Dynamics of Thick Viscoelastic Beams

1997 ◽  
Vol 119 (3) ◽  
pp. 273-278 ◽  
Author(s):  
A. R. Johnson ◽  
A. Tessler ◽  
M. Dambach
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Constitutive Law ◽  
Finite Element Formulation ◽  
Internal Variables ◽  
Element Formulation ◽  
Modal Interactions ◽  
Cantilevered Beam ◽  
Thick Beam

A viscoelastic higher-order thick beam finite element formulation is extended to include elastodynamic deformations. The material constitutive law is a special differential form of the Maxwell solid, which employs viscous strains as internal variables to determine the viscous stresses. The total time-dependent stress is the superposition of its elastic and viscous components. In the constitutive model, the elastic strains and the conjugate viscous strains are coupled through a system of first-order ordinary differential equations. The use of the internal strain variables allows for a convenient finite element formulation. The elastodynamic equations of motion are derived from the virtual work principle. Computational examples are carried out for a thick orthotropic cantilevered beam. Relaxation, creep, relaxation followed by free damped vibrations, and damping related modal interactions are discussed.

scholarly journals On the Stream Function-Vorticity Finite Element Formulation for Incompressible Flow in Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Abdellatif Agouzal ◽  
Karam Allali ◽  
Siham Binna
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Stream Function ◽  
Incompressible Flow ◽  
Equations Of Motion ◽  
Finite Element Formulation ◽  
Flow In Porous Media ◽  
Darcy Law ◽  
Element Formulation ◽  
Discrete Problem

Stream function-vorticity finite element formulation for incompressible flow in porous media is presented. The model consists of the heat equation, the equation for the concentration, and the equations of motion under the Darcy law. The existence of solution for the discrete problem is established. Optimal a priori error estimates are given.

Two-Dimensional Geometrically Nonlinear Finite Element Formulation for Analysis of Straight Pipes

2020 ◽  
Author(s):  
Saher Attia ◽  
Magdi Mohareb ◽  
Michael Martens ◽  
Nader Yoosef Ghodsi ◽  
Yong Li ◽  
...  
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Strain Tensor ◽  
Structural Response ◽  
Small Strain ◽  
Nonlinear Finite Element ◽  
Finite Element Formulation ◽  
Single Element ◽  
Element Formulation ◽  
Geometrically Nonlinear

Abstract The paper presents a new and simple geometrically nonlinear finite element formulation to simulate the structural response of straight pipes under in-plane loading and/or internal pressure. The formulation employs the Green-Lagrange strain tensor to capture finite deformation-small strain effects. Additionally, the First Piola-Kirchhoff stress tensor and Saint Venant-Kirchhoff constitutive model are adopted within the principle of virtual work framework in conjunction with a total Lagrangian approach. The formulation is applied for a cantilever beam under three loading conditions. Results are in good agreement with shell models in ABAQUS. Although the solution is based on a single element, the formulation provides reasonable displacement and stress predictions.

A Finite Element Formulation for the Analysis of Horizontally-Curved Thin-Walled Beams

2015 ◽  
Author(s):  
Ashkan Afnani ◽  
Vida Niki ◽  
R. Emre Erkmen
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Curved Beams ◽  
Equilibrium Equations ◽  
Rotation Tensor ◽  
Initial Curvature ◽  
Horizontally Curved ◽  
Thin Walled

In this study, a finite element formulation is developed for the elastic analysis of thin-walled curved beams. Using a second-order rotation tensor, the strains of the deformed configuration are calculated in terms of the displacement values and the initial curvature. The principle of virtual work is then used to obtain the nonlinear equilibrium equations, based on which a finite element beam formulation is developed. The accuracy of the method is confirmed through comparisons with test results and shell-type finite element formulations and other curved beam formulations from the literature. It is also shown that the results of the developed formulation are very accurate for cases where initial curvature is very large.

Dynamics of Branched Pipeline Systems Conveying Internal Unsteady Flow

1999 ◽  
Vol 121 (1) ◽  
pp. 114-122 ◽  
Author(s):  
Usik Lee ◽  
Joohong Kim
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Fluid Pressure ◽  
Finite Element Formulation ◽  
Dynamic Equations ◽  
Pipeline System ◽  
Element Formulation ◽  
Nonlinear Coupling ◽  
Coupling Terms ◽  
Fully Coupled

The pipeline system conveying high pressurized unsteady internal flow may experience severe transient vibrations due to the fluid-pipe interaction under the time-varying conditions imposed by the pump and valve operations. In the present work, a set of fully coupled dynamic equations of motion for the pipeline system are developed to include the effect of the circumferential strain due to the internal fluid pressure. A finite element formulation for the fully coupled dynamic equations of motion is introduced and applied to several sample pipeline systems. The connectivity conditions for both fluid and structural variables at the junction of a branched pipeline system are properly incorporated in the finite element formulation. To ensure the validity and accuracy of the present theory of pipedynamics, the same pipeline system considered in a reference work is revisited and the present numerical results are compared with those given in the reference work. A series pipeline system with high reservoir head is then analyzed to investigate the effect of the additional linear/nonlinear coupling terms in the present pipedynamic theory. Numerical tests show that the nonlinear coupling terms may become significant at high fluid pressure and velocity.

A Nonlinear Multi-Field Coupling Finite Element Method for Polarization Switching in Ferroelectrics

2008 ◽  
Author(s):  
Jie Wang ◽  
Marc Kamlah
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Three Dimensional ◽  
Polarization Switching ◽  
Ferroelectric Materials ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Polarization Distribution ◽  
Field Coupling ◽  
Simulated System

A three-dimensional nonlinear finite element formulation for ferroelectric materials is developed based on a principle of virtual work. The formulation includes the coupling of three physical fields, namely polarization field, electric field and strain field. The developed finite element formulation is employed to investigate the polarization distribution near a flaw in a ferroelectric single crystal under mechanical loadings. It is found that the polarization switching takes place near the flaw tip if the loadings exceed a critical value. In the simulation, we do not take any prior assumptions, i.e. without any switching criterion, on the polarization switching. The polarization switching is a result of the minimization of the total energy in the simulated system.

Control of Largely-Deformed Nonlinear Electro/Elastic Beam and Plate Systems: Finite Element Formulation and Analysis

2002 ◽  
Author(s):  
D. W. Wang ◽  
H. S. Tzou ◽  
H.-J. Lee
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Nonlinear Dynamic Analysis ◽  
Elastic Beam ◽  
Shell Element ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Control Analysis ◽  
Control Force ◽  
Piezoelectric Shell

Adaptive structures involving large imposed deformation often go beyond the boundary of linear theory and they should be treated as “nonlinear” structures. A generalized nonlinear finite element formulation for vibration sensing and control analysis of laminated electro/elastic nonlinear shell structures is derived based on the virtual work principle. A generic curved triangular piezoelectric shell element is proposed based on the layerwise constant shear angle theory. The dynamic system equations, equations of electric potential output and feedback control force defined in a matrix form are derived. The modified Newton-Raphson method is adopted for nonlinear dynamic analysis of large and complex piezoelectric/elastic/control structures. The developed piezoelectric shell element and finite element code are validated and then applied to control analysis of flexible electro-elastic (piezoelectric/elastic) structural systems. Vibration control of constant-curvature electro/elastic beam and plate systems is studied. Time-history responses of free and controlled nonlinear electro/elastic beam and plate systems are presented and nonlinear effects discussed.

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