1. 1 NONLINEAR ANALYSIS

2. 2 SOURCES OF NON LINEAR BEHAVIOUR non-linear supports contact stress tension/compression only links elastic foundation offset or eccentric loads loads causing the loss of elastic stability (buckling) geometric non-linearity displacements of the structure significantly changes structure's stiffness material non-linearity stresses exceed elastic limits so stress is no longer proportional to strain combined large displacements causing plastic flow crash analysis metal stamping …

3. 3 Non linear supports analysis EXAMPLES OF NON-LINEAR PROBLEMS

4. 4 crane potential buckling stamped steel pulley potential buckling angle under bending load potential buckling plate under compressive off-center load; potential buckling dome potential buckling Buckling EXAMPLES OF NON-LINEAR PROBLEMS

5. 5 NL002.SLDPRT

6. 6 Linear solutionNon-linear solution

7. 7 ROUND PLATE.SLDPRT

8. 8

9. 9 Displacement of the center of membrane as function of applied pressure for linear and nonlinear model. Δ F Δ d

10. 10 link 02.SLDPRT

11. 11 Linear solutionNon-linear solution link 02.SLDPRT

12. 12 Horizontal reaction -7.7N Non-linear solution Linear solution Horizontal reaction 3300N

13. 13 Chapter 5

14. 14 Fixed support Sliding support 1,200N normal load to shaded face NL001 FLAT BEAM model fileNL001 model typesolid materialalloy steel restraintstbuilt-in to left end sliding to right end load1,200 N normal force to top face objectives calculate maximum displacement calculate horizontal displacement of the sliding end compare linear and non-linear displacement solution Fixed support Sliding support

15. 15 ec019.SLDPRT QUESTION: why does shaft grow in diameter and lugs stretch?

16. 16 square hole.SLDPRT QUESTION: why does hole grow in size. Is there something wrong with the code?

17. 17 This corner must travel along a straight line that is perpendicular to the radius so after deformation it will be here The same applies to the other three corners. The combined effect gives the illusion of square growing in size even though it is “frozen” in size by rigid links. Square after deformation Square before deformation