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Erschienen in:
2022 | OriginalPaper | Buchkapitel
12. Finite Element Analysis of Linear Planar Beams
verfasst von : Keith D. Hjelmstad
Erschienen in: Fundamentals of Structural Dynamics
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Abstract
In the previous chapter we were able to find solutions to the beam dynamics problem using the separation of variables technique. The process went very much like it did for the axial bar problem. But the beam differential equation involves fourth order derivatives with respect to x, and consequently the spatial part of the solution was more complicated. While the classical techniques provide a good route to solving wave propagation problems in beams, we want to solve more general problems (e.g., problems with time-dependent forcing functions and possibly non-prismatic cross sections). In this chapter we will approach the problem in a different way. We will start by introducing the principle of virtual work and develop an approximate numerical approach using the Ritz method with finite element base functions.