By Chia-Shung Yih
This hugely acclaimed sequence presents survey articles at the current country and destiny course of study in vital branches of utilized mechanics
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Additional info for Advances in Applied Mechanics, Vol. 12
1) the present problem corresponds to the case where the heat source H is zero and u1 and c i j are respectively scalar constants, u and c. 3) are simply a, = 1, a2 = 0, 8 = 1 at x = 0 and a2= 1, a, = 0 = 0 at x = L. We divide the region into N uniform elements with length E (= L / N ) . The generalized coordinate qn (n = 1, . . , N 1) is the value of T at xn ( = ( n - 1 ) ~ ) The . 4). 15) 1 &pU& c + $pU& ' and g,, is zero for every element. 17) at t = 0. 18) are presented in Fig. 6. 18) Theodore H .
The coefficients A,, and B,, are obtained respectively by assembling the corresponding elements in an and b,. 38) v = Bq. e. 41) a2 - -OfdS, a1 a v n - a V f i a2 where aPnis the portion of aVn where a2 is zero. 38), n becomes =1 2 9T (BTC -1- A7'D)Aq- qTArQ. 29). 43). c. APPLICATIONTO 'rWO-DIMENSIONAL OR AXIAL SYMMETRIC STOKES FLOW In the case of slow motion of fluid the inertia force can be neglected as compared to the viscous force. 46) and pv . 47) where v is the velocity vector, p the pressure, and p the coefficient of viscosity.
I. (1960). Smooth surface interpolation. J . Math. Phys. 39,258-268. , SCHULTZ, M. , and VARGA, R. S. (1968). Piecewise Hermite interpolation in one and two variables with applications to partial differential equations. Numer. Math. 11, 232-256. CLOUGH,R. W. (1960). T h e finite element method in plane stress analysis. Proc. Amer. Civil Eng. 87, 345-378. CLOUGH, R. , and TOCHER, J. L. (1966). Finite element stiffness matrices for analysis of plate bending. Proc. Conf. Matrix Methods Struct. , lst, 1965 AFFDL-TR66-80, pp.
Advances in Applied Mechanics, Vol. 12 by Chia-Shung Yih