Quest for the control on the second order derivatives: topology optimization with functional includes the state’s curvature

Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to consistently control the underlaying process. However, this type of control is nontrivial and to the best … Read more

Minimum weight Topology optimization subject to unsteady heat equation and space-time pointwise constraints — toward automatic optimal riser design in the shape casting process

The automatic optimal design of feeding system in the shape casting process is considered in the present work. In fact, the goal is to find the optimal position, size, shape and topology of risers in the shape casting process. This problem is formulated as a minimum weight topology optimization problem subjected to a nonlinear transient … Read more