widely studied under static and dynamic forcing conditions with deterministic input data. In this paper, structural response and reliability sensitivities are determined by means of the time domain covariance analysis in both classically and nonclassically damped linear structural systems. A time integration scheme is proposed for covariance sensitivity. A modulated, filtered, white noise input process is adopted to model the stochastic nonstationary loads. The method allows for the evaluation of sensitivity statistics of different quantities of dynamic response with respect to structural parameters. Finally, numerical examples are presented regarding a multistorey shear frame building.

scholarly journals A new energy–momentum time integration scheme for non-linear thermo-mechanics

2020 ◽  
Vol 372 ◽  
pp. 113395 ◽  
Author(s):  
R. Ortigosa ◽  
A.J. Gil ◽  
J. Martínez-Frutos ◽  
M. Franke ◽  
J. Bonet
Keyword(s):  
Time Integration ◽  
Integration Scheme ◽  
Non Linear ◽  
New Energy ◽  
Time Integration Scheme

New insights into the β1/β2-Bathe time integration scheme when L-stable

2021 ◽  
Vol 245 ◽  
pp. 106433
Author(s):  
Mohammad Mahdi Malakiyeh ◽  
Saeed Shojaee ◽  
Saleh Hamzehei-Javaran ◽  
Klaus-Jürgen Bathe
Keyword(s):  
Time Integration ◽  
Integration Scheme ◽  
Time Integration Scheme

Energy‐momentum consistent time integration scheme for non‐linear electro‐elastodynamics

PAMM ◽  
2018 ◽  
Vol 18 (1) ◽  
Author(s):  
Alexander Janz ◽  
Peter Betsch ◽  
Marlon Franke ◽  
Rogelio Ortigosa
Keyword(s):  
Time Integration ◽  
Integration Scheme ◽  
Non Linear ◽  
Time Integration Scheme
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