Autumn Semester (Odd Years)

Shojiro Motoyui

Department of Built Environment

This course discusses analytical methods to simulate collapse behavior of building
structures. Particularly, it presents treatment of both geometrical nonlinearity and
complex material nonlinearity which are essential in these analytical methods.

1. Formulation of Geometrical Nonlinearity
   　　- Assumption of finite displacement and small strain, definition of Green's strain
   tensor and 2nd Piola-Kirchhoff stress tensor, Polar Decomposition of Deformation
   Gradient Tensor.
2. Beam Element including Geometrical Nonlinearity
   　　- Rigid motion and Relative displacement, Displacement field and Shape function,
   Numerical unstable phenomenon like Membrane Locking and Shear locking.
3. Complex Material Nonlinearity like Baushinger's effect
   　　- 2nd low of Thermodynamics, Principle of the Maximum Plastic Dissipation, Yield
   Function, Flow rule, Complex Hardening rule. Sub-layer model.