Dynamics of Curved Beams Undergoing Large Overall Motions Using the Mode Decomposition Concept

1993 ◽  
Author(s):  
Joseph F. D’Costa ◽  
Henryk K. Stolarski ◽  
Arthur G. Erdman
Keyword(s):  
Multibody Systems ◽  
Inertial Frame ◽  
Curved Beams ◽  
Nonlinear Formulation ◽  
Element Discretization ◽  
Inertia Effects ◽  
Mode Decomposition ◽  
Curved Elements ◽  
Finite Bending ◽  
Locking Phenomena

Abstract A fully nonlinear formulation for the dynamics of initially curved and twisted beams, undergoing arbitrary spatial motions, is presented. The formulation admits finite bending, shearing and extension of the beam. The Mode decomposition method is employed to modify the strains in the finite element discretization process leading to the elimination of shear and membrane locking phenomena that arise in curved elements. The model incorporates all inertia effects and is capable of accurately capturing the phenomena of dynamic stiffening due to the coupling of the axial and membrane forces to the flexural deformation. All motion is referred to the inertial frame. The nonlinear formulation is suitable for modeling flexible multibody systems. Examples are presented to illustrate the validity of the proposed formulation.

Eulerian Bond Graphs for Fluid Continuum Dynamics Modeling

1996 ◽  
Vol 118 (1) ◽  
pp. 48-57 ◽  
Author(s):  
E. P. Fahrenthold ◽  
M. Venkataraman
Keyword(s):  
Compressible Flows ◽  
System Modeling ◽  
General Purpose ◽  
Dynamics Modeling ◽  
Modeling Tools ◽  
Element Discretization ◽  
Inertia Effects ◽  
Flow Geometry ◽  
Viscous Compressible Flows ◽  
Continuum Dynamics

The development of high resolution, general purpose models of viscous, compressible flows is extremely difficult with existing system dynamics modeling tools. Published work admits to significant limitations, with regards to the treatment of flow geometry, inertia effects, or mass and energy convection. Combining a finite element discretization scheme with a bond graph based model formulation procedure provides a very general purpose tool for continuum fluid system modeling.

Locking Removal Techniques for the Isogeometric Formulation of Curved Beams

2017 ◽  
Vol 1144 ◽  
pp. 109-114
Author(s):  
Edita Dvořáková ◽  
Bořek Patzák
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Beam Element ◽  
Basis Functions ◽  
Shear Locking ◽  
Curved Beams ◽  
Straight Beam ◽  
Discrete Shear Gap ◽  
Thin Beams ◽  
Locking Phenomena

The isogeometric formulation seems to be advantageous especially when it comes to curved geometries such as curved beams and shells. In this paper, the NURBS isogeometric formulation of beam element is presented. The same basis functions are used for both geometry description and unknown approximations so there is no accuracy loss caused by a geometry approximation. The element is based on Timoshenko beam theory which enables the use of the element for both thick and thin beams, nevertheless in case of thin beams the shear-locking phenomena is observed. In the paper it is shown that the reduced integration is insufficient for locking removal and capability of Discrete Shear Gap (DSG) method to unlock the elements is examined. For clear demonstration of locking-removal techniques the implemented element is first tested for the case of straight beam, then the performance is demonstrated on the curved geometry.

scholarly journals Modelling of a Flexible Quadrirotor Helicopter

2006 ◽  
Author(s):  
Alexis Mouhingou ◽  
Naoufel Azouz
Keyword(s):  
Finite Element ◽  
Complex Systems ◽  
Reference Frame ◽  
Multibody Systems ◽  
Finite Element Discretization ◽  
Numerical Application ◽  
Elastic Deformations ◽  
Element Discretization ◽  
Body Reference ◽  
Discretization Technique

This paper describes the dynamical modelling for the simulation of the quadrirotor Helicopter in order to see the influence of the flexibility on the dynamical model. We consider a quadrirotor Helicopter like a multibody systems constituted of the flexible and rigid substructures interconnected by of articulation joint. We use the variationnal Lagrangian approach to define the equations governing the motion. Deformations modes are used to represent elastic deformations of the substructure relative to a body reference frame. The displacement functions shape of the flexible components is obtained by a finite element discretization technique. The numerical application is related to the quadrirotor XSF developed in the LSC (Laboratory of Complex Systems).

Linear Visco-Resistive Computations of Magnetohydrodynamic Waves: I. The Code and Test Cases

1994 ◽  
Vol 144 ◽  
pp. 503-505
Author(s):  
R. Erdélyi ◽  
M. Goossens ◽  
S. Poedts
Keyword(s):  
Resonant Absorption ◽  
Numerical Code ◽  
Mhd Waves ◽  
Test Cases ◽  
Numerical Accuracy ◽  
Element Discretization ◽  
Flux Tubes ◽  
Magnetohydrodynamic Waves ◽  
Viscosity Coefficients ◽  
Magnetic Flux Tubes

AbstractThe stationary state of resonant absorption of linear, MHD waves in cylindrical magnetic flux tubes is studied in viscous, compressible MHD with a numerical code using finite element discretization. The full viscosity tensor with the five viscosity coefficients as given by Braginskii is included in the analysis. Our computations reproduce the absorption rates obtained by Lou in scalar viscous MHD and Goossens and Poedts in resistive MHD, which guarantee the numerical accuracy of the tensorial viscous MHD code.

Microstructure simulation of early paper forming using immersed boundary methods

TAPPI Journal ◽  
2011 ◽  
Vol 11 (11) ◽  
pp. 23-30 ◽  
Author(s):  
ANDREAS MARK ◽  
ERIK SVENNING ◽  
ROBERT RUNDQVIST ◽  
FREDRIK EDELVIK ◽  
ERIK GLATT ◽  
...  
Keyword(s):  
Early Paper ◽  
Contact Model ◽  
Fiber Suspension ◽  
Beam Equation ◽  
Immersed Boundary ◽  
Paper Machine ◽  
Immersed Boundary Methods ◽  
Element Discretization ◽  
Microstructure Simulation ◽  
Boundary Methods

Paper forming is the first step in the paper machine where a fiber suspension leaves the headbox and flows through a forming fabric. Complex physical phenomena occur as the paper forms, during which fibers, fillers, fines, and chemicals added to the suspension interact. Understanding this process is important for the development of improved paper products because the configuration of the fibers during this step greatly influences the final paper quality. Because the effective paper properties depend on the microstructure of the fiber web, a continuum model is inadequate to explain the process and the properties of each fiber need to be accounted for in simulations. This study describes a new framework for microstructure simulation of early paper forming. The simulation framework includes a Navier-Stokes solver and immersed boundary methods to resolve the flow around the fibers. The fibers were modeled with a finite element discretization of the Euler-Bernoulli beam equation in a co-rotational formulation. The contact model is based on a penalty method and includes friction and elastic and inelastic collisions. We validated the fiber model and the contact model against demanding test cases from the literature, with excellent results. The fluid-structure interaction in the model was examined by simulating an elastic beam oscillating in a cross flow. We also simulated early paper formation to demonstrate the potential of the proposed framework.

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