Construction of a Three Dimensional Displacement Field From a Solution to the Vo

Cover Construction of a Three Dimensional Displacement Field From a Solution to the Vo
Construction of a Three Dimensional Displacement Field From a Solution to the Vo
Chester B Sensenig
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, + ^ | 2(3X+2y) ^ ^^aB-" ^ 6(X-H2y) ^ " -XTI^ "^^^, aB ^ ^^, Y^'3Y. A-'V, 3-^a3, Y^^'^, a6t3xkl"'^- ^, y", y" 20^"'"^ - 3xW ^(^^a^, 3^'^3^, a-^^Y^, Y'a3^-^ K, a^, a"^ i^, Ya^, Y3} ^'^^D^^')- -15- From (1. 6) and (1. 8) (3. 4) From (3. 1) e -, = —K -. , ^ (z -1) Aw a3 3 X+2]i, a + 0(h-e2) V WW =T-(v +v )w w = ww [--^-ww+T - -, >■-. All; 6 ] . , Y /\^ 2, Y /V Y^ 3A+2m ^ y^ From the above, (1. 6), and (1. 8) ©o-a = ~t" f~ -, -, . T Aljj +, ^- Z Aw) 33 2 *• 3A+2p ^ A+2y -' V V 4p^A-A(3X+8m)B+A^C, ...^^)^ ^4 1 2(A+2m) y. V y, v (x+2y)(3A+2y)2 2 ^ -J^ .. I', . +[• "^ ^ 8y^A-12AyB+2A^C i . , . + — ^- ;r^^- J z Alp Aw A+2y, YV, YV (x+2y) (3A+2y) ( A+2y) ^ (3A + 2y) (3. 5) ^ A A, j^ r3A+y+2B 3A+2y 3, +, . ^ zw Atii + [, ■ 'Z z - . , .. , . Z J w T A+2y, Y /Y A + 2y 4 (A+y), yv yv + f 3C -, z - . , !: J w w + „, . - — r *■ 3 A+2y'^, YV, YV 2 (A+2y) z Aw w w /Y /Y 4y^A+A(A-4y)B+A^C 2 8(A-Hy)(A+2y) " (^^^y)^ ' " (A+2y) A(5A+4y) Xy 1 + 2u)2j (Aw) + ^[4^') • From (3. 3) and (1. 3), 2 h f A+2y .

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