Download e-book for kindle: An Introduction to Nonlinear Finite Element Analysis by J. N. Reddy

By J. N. Reddy

ISBN-10: 019852529X

ISBN-13: 9780198525295

Reddy (mechanical engineering, Texas A&M U.) writes for graduate scholars in engineering and utilized arithmetic, or for these practising in such fields as aerospace or the car industries. He works during the finite aspect strategy after which applies it to such events as warmth move in a single and dimensions, nonlinear bending of hetero beams and elastic plates, and flows of viscous incompressible fluids. From there he strikes to nonlinear research of time-dependent difficulties after which to finite point formulations of reliable continua. The appendices describe resolution methods for liner and non-linear algebraic equations. Reddy offers workouts and references for normal themes.

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Linear Global Shape Functions. The tent-shaped functions 1(x), . , N+l (x), defined on [0, L] and shown in Fig . 2, are called the global piecewise li near shape fun ctions associated with the partition 0 = Xl < X2 < .. < XN < XN+! = L , or simply, the lin ear global shape functions associated with the above partition . They can be represented as 'f Xe - l ::; X ::; Xe' d,(e -l) '1'2 e -- d,(e) { '1'1 o 1 'f Xe < _ X ::; Xe+I, 1 elsewhere. 6) 28 2. ONE-DIMENSIONAL SHAPE FUNCTIONS This result will be useful in defining the function u continuously for any value of x E (0, l) in terms of the nodal values Ui, i = 1, ..

Ua(x ) = LX (e )(x)u~e ) (x), e= I LetUI ( 1) = UI (1) , U2 =U 2 "", UN ( N) =U 1 , ( N) and UN+I =u2 . (X) = X( N)(x) ¢~N)(x), ,, ,, + X(N)(x) ¢iN)(x ), x E [O ,L] . ,:- - - - - __- - - e-2 e e -1 e+1 Fig. 2. Linear Global Shape Functions. The tent-shaped functions 1(x), . , N+l (x), defined on [0, L] and shown in Fig . 2, are called the global piecewise li near shape fun ctions associated with the partition 0 = Xl < X2 < .. < XN < XN+! = L , or simply, the lin ear global shape functions associated with the above partition .

2. 5. - -d {a[ -dU + -1 (dV)2 - ]} dx dx 2 dx + 9 = 0, 2 2 d { dv [dU 1 (dV)2]} d (d V) dx2 bdx2 - dx a dx dx +"2 dx + f = 0; 20 1. INTRODUCTION u = V = dVI 0 at x = 0, l; -d x 2V] x =O = 0, [d b -2 dX x =1 = mo (large-deflection bending of a beam). ANS . Let WI and W2 be the two test functions, one for each equation, such that they satisfy the essential boundary conditions on u and v. Then l r [ dWI {dU (dV) 2 }+ WIg]dx , 0= io a dx dx + 2" dx 1 -1 2v [bd2W2 dW2-dv - -2-d-2+ a - {dU o dx dx dx dx dx dW2 - mo dx (l) .

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An Introduction to Nonlinear Finite Element Analysis by J. N. Reddy


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