Summary
We have successfully demonstrated the implementation of a basic 2D mass-spring simulator encompassing several critical components:
- Mesh Generation: This involves the creation of nodes and connecting elements. In practical scenarios, simulators often import meshes from pre-existing files.
- Incremental Potential Energy Evaluation: Comprises the computation of the potential energy value, its gradient, and the Symmetric Positive Definite (SPD)-projected Hessian.
- Optimization Time Integrator: This includes linear solves for determining search directions, line search techniques to ensure global convergence, and rules for updating nodal positions and velocities.
- Simulator Structure: Encompasses scene setup, variable initialization, and the execution of the simulation loop. (Note: Visualization aspects can be decoupled from the simulator itself.)
In the forthcoming chapter, we will delve into boundary treatments, including prescribed motion and frictional contact, which are implemented through equality or inequality constraints in the optimization framework. This discussion will be enriched with practical case studies, illustrating the application of each boundary treatment in computational simulations.