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

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Presentation on theme: "ECIV 720 A Advanced Structural Mechanics and Analysis Non-Linear Problems in Solid and Structural Mechanics Special Topics."— Presentation transcript:

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


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