Finite Element Solver for Nonlinear Dynamics

Main

Home

About Me

Contact Info Resume

Projects

All Projects

Simulation

Finite Element Solver Cloth Fluids Reduced Fluid

Graphics

Moog and Blith Doom 3 md5 Resources Ray Tracer

About

This is a finite element solver that I wrote in November and December of 2006. The solver is fairly general and should be able to handle any type of volumetric element (the examples only use mapped brick elements) as well as a wide class of FE analysis problems.

Code

The code can be found in fe_dynamics_simulator.tar.gz.

To build and run the code on OS X, enter the source directory and type make -f Makefile.apple run. For other platforms, substitute Makefile.cygwin or Makefile.linux.

A short introduction to the code is as follows.

• trace has just one header file for tracing and asserts. No dependencies.
• matrix has dense and sparse matrix code. Functionality includes sparse matrix assmebly, BLAS operations, CG solver. This code depends on trace
• fem is the core finite element library. It includes mesh loading and visualization, a framework for taking integrals over meshes, and a few sample integrals (mass matrix computation, gravity force computation, and StVK force and stiffness computation). It depends on matrix and trace.
• fe-dynamics-simulator is the actual simulator. It includes code for integration of the equation of motions, Dirichlet boundary conditions, and basic window and interaction (using GLUT).

Sample Output

The following videos show simulations of the dynamics of an object as it deforms due to various external forces being applied. The material model used in these examples is the Saint-Venant Kirchoff material model. The system was integrated in time using Newmark integration.

For mathematical purity (and at the expense of realism), damping was not modeled in these simulations. As a result, in the absense of numerical error, the objects being simulated will oscillate forever.

The color at each point on the object is linearly related to the Von Mises stress experienced at that point (blue is low stress and red is high stress).

Videos

	An I-beam fixed to the ground at the bottom being twisted at the top and then released.
	An I-beam fixed to a wall near the viewerg being bent by a downward gravitational force.
	A bizarre shape fixed to the ground at its base, deforming under the force of gravity.
	The same bizarre shape, flipped vertically and fixed at the new based, deforming under the force of gravity.
	A cow being tipped by a horizontal gravitational force.