scholarly journals Two-scale Reissner-Mindlin plate model

2017 ◽  
Vol 50 (3) ◽  
pp. 158-161
Author(s):  
Jouni Tapani Freund
Keyword(s):  
Mindlin Plate ◽  
Plate Model ◽  
Homogeneous Plate ◽  
Elasticity Equations ◽  
3D Elasticity ◽  
Modelling Error

A two-scale plate model, in which the displacement assumption consists of the Reissner-Mindlin and warping parts, is presented. To reduce the modelling error of the classical Reissner-Mindlin model, the warping part is chosen so that the overall displacement satisfies the full 3D elasticity equations as well as possible. Pressure loaded isotropic homogeneous plate is used as an application example.

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.

Analytical particular solutions of augmented polyharmonic spline associated with Mindlin plate model

2011 ◽  
Vol 28 (6) ◽  
pp. 1778-1793 ◽  
Author(s):  
Chia-Cheng Tsai ◽  
Edward Ming-Yang Wu
Keyword(s):  
Mindlin Plate ◽  
Plate Model ◽  
Particular Solutions ◽  
Polyharmonic Spline

Research of combined hybrid method applied in the Reissner–Mindlin plate model

2006 ◽  
Vol 182 (1) ◽  
pp. 49-66 ◽  
Author(s):  
Zhu Wang ◽  
Bing Hu
Keyword(s):  
Hybrid Method ◽  
Mindlin Plate ◽  
Plate Model

A New Family of Mixed Methods for the Reissner-Mindlin Plate Model Based on a System of First-Order Equations

2010 ◽  
Vol 49 (2) ◽  
pp. 137-166 ◽  
Author(s):  
Edwin M. Behrens ◽  
J. Guzmán
Keyword(s):  
Mixed Methods ◽  
Mindlin Plate ◽  
Plate Model ◽  
First Order ◽  
Model Based ◽  
New Family

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

scholarly journals Asymptotic Analysis of the Boundary Layer for the Reissner–Mindlin Plate Model

1996 ◽  
Vol 27 (2) ◽  
pp. 486-514 ◽  
Author(s):  
Douglas N. Arnold ◽  
Richard S. Falk
Keyword(s):  
Boundary Layer ◽  
Asymptotic Analysis ◽  
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.

scholarly journals An asymptotic strain gradient Reissner-Mindlin plate model

Meccanica ◽  
2013 ◽  
Vol 48 (8) ◽  
pp. 2007-2018 ◽  
Author(s):  
Michele Serpilli ◽  
Françoise Krasucki ◽  
Giuseppe Geymonat
Keyword(s):  
Strain Gradient ◽  
Mindlin Plate ◽  
Plate Model

Failure behavior of hierarchical corrugated sandwich structures with second-order core based on Mindlin plate theory

2017 ◽  
Vol 21 (2) ◽  
pp. 552-579 ◽  
Author(s):  
Gang Li ◽  
Zhaokai Li ◽  
Peng Hao ◽  
Yutian Wang ◽  
Yaochu Fang
Keyword(s):  
Thick Plate ◽  
Failure Modes ◽  
Sandwich Structures ◽  
Plate Theory ◽  
Second Order ◽  
Mindlin Plate ◽  
Failure Behavior ◽  
Plate Model ◽  
Moderately Thick Plate ◽  
Mindlin Plate Theory

For hierarchical corrugated sandwich structures with second-order core, the prediction error of failure behavior by existing methods becomes unacceptable with the increase of structure thickness. In this study, a novel analytical model called moderately thick plate model is developed based on Mindlin plate theory, which can be used to analyze the failure behavior of hierarchical corrugated structures with second-order core under compression or shear loads. Then, the analytical expressions of nominal stress for six competing failure modes are derived based on the moderately thick plate model. The results of six different unit structures based on the moderately thick plate model agree quite well the ones by finite element methods. Furthermore, the influence of different structure thicknesses is investigated to validate the applicability of the moderately thick plate model. According to the comparative results with the thin plate model, the proposed moderately thick plate model has a better precision with the increase of the ratio of thickness to width for failure components.

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