Finite Elements Methods in Mechanics by M. Reza Eslami

Author:M. Reza Eslami
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Fig. 8.8Simply supported beam under linear load

Using a -continuous element and the Galerkin method, divide the beam into four elements and obtain the elements of the global stiffness and force matrices.

Fig. 8.9 continuous element

Solution: Each of the following equations may be used to employ the Galerkin method

(8.6.25)

(8.6.26)

(8.6.27)

The last equation of beam deflection under linear distributed load is written in the form

(8.6.28)

To solve the equation by the finite element method, the solution domain is discredited into NE elements and NN nodes. Then, in each element a shape function is used to approximate the lateral deflection.

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