Finite Element Analysis of Solids with Energy Minimization

The Classical Finite Element Method can easily perform analysis for linear and well-constrained systems. But it fails to solve nonlinear, unstable systems. An alternative way for structural analysis is the Finite Element Method with Optimization, which is based on the principle that the equilibrium state of the structure is the same as its configuration with the smallest total potential. Finite Element Method with Optimization was introduced by Toklu in 2004 under the name TPO Method. Finite Element Method with Optimization solves the problem as an optimization problem using an iterative procedure for both linear and nonlinear systems. The biggest advantage of this method is that its formulation is extremely simple, its implementation is very easy, and it is promising in solving complex problems. The mentioned method has been tested on various problems modeled using three-dimensional elements. In the presented study, it has been revealed that the Finite Element Method with Optimization is an important alternative in solving complex problems whose working area has been expanded.