An analytical solution for the large deflection problem of Timoshenko beams under three-point bending

2014 ◽  
Vol 78 ◽  
pp. 135-139 ◽  
Author(s):  
Ali Mohyeddin ◽  
Abdolhosein Fereidoon
Keyword(s):  
Analytical Solution ◽  
Large Deflection ◽  
Timoshenko Beams ◽  
Three Point Bending ◽  
Large Deflection Problem

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 Deflections of Elliptical Plates

1956 ◽  
Vol 23 (1) ◽  
pp. 21-26
Author(s):  
N. A. Weil ◽  
N. M. Newmark
Keyword(s):  
Circular Plate ◽  
Maximum Stress ◽  
Large Deflection ◽  
Ritz Method ◽  
Constant Thickness ◽  
Infinite Strip ◽  
Elliptical Plate ◽  
Arbitrary Dimensions ◽  
Center Deflection ◽  
Large Deflection Problem

Abstract A solution is obtained by means of the Ritz method for the “large-deflection” problem of a clamped elliptical plate of constant thickness, subjected to a uniformly distributed load. Two shapes of elliptical plate are treated, in addition to the limiting cases of the circular plate and infinite strip, for which the exact solutions are known. Center deflections as well as total stresses at the center and edge decrease as one proceeds from the infinite strip through the elliptical shapes to the circular plate, holding the width of the plates constant. The relation between edge-stress at the semiminor axis (maximum stress in the plate) and center deflection is found to be practically independent of the proportions of the elliptical plate. Hence the governing stress may be determined from a single curve for a given load on an elliptical plate of arbitrary dimensions, if the center deflection is known.

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