OpenMP Parallelization of a Mickens Time-Integration Scheme for a Mixed-Culture Biofilm Model and Its Performance on Multi-core and Multi-processor Computers

2010 ◽  
pp. 180-195 ◽  
Author(s):  
Nasim Muhammad ◽  
Hermann J. Eberl
Keyword(s):  
Mixed Culture ◽  
Time Integration ◽  
Integration Scheme ◽  
Biofilm Model ◽  
Time Integration Scheme

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

Transonic Flow Computations in Cascades Using Finite Element Method

1981 ◽  
Vol 103 (4) ◽  
pp. 657-664 ◽  
Author(s):  
H. U. Akay ◽  
A. Ecer
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transonic Flow ◽  
Method Development ◽  
Time Integration ◽  
Integration Scheme ◽  
Complex Flow ◽  
Time Integration Scheme ◽  
Naca 0012 ◽  
Element Method

Analysis of transonic flow through a cascade of airfoils is investigated using the finite element method. Development of a computational grid suitable for complex flow structures and different types of boundary conditions is presented. An efficient pseudo-time integration scheme is developed for the solution of equations. Modeling of the shock and the convergence characteristics of the developed scheme are discussed. Numerical results include a 45 deg staggered cascade of NACA 0012 airfoils with inlet flow Mach number of 0.8 and angles of attack 1, 0, and −1 deg.

scholarly journals Numerical Integration of Multibody Dynamic Systems Involving Nonholonomic Equality Constraints

2021 ◽  
Author(s):  
Sotirios Natsiavas ◽  
Panagiotis Passas ◽  
Elias Paraskevopoulos
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
Time Integration ◽  
Nonholonomic Constraints ◽  
Coupled System ◽  
Weak Form ◽  
Integration Scheme ◽  
Motion Constraints ◽  
Multibody Dynamic ◽  
Time Integration Scheme

Abstract This work considers a class of multibody dynamic systems involving bilateral nonholonomic constraints. An appropriate set of equations of motion is employed first. This set is derived by application of Newton’s second law and appears as a coupled system of strongly nonlinear second order ordinary differential equations in both the generalized coordinates and the Lagrange multipliers associated to the motion constraints. Next, these equations are manipulated properly and converted to a weak form. Furthermore, the position, velocity and momentum type quantities are subsequently treated as independent. This yields a three-field set of equations of motion, which is then used as a basis for performing a suitable temporal discretization, leading to a complete time integration scheme. In order to test and validate its accuracy and numerical efficiency, this scheme is applied next to challenging mechanical examples, exhibiting rich dynamics. In all cases, the emphasis is put on highlighting the advantages of the new method by direct comparison with existing analytical solutions as well as with results of current state of the art numerical methods. Finally, a comparison is also performed with results available for a benchmark problem.

scholarly journals EULER AND EXPONENTIAL ALGORITHM IN VISCOELASTIC ANALYSES OF LAMINATED GLASS

2020 ◽  
Vol 26 ◽  
pp. 86-93
Author(s):  
Jaroslav Schmidt ◽  
Alena Zemanová
Keyword(s):  
Time Integration ◽  
Optimal Time ◽  
Integration Scheme ◽  
Laminated Glass ◽  
Aesthetic Value ◽  
Rate Dependent ◽  
Time Integration Scheme ◽  
One Step ◽  
Sectional Plane ◽  
The Aesthetic

Laminated glass combines two remarkable materials: glass and a polymer ply. While glass is stiff and brittle, the polymer ply is a rate-dependent compliant material. Together, they form a material which keeps the aesthetic value of glass, and due to the polymer, no fragile collapse appears. The polymer ply exhibits time- and temperature-dependency, whereas glass suffers from brittle fracture, which makes the analysis difficult. In this article, a 2D sectional plane-stress model for the viscoelastic analysis of laminated glass is presented. This study presents one step in the development of a phase-field-based damage solver for laminated glass to select the optimal time-integration scheme for a quasistatic-analysis and later also for dynamics. The validation against experimental data is provided, and the model reduction is also discussed.

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