Nonlinear Dynamic Analysis of Planar Beams

Abstract

In this chapter we develop an approach to solve the fully nonlinear equations governing the dynamic response of beams derived in Chap. 10. Of course, the only route forward is numerical analysis. We will use Newmark’s method for the temporal integration and Newton’s method to solve the resulting nonlinear algebraic equations. The main additional task in setting up and solving the nonlinear problem is to compute the residual and tangent for Newton’s method. As was the case for the truss, the most complicated part of the derivation is in the internal resistance, which is present in both a static and dynamic analysis. This chapter shows how the techniques of the previous chapter can be generalized to deal with nonlinearity, opening up the possibility of modeling scenarios that involve large motions and instability.

Electronic Supplementary Material The online version of this chapter (https://doi.org/10.1007/978-3-030-89944-8_13) contains supplementary material, which is available to authorized users.