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By Robert C. Stern

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3. Since the natural boundary condition explicitly arises when we perform integration by parts, we can directly substitute the prescribed natural boundary conditions. Only the remaining essential boundary conditions have to be satisfied by the trial solution of the weak form equation. 4. g. significantly lower order polynomials than is possible with weighted residual forms) is available. 5. The weak form can be developed for the weighted residual form of any given second- and higher-order differential equation or its corresponding weighted residual form.

3. Since the natural boundary condition explicitly arises when we perform integration by parts, we can directly substitute the prescribed natural boundary conditions. Only the remaining essential boundary conditions have to be satisfied by the trial solution of the weak form equation. 4. g. significantly lower order polynomials than is possible with weighted residual forms) is available. 5. The weak form can be developed for the weighted residual form of any given second- and higher-order differential equation or its corresponding weighted residual form.

122) These characteristic functions [1 – (x/l)] and [x/l] used in our interpolation are called interpolation functions or shape functions since they determine the shape of variation of the function within each sub-domain. We will use the notation Ni(i = 1, 2, in this case) to designate the shape functions. These characteristic functions dictate the contribution of a given fk to the value of the function at any point P within the domain 0 < X < L. 17 shows these interpolation functions for the two-line segment case discussed earlier.

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America's Fighters of the 1980s - F-16 & F-18 by Robert C. Stern


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