(Solved): (a) Give a brief definition of what makes a structural finite element problem nonlinear, stating th ...
(a) Give a brief definition of what makes a structural finite element problem nonlinear, stating the 3 main sources of nonlinearity typically encountered and why they give rise to nonlinearity. (4 marks) (b) A nonlinear spring has a stiffness,
k(u), which is a function of displacement described below.
Aload of
8Nis applied to this spring:
k(u)=(10)/((u+1)^(2)),(N)/(m)mExplain the operation of the Newton-Raphson method for such problems, and use it to obtain an estimate of the displacement by carrying out three iterations. State the force imbalance after the third iteration. Note: you may assume that the internal force is given by
F_(int )(u)=10(u)/(u+1)but you may not directly solve the problem with this equation. ( 8 marks) (c) Bolted joints can be analysed using a variety of linear and nonlinear methods of varying complexity. Briefly discuss any approaches you know of, outlining why you might use each approach and evaluating them in terms of complexity.
