Читать книгу Finite Element Analysis - Barna Szabó - Страница 30

Computation of the right hand side vector involves evaluation of the functional , usually by numerical means. In particular, we write:

(1.73)

The element‐level integral is computed from the definition of vn on Ik:

(1.74)

where

(1.75)

which is computed from the given data and the shape functions.

Example 1.5 Let us assume that is a linear function on Ik. In this case can be written as

Using the Legendre shape functions we have:

Exercise 1.11 Assume that is a linear function on Ik. Using the Legendre shape functions compute and show that for . Hint: Make use of eq. (1.55).

Exercise 1.12 Let

where fk is a constant. Compute numerically in terms of fk and ℓk using 3, 4 and 5 Gauss points. See Appendix E. Use the Legendre basis functions.

Exercise 1.13 Assume that is a linear function on I. Using the Lagrange shape functions for , compute .