Computer Animation (CS 395T) Course Project

Animating thin Shell structures – FEM approach

Instructor: Okan Arikan

 

Need

Framework to Predict the shape of thin shell structures under its own weight

Approximate Finite element simulation to predict the shape of the deforming objects in real-time subject to changes in the applied forces.

Shape prediction of thin shell structures – deflection due to self weight

System of Equations

A forward Euler method with adaptive time stepping was used to solve the dynamic equations.

Energy of the deformable body

Shell Element – Coupling

Assigning artificial stiffness factor to the rotation about ‘z’ direction d.o.f  to bring about coupling between membrane action and bending phenomenon in shell structures.

 

 

Shell Element  - Transformation Matrix

Transforming the reaction forces and the nodal displacements to the r-s-t co-ordinate frame from the global X-Y-Z frame is essential for shell elements. The direction cosines of the individual elements are used in the global transformation matrix

             Global transformation Matrix

Mass Matrix

Mass of a node is computed based on the area and thickness of the element. A node which is shared by two or more elements would receive ¼ of weight of all elements sharing the node.

Collision Detection and Response

Deformable objects were tested for collision with ground plane (Z =0).

—  (Z_vertice-Z_plane) < Threshold             (collision occurred )

—  Penetration (j)= Threshold - (Z_vertice-Z_plane)

—  F_collision = -k_spring x j, k_spring is computed using 0.1 x max(F_vertice)

—  F_friction = m x F_{collision  ,} m is assumed to be 0.3

Collision force is applied on the vertice which collides with the ground plane in the direction normal to the plane

Friction force is computed based on the collision force and it is applied in the tangential direction

 

Test Cases  

 

 

 

 

 

 

Shape	Vertex Count	Poly Count	Simulation Time (sec)
Cylinder	174	140	75
Airfoil	204	252	110
S shaped Arch	108	90	90

 

Animation Examples

                                  

              Animating flexible cylinder                                              Flexible cylinder – falling from an angle

                  

                Airfoil falling from above                                                        Airfoil dropped from the top

                       

               Arch dropped from top                                           Pot dropped from above – with constraints                                             

References

·         “Advanced Topics in Finite Element Analysis of Structures” – M. Asghar Bhatti

·         “Introduction to Finite Elements in Engineering” – Tirupathi R. Chandrupatla & Ashok. D. Belegundu

·         “Large Steps in Cloth Simulation”, David Baraff & Andrew Witkin

·        “Robust Treatment of Collisions, Contact and Friction for Cloth Simulation”, Robert Bridson, Ronald Fedkiw, John Anderson