1. ECIV 720 A Advanced Structural Mechanics and Analysis Non-Linear Problems in Solid and Structural Mechanics Special Topics

2. Introduction Nonlinear Behavior: Response is not directly proportional to the action that produces it. P 

3. Introduction Recall Assumptions Small Deformations Linear Elastic Behavior

4. Introduction Linear Behavior

5. Introduction A. Small Displacements Inegrations over undeformed volume Strain-displacement matrix does not depend on

6. Introduction B. Linear Elastic Material Matrix [E] does not depend on

7. Introduction C. Boundary Conditions do not change (Implied Assumption) Constraints do not depend on

8. Introduction If any of the assumptions is NOT satisfied NONLINEARITIES Material Assumption B not satisfied Geometric Assumption A & or C not satisfied

9. Classification of Nonlinear Analysis Small Displacements, small rotations Nonlinear stress-strain relation

10. Classification of Nonlinear Analysis Large Displacements, large rotations and small strains – Linear or nonlinear material behavior

11. Classification of Nonlinear Analysis Large Displacements, large rotations and large strains – Linear or nonlinear material behavior

12. Classification of Nonlinear Analysis Change in Boundary Condition

13. Classification of Nonlinear Analysis

14. Nonlinear Analysis Cannot immediately solve for {d} Iterative Process Required to obtain {d} so that equilibrium is satisfied

15. Solution Methods

16. Newton-Raphson

17. Newton Raphson With initial conditions

18. Modified Newton-Raphson