By Chia-Shung Yih
This hugely acclaimed sequence presents survey articles at the current kingdom and destiny course of study in vital branches of utilized mechanics
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Elastic plates. Phil. Trans. Roy. SOC. FRAEIJS DE VEUBEKE, B. (1964). Upper and lower bounds in matrix structural analysis. AGARDograph 72,165-201. FRAEIJS DE VEUBEKE, B. (1965). Displacement and equilibrium models in the finite element method. Zn “Stress Analysis” (0. C. Zienkiewicz and G . S. ), pp. 145-197. Wiley, New York. FRAEIJS DE VEUBEKE, B. (1966). Bending and stretching of plates-special models for upper and lower bounds. Proc. Conf. Matrix Methods Struct. , l s t , 1965 AFFDL-TR-66-80, pp.
11. Triangular elements using quadratic interpolation. Isoparametric transformations can also be used to construct the interpolation formulas of triangular elements with curved sides. More detailed discussions of the interpolation functions over triangular elements can be found in the article by Felippa and Clough (1970). The linear interpolation over an area which is decomposed into triangular elements can also be depicted by Fig. 12. e. it is equal to unity at the node i and slopes linearly toward the opposite edges of the triangles around this node.
The lth node, refers to summation over over all elements on the surface aVn and all nodes on the surface. 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.
Advances in Applied Mechanics, Vol. 12 by Chia-Shung Yih