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We present new numerical results for shape optimization problems of interior Neumann eigenvalues. This field is not well understood from a theoretical standpoint. The existence of shape maximizers is not proven beyond the first two eigenvalues, so we study the problem numerically. We describe a method to compute the eigenvalues for a given shape that combines the boundary element method with an algorithm for nonlinear eigenvalues. As numerical optimization requires many such evaluations, we put a focus on the efficiency of the method and the implemented routine. The method is well suited for parallelization. Using the resulting fast routines and a specialized parametrization of the shapes, we found improved maxima for several eigenvalues.
Three-dimensional (3D) full-field measurements provide a comprehensive and accurate validation of finite element (FE) models. For the validation, the result of the model and measurements are compared based on two respective point-sets and this requires the point-sets to be registered in one coordinate system. Point-set registration is a non-convex optimization problem that has widely been solved by the ordinary iterative closest point algorithm. However, this approach necessitates a good initialization without which it easily returns a local optimum, i.e. an erroneous registration. The globally optimal iterative closest point (Go-ICP) algorithm has overcome this drawback and forms the basis for the presented open-source tool that can be used for the validation of FE models using 3D full-field measurements. The capability of the tool is demonstrated using an application example from the field of biomechanics. Methodological problems that arise in real-world data and the respective implemented solution approaches are discussed.
Thermohydrodynamic analysis of thrust-bearing with circular pads running on bubbly oil (BTHD-theory)
(1985)
Traditional vulcanization mold manufacturing is complex, costly, and under pressure due to shorter product lifecycles and diverse variations. Additive manufacturing using Fused Filament Fabrication and high-performance polymers like PEEK offer a promising future in this industry. This study assesses the compressive strength of various infill structures (honeycomb, grid, triangle, cubic, and gyroid) when considering two distinct build directions (Z, XY) to enhance PEEK’s economic and resource efficiency in rapid tooling. A comparison with PETG samples shows the behavior of the infill strategies. Additionally, a proof of concept illustrates the application of a PEEK mold in vulcanization. A peak compressive strength of 135.6 MPa was attained in specimens that were 100% solid and subjected to thermal post-treatment. This corresponds to a 20% strength improvement in the Z direction. In terms of time and mechanical properties, the anisotropic grid and isotropic cubic infill have emerged for use in rapid tooling. Furthermore, the study highlights that reducing the layer thickness from 0.15 mm to 0.1 mm can result in a 15% strength increase. The study unveils the successful utilization of a room-temperature FFF-printed PEEK mold in vulcanization injection molding. The parameters and infill strategies identified in this research enable the resource-efficient FFF printing of PEEK without compromising its strength properties. Using PEEK in rapid tooling allows a cost reduction of up to 70% in tool production.