Optimized One-Click Development for Topology-Optimized Structures

Topology optimization is a powerful digital engineering tool for the development of lightweight products. Nevertheless, the transition of obtained design proposals into manufacturable parts is still a challenging task. In this article, the development of a freeware framework is shown, which uses a hybrid topology optimization algorithm for stiffness and strength combined with manufacturing constraints based on finite spheres and a two-step smoothing algorithm to design manufacturable prototypes with “one click”. The presented workflow is shown in detail on a rocker, which is “one-click”-optimized and manufactured. These parts were experimentally tested using a universal testing machine. The objective of this article was to investigate the performance of “one-click”-optimized parts in comparison with manually redesigned optimized parts and the initial design space. The test results show that the design proposals created while applying the finite-spheres and two-step smoothing are equal to the manual redesigned parts based on the optimization results, proposing that the “one-click”-development can be used for the fast and direct development and fabrication of prototypes.

The method of finite spheres in acoustic wave propagation through nonhomogeneous media: Inf-sup stability conditions

When the method of finite spheres is used for the solution of time-harmonic acoustic wave propagation problems in nonhomogeneous media, a mixed (or saddle-point) formulation is obtained in which the unknowns are the pressure fields and the Lagrange multiplier fields defined at the interfaces between the regions with distinct material properties. Then certain inf-sup conditions must be satisfied by the discretized spaces in order for the finite-dimensional problems to be well-posed. We discuss in this paper the analysis and use of these conditions. Since the conditions involve norms of functionals in fractional Sobolev spaces, we derive ‘stronger’ conditions that are simpler in form. These new conditions pave the way for the inf-sup testing, a tool for assessing the stability of the discretized problems.

POD for Real-Time Simulation of Hyperelastic Soft Biological Tissue Using the Point Collocation Method of Finite Spheres

The point collocation method of finite spheres (PCMFS) is used to model the hyperelastic response of soft biological tissue in real time within the framework of virtual surgery simulation. The proper orthogonal decomposition (POD) model order reduction (MOR) technique was used to achieve reduced-order model of the problem, minimizing computational cost. The PCMFS is a physics-based meshfree numerical technique for real-time simulation of surgical procedures where the approximation functions are applied directly on the strong form of the boundary value problem without the need for integration, increasing computational efficiency. Since computational speed has a significant role in simulation of surgical procedures, the proposed technique was able to model realistic nonlinear behavior of organs in real time. Numerical results are shown to demonstrate the effectiveness of the new methodology through a comparison between full and reduced analyses for several nonlinear problems. It is shown that the proposed technique was able to achieve good agreement with the full model; moreover, the computational and data storage costs were significantly reduced.