Structural Mechanics with a Pen by Andreas Öchsner

Author:Andreas Öchsner
Language: eng
Format: epub
ISBN: 9783030658922
Publisher: Springer International Publishing

(3.138)

The corresponding system of equations reads in matrix notation as:

(3.139)

The solution of this linear system of equations gives the unknown nodal values as:

(3.140)

and the relative error right-hand side of the beam is obtained as:

(3.141)

From the above calculations, it is easy to derive a general scheme for n nodes . In generalization of Eq. (3.139), the following scheme can be proposed:

(3.142)

where for equidistant spacing.

Let us look now on the second approach which is based on the second-order partial differential equation for the moment distribution, see Table 3.1, 3rd form of the PDE. Using a centered difference scheme for the second-order derivative (see Table 1.​1), one can state the following approximation:

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