Chapter 9 Finite Element Method

• 9.1 static deformation of beam (constant cross-sectional area)
• 9.1 static deformation of beam (non-constant cross-sectional area)
• 9.1 static deformation of beam (both ends fixed)
• 9.2 dynamic deformation of beam (constant cross-sectional area)
• equations of motion of deforming beam
• external force applied to beam
• 9.3 example of calculating connection matrices

• Problem 2 (1) calculating partial connection matrices
• Problem 2 (2) calculating connection matrices
• calculating partial inertia matrix
• calculating inertia matrix
• example of calculating connection matrices and inertia matrix
• Problem 5 dynamic elastic deformation of a square object (4×4)
• Problem 5 dynamic elastic deformation of a square object (10×10)
• nodal points and triangles of a rectangular
• displacement of pushing points
• velocity of pushing points
• equation of motion (when pushing the square top)
• equation of motion (after releasing the pushing)
• drawing object shape



• Problem 5 dynamic elastoplastic deformation of a square object (4×4)
• Problem 5 dynamic elastoplastic deformation of a square object (10×10)
• equation of motion (when pushing the elastoplastic square top)
• equation of motion (after releasing the pushing)



• Problem 6 flexural deformation of a paper
• potential energy
• equation constraints (boundary conditions)
• inequality constraints and equation constraints
• integral of \cos(\theta(s))
• integral of \sin(\theta(s))
• computing the deformed shape of a linear object