A VBCM-RBF based meshless method for large deflection of thin plates

2011 ◽  
Author(s):  
Xiaokun Zhang ◽  
Rui Ding ◽  
Hua Wan
Keyword(s):  
Meshless Method ◽  
Large Deflection ◽  
Thin Plates

scholarly journals RBF-Based Meshless Method for Large Deflection of Elastic Thin Rectangular Plates with Boundary Conditions Involving Free Edges

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammed M. Hussein Al-Tholaia ◽  
Husain Jubran Al-Gahtani
Keyword(s):  
Boundary Condition ◽  
Basis Function ◽  
Meshless Method ◽  
Iterative Procedure ◽  
Large Deflection ◽  
Free Edge ◽  
Thin Plates ◽  
Rectangular Plates ◽  
Numerical Examples ◽  
Complex Boundary

An RBF-based meshless method is presented for the analysis of thin plates undergoing large deflection. The method is based on collocation with the multiquadric radial basis function (MQ-RBF). In the proposed method, the resulting coupled nonlinear equations are solved using an incremental-iterative procedure. The accuracy and efficiency of the method are verified through several numerical examples. The inclusion of the free edge boundary condition proves that this method is accurate and efficient in handling such complex boundary value problems.

Nondestructive Measurement of In-Plane Residual Stress in Silicon Strips

1999 ◽  
Vol 591 ◽  
Author(s):  
Tieyu Zheng ◽  
Steven Danyluk
Keyword(s):  
Residual Stress ◽  
Residual Stresses ◽  
Large Deflection ◽  
Thin Plates ◽  
Nondestructive Measurement ◽  
Three Point Bending ◽  
Phase Stepping ◽  
Bending Load ◽  
Bending Loads ◽  
Processing Techniques

ABSTRACTThis paper reports the development of a shadow moiré technique to measure the in-plane residual stresses of thin, flat strips. This is an extension of prior work on the measurement of in-plane residual stresses in silicon plates and wafers. Phase stepping shadow moir6 and digital image processing techniques are employed to measure the deflections of the silicon plate specimens subjected to three-point-bending at several different loads. The measured deflections over the area of the silicon plates are fitted with an equation represented by a 2-D polynomial. With the theory of thin plates with large deflection, the fitting coefficients are used to extract the in-plane stresses at the different bending load. The residual stress is resolved by linear regression of the in-plane stresses versus bending loads.

Large Deflection of Thin Plates in Convex or Concave Cylindrical Bending

2012 ◽  
Vol 138 (2) ◽  
pp. 230-234 ◽  
Author(s):  
Vivek A. Jairazbhoy ◽  
Pavel Petukhov ◽  
Jianmin Qu
Keyword(s):  
Large Deflection ◽  
Thin Plates ◽  
Cylindrical Bending

scholarly journals Large deflection of thin plates in cylindrical bending – Non-unique solutions

2008 ◽  
Vol 45 (11-12) ◽  
pp. 3203-3218 ◽  
Author(s):  
Vivek A. Jairazbhoy ◽  
Pavel Petukhov ◽  
Jianmin Qu
Keyword(s):  
Large Deflection ◽  
Thin Plates ◽  
Cylindrical Bending

On the Large Axisymmetrical Deflection of Thin Plates Made of the Mooney-Rivlin Material

1974 ◽  
Vol 41 (3) ◽  
pp. 725-730 ◽  
Author(s):  
H. Abe´ ◽  
M. Utsui
Keyword(s):  
Large Deflection ◽  
Lateral Pressure ◽  
Three Dimensional ◽  
Thin Plates ◽  
Axially Symmetric ◽  
Dimensional Theory ◽  
Plate Equations ◽  
Basic Equations ◽  
Deflection Theory ◽  
Large Deflection Theory

A large deflection theory of axially symmetric and thin plates made of the Mooney-Rivlin material is developed by making a systematic and consistent approximation from the exact three-dimensional theory. The problem of a circular plate made of the neo-Hookean material subjected to uniform lateral pressure is investigated with the use of the basic equations just derived, and the results are compared with the solutions based on the von Karman plate equations.

scholarly journals Nonlinear Deflection Model for Corner-Supported, Thin Laminates Shape-Controlled With Moment Actuators

2007 ◽  
Author(s):  
Jordan E. Massad ◽  
Pavel M. Chaplya ◽  
Jeffrey W. Martin ◽  
Philip L. Reu ◽  
Hartono Sumali
Keyword(s):  
Shape Control ◽  
Large Deflection ◽  
Flexible Structures ◽  
Piezoelectric Actuators ◽  
Input Voltage ◽  
Thin Plates ◽  
Small Deflection ◽  
Shape Controlled ◽  
Rectangular Laminate ◽  
Small Deformations

The shape control of thin, flexible structures has been studied primarily for edge-supported thin-plates. For applications such as electromagnetic wave reflectors, corner-supported configurations may prove more applicable since they allow for greater flexibility and larger achievable deflections when compared to edge-supported geometries under similar actuation conditions. Models of such structures provide insight for effective, realizable designs, enable design optimization, and provide a means of active shape control. Models for small deformations of corner-supported, thin laminates actuated by integrated piezoelectric actuators have been developed. However, membrane deflections expected for nominal actuation exceed those stipulated by linear, small deflection theories. In addition, large deflection models have been developed for membranes; however these models are not formulated for shape control. This paper extends a previously-developed linear model for a corner-supported thin, rectangular laminate to a more general large deflection model for a clamped-corner laminate composed of moment actuators and an array of actuating electrodes. First, a nonlinear model determining the deflected shape of a laminate given a distribution of actuation voltages is derived. Second, a technique is employed to formulate the model as a map between input voltage and deflection alone, making it suitable for shape control. Finally, comparisons of simulated deflections with measured deflections of a fabricated active laminate are investigated.

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