An energy conserving non-linear dynamic finite element formulation for flexible composite laminates

2002 ◽  
Vol 80 (7-8) ◽  
pp. 677-689 ◽  
Author(s):  
Boštjan Brank
Keyword(s):  
Finite Element ◽  
Composite Laminates ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Linear Dynamic ◽  
Dynamic Finite Element ◽  
Non Linear ◽  
Energy Conserving

scholarly journals A Framework for Extension of Dynamic Finite Element Formulation to Flexural Vibration Analysis of Thin Plates

2021 ◽  
Author(s):  
Mohammad M. Elahi ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Solution Space ◽  
Flexural Vibration ◽  
Finite Element Formulation ◽  
Thin Plates ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Good Convergence ◽  
Dynamic Finite Element ◽  
Numerical Testing

Dynamic Finite Element formulation is a powerful technique that combines the accuracy of the exact analysis with wide applicability of the finite element method. The infinite dimensionality of the exact solution space of plate equation has been a major challenge for development of such elements for the dynamic analysis of flexible two-dimensional structures. In this research, a framework for such extension based on subset solutions is proposed. An example element is then developed and implemented in MAT LAB software for numerical testing, verification, and validation purposes. Although the presented formulation is not exact, the element exhibits good convergence characteristics and can be further enriched using the proposed framework.

Anisotropic Turbulence Modelling of Near Wall Effects Pertinent to Turbomachinery Flows

2002 ◽  
Author(s):  
Alessandro Corsini ◽  
Franco Rispoli
Keyword(s):  
Finite Element ◽  
Finite Element Formulation ◽  
Transition To Turbulence ◽  
Element Formulation ◽  
Base Line ◽  
Stress Model ◽  
Compressor Cascade ◽  
Non Linear ◽  
Near Wall ◽  
Non Equilibrium

A computational study is presented which investigates the predictive performance of two non-linear turbulence closures in simulating the physics pertinent to decelerating turbomachinery flows. The compared approaches are a cubic non-linear k-ε model and an algebraic Reynolds stress model. They have been considered as promising closures for improving the industry CFD state-of-the-art accounting for non-equilibrium effects. The authors adopt a parallel multi-grid algorithm, which is developed with a finite element formulation based on a highly accurate stabilized Petrov-Galerkin method. The finite element formulation is here applied on equal-order Q1-Q1 as well as mixed Q2-Q1 element pairs, and the accuracy of the latter approximation is assessed on near-wall flows simulation. The parallel solution algorithm for Reynolds Averaged Navier-Stokes modeling exploits an overlapping domain decomposition technique based on an “inexact explicit non linear Schwarz method”. The compressor flow considered for model benchmarking is highly challenging because of the transitional nature of the flow and the existence of significant leading- and trailing-edge separations. The potential of non-isotropic closures has been investigated. The algebraic stress model is shown to provide a better base-line for non-equilibrium effects simulation with respect to the cubic k-ε model. As it is shown for the studied compressor cascade, the cubic eddy-viscosity model exhibits some predictive weaknesses, among them an excessive turbulence attenuation that results in un-realistically delayed transition to turbulence.

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