scholarly journals Uniform interior error estimates for the Reissner-Mindlin plate model

1993 ◽  
Vol 61 (204) ◽  
pp. 539-539 ◽  
Author(s):  
Lucia Gastaldi
Keyword(s):  
Error Estimates ◽  
Mindlin Plate ◽  
Plate Model

A REFINED ERROR ANALYSIS OF MITC PLATE ELEMENTS

2006 ◽  
Vol 16 (07) ◽  
pp. 967-977 ◽  
Author(s):  
MIKKO LYLY ◽  
JARKKO NIIRANEN ◽  
ROLF STENBERG
Keyword(s):  
Finite Element ◽  
Error Analysis ◽  
Boundary Conditions ◽  
Error Estimates ◽  
Convex Domain ◽  
Mindlin Plate ◽  
Plate Model ◽  
Plate Elements ◽  
Regularity Results ◽  
Thickness Parameter

We consider the Mixed Interpolated (Tensorial Components) finite element families for the Reissner–Mindlin plate model. For the case of a convex domain with clamped boundary conditions, we prove regularity results and derive new error estimates which are uniformly valid with respect to the thickness parameter.

Modelling the radially polarised annular stator of a piezoelectric travelling wave ultrasonic motor based on the shear effect

2019 ◽  
Vol 30 (8) ◽  
pp. 1225-1238 ◽  
Author(s):  
Ana Costa Conrado
Keyword(s):  
Travelling Waves ◽  
Travelling Wave ◽  
Ultrasonic Motor ◽  
Free Vibrations ◽  
Mindlin Plate ◽  
Vibration Modes ◽  
Shear Effect ◽  
Plate Model ◽  
Voltage Inverter ◽  
Contact Points

This article deals with the mathematical–analytical model of a radially polarised stator, part of a piezoelectric travelling wave ultrasonic motor based on the shear effect. The stator is treated with a Reissner–Mindlin plate model containing piezoelectric terms. The so-obtained mathematical description of the disc stator takes into account its geometry, kinematics and characteristics that influence efficiency and torque. Rayleigh–Ritz discretisation is used to obtain eigenfrequencies and eigenmodes of the stator plate. In addition, there are often teeth over the contact surface of ring-shaped stators to minimise the friction losses during operation of the motor, and possible vibration modes are compared with respect to the deflexion of the contact points. In the laboratory, measured eigenfrequencies of the free vibrations of the plate corroborate the numerical method. Particularly, the generation of travelling waves requests the excitation of two degenerated vibration modes in a certain electrode configuration. A voltage inverter was designed for this purpose.

scholarly journals Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model

CALCOLO ◽  
2014 ◽  
Vol 52 (3) ◽  
pp. 343-369
Author(s):  
Gabriel R. Barrenechea ◽  
Tomás P. Barrios ◽  
Andreas Wachtel
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Bending Moment ◽  
Mindlin Plate ◽  
Plate Model

AN OPTIMAL LOW-ORDER LOCKING-FREE FINITE ELEMENT METHOD FOR REISSNER–MINDLIN PLATES

1998 ◽  
Vol 08 (03) ◽  
pp. 407-430 ◽  
Author(s):  
D. CHAPELLE ◽  
R. STENBERG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Convergence Rates ◽  
A Priori ◽  
Mindlin Plate ◽  
Plate Model ◽  
Simple Modification ◽  
Optimal Convergence Rates ◽  
Priori Error Estimates ◽  
Element Method

We propose a simple modification of a recently introduced locking-free finite element method for the Reissner–Mindlin plate model. By this modification, we are able to obtain optimal convergence rates on numerical benchmarks. These results are substantiated by a complete mathematical analysis which provides optimal a priori error estimates.

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