Solution of finite element equations by particle swarm optimization technique - Ankamreddy Bhargavi (2013)
This project investigates a new iterative finite element solution methodology based on particle swarm optimization technique and describes its application to linear static problems with an overall objective of increasing the computational efficiency. Efficient techniques for solving of finite element equations can make tremendous impact in structural mechanics problems particularly for large problems. In the usual finite element solution procedure, consequent to meshing of the domain, the globalised stiffness matrix (K) is assembled from the element stiffness matrices. Then, the finite element equations, Ku=F, are solved by standard procedures which usually involves inverting the global stiffness matrix explicitly or implicitly. On the contrary, in the present work, the equations are solved by a stochastic minimization of the total potential rather than by inverting the global stiffness matrix. The proposed methodology is based on the concept that solving the equations Ku=F is equivalent to minimization of the total potential π = 1/2 uTKu — UTF. In the present work, the Particle swam optimization technique (PSO) is used for the minimization of the total potential n.