Modeling of a One-Sided Bonded and Rigid Constraint Using Beam Theory

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Peter J. Ryan ◽  
George G. Adams ◽  
Nicol E. McGruer
Keyword(s):  
Boundary Conditions ◽  
Microelectromechanical Systems ◽  
Three Dimensional ◽  
Beam Theory ◽  
Rotational Stiffness ◽  
Element Analysis ◽  
Transverse Loads ◽  
Rigid Constraint ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

In beam theory, constraints can be classified as fixed/pinned depending on whether the rotational stiffness of the support is much greater/less than the rotational stiffness of the freestanding portion. For intermediate values of the rotational stiffness of the support, the boundary conditions must account for the finite rotational stiffness of the constraint. In many applications, particularly in microelectromechanical systems and nanomechanics, the constraints exist only on one side of the beam. In such cases, it may appear at first that the same conditions on the constraint stiffness hold. However, it is the purpose of this paper to demonstrate that even if the beam is perfectly bonded on one side only to a completely rigid constraining surface, the proper model for the boundary conditions for the beam still needs to account for beam deformation in the bonded region. The use of a modified beam theory, which accounts for bending, shear, and extensional deformation in the bonded region, is required in order to model this behavior. Examples are given for cantilever, bridge, and guided structures subjected to either transverse loads or residual stresses. The results show significant differences from the ideal bond case. Comparisons made to a three-dimensional finite element analysis show a good agreement.

scholarly journals Nonlinear Mechanics of Beams With Partial Piezoelectric Layers

2019 ◽  
Vol 86 (10) ◽  
Author(s):  
Hamed Farokhi ◽  
Mergen H. Ghayesh
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Coupled Model ◽  
Beam Theory ◽  
Internal Resonances ◽  
Element Analysis ◽  
Nonlinear Dynamical ◽  
Dimensional Finite Element ◽  
Resonant Region ◽  
Three Dimensional Finite Element

Abstract This paper investigates the nonlinear static response as well as nonlinear forced dynamics of a clamped–clamped beam actuated by piezoelectric patches partially covering the beam from both sides. This study is the first to develop a high-dimensional nonlinear model for such a piezoelectric-beam configuration. The nonlinear dynamical resonance characteristics of the electromechanical system are examined under simultaneous DC and AC piezoelectric actuations, while highlighting the effects of modal energy transfer and internal resonances. A multiphysics coupled model of the beam-piezoelectric system is proposed based on the nonlinear beam theory of Bernoulli–Euler and the piezoelectric constitutive equations. The discretized model of the system is obtained with the help of the Galerkin weighted residual technique while retaining 32 degrees-of-freedom. Three-dimensional finite element analysis is conducted as well in the static regime to validate the developed model and numerical simulation. It is shown that the response of the system in the nonlinear resonant region is strongly affected by a three-to-one internal resonance.

On the Three-Dimensional Finite Element Analysis of Dovetail Attachments

2003 ◽  
Vol 125 (2) ◽  
pp. 372-379 ◽  
Author(s):  
J. R. Beisheim ◽  
G. B. Sinclair
Keyword(s):  
Boundary Conditions ◽  
Dimensional Analysis ◽  
High Stress ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Element Analysis ◽  
Computational Costs ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The stress analysis of dovetail attachments presents some challenges. These stem from the high stress gradients at the edges of contact. They also stem from the nonlinearities accompanying conforming contact. Even with two-dimensional analysis, obtaining converged peak stresses is not trivial. With three-dimensional analysis, convergence can be expected to be more difficult to achieve because of the added computational costs of refinement in three dimensions. To meet these challenges, this paper describes a submodeling procedure with finite elements. The submodeling approach features bicubic surface fits to displacements for submodel boundary conditions. The approach also features a means of verifying these boundary conditions have converged; this is crucial to obtaining accurate converged peak stresses. The approach is applied to a three-dimensional test piece used to simulate a dovetail attachment. This application leads to converged three-dimensional stresses. These stresses serve to quantify the sort of increases in contact stresses in attachments due to three-dimensional effects.

On the Three-Dimensional Finite Element Analysis of Dovetail Attachments

2002 ◽  
Author(s):  
J. R. Beisheim ◽  
G. B. Sinclair
Keyword(s):  
Boundary Conditions ◽  
Dimensional Analysis ◽  
High Stress ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Element Analysis ◽  
Computational Costs ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The stress analysis of dovetail attachments presents some challenges. These stem from the high stress gradients at the edges of contact. They also stem from the nonlinearities accompanying conforming contact. Even with two-dimensional analysis, obtaining converged peak stresses is not trivial. With three-dimensional analysis, convergence can be expected to be more difficult to achieve because of the added computational costs of refinement in three dimensions. To meet these challenges, this paper describes a submodeling procedure with finite elements. The submodeling approach features bicubic surface fits to displacements for submodel boundary conditions. The approach also features a means of verifying these boundary conditions have converged: This is crucial to obtaining accurate converged peak stresses. The approach is applied to a three-dimensional test piece used to simulate a dovetail attachment. This application leads to converged three-dimensional stresses. These stresses serve to quantify the sort of increases in contact stresses in attachments due to three-dimensional effects.

Finite Element Analysis of Nonuniformity of Tires with Imperfections5

2007 ◽  
Vol 35 (3) ◽  
pp. 226-238 ◽  
Author(s):  
K. M. Jeong ◽  
K. W. Kim ◽  
H. G. Beom ◽  
J. U. Park
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Three Dimensional ◽  
Element Model ◽  
Radial Force ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Dimensional Finite Element ◽  
Force Variation ◽  
Three Dimensional Finite Element

Abstract The effects of variations in stiffness and geometry on the nonuniformity of tires are investigated by using the finite element analysis. In order to evaluate tire uniformity, a three-dimensional finite element model of the tire with imperfections is developed. This paper considers how imperfections, such as variations in stiffness or geometry and run-out, contribute to detrimental effects on tire nonuniformity. It is found that the radial force variation of a tire with imperfections depends strongly on the geometrical variations of the tire.

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