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

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

Fast Solution of Three-Dimensional Modified Helmholtz Equations by the Method of Fundamental Solutions

2016 ◽  
Vol 20 (2) ◽  
pp. 512-533 ◽  
Author(s):  
Ji Lin ◽  
C. S. Chen ◽  
Chein-Shan Liu
Keyword(s):  
Three Dimensional ◽  
Homogeneous Solution ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Singular Problem ◽  
Helmholtz Equations ◽  
Particular Solutions ◽  
Radial Basis ◽  
Particular Solution ◽  
Polyharmonic Spline

AbstractThis paper describes an application of the recently developed sparse scheme of the method of fundamental solutions (MFS) for the simulation of three-dimensional modified Helmholtz problems. The solution to the given problems is approximated by a two-step strategy which consists of evaluating the particular solution and the homogeneous solution. The homogeneous solution is approximated by the traditional MFS. The original dense system of the MFS formulation is condensed into a sparse system based on the exponential decay of the fundamental solutions. Hence, the homogeneous solution can be efficiently obtained. The method of particular solutions with polyharmonic spline radial basis functions and the localized method of approximate particular solutions in combination with the Gaussian radial basis function are employed to approximate the particular solution. Three numerical examples including a near singular problem are presented to show the simplicity and effectiveness of this approach.

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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