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

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

Introduction Recall Assumptions Small Deformations Linear Elastic Behavior

Introduction Linear Behavior

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

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

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

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

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

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

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

Classification of Nonlinear Analysis Change in Boundary Condition

Classification of Nonlinear Analysis

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

Solution Methods

Newton-Raphson

Newton Raphson With initial conditions

Modified Newton-Raphson