Topology optimization with pressure load through a level set method

The topology optimization problem with pressure load is solved by using a level set method. The free boundary and the pressure boundary of a structure are represented separately as two zero-level sets of two level set functions, and they are independently propagated during the optimization by solving two Hamilton-Jacobi equations. In order to prevent the two boundaries from touching or crossing each other, the design velocities of the two boundaries that amount to the steepest descent directions are modified. The optimization problem of minimum compliance with perimeter regularization is considered. The shape derivatives of the two boundaries are derived by using the material derivative approach and the adjoint method. The finite element analysis is done through an Eulerian method by employing a fixed mesh and an artificial weak material that represents void. Numerical examples in two dimensions are investigated.