A key requirement in 3D fabrication is to generate objects with individual exterior shapes and their interior being optimized to application-specific force constraints and low material consumption. Accomplishing this task is challenging on desktop computers, due to the extreme model resolutions that are required to accurately predict the physical shape properties, requiring memory and computational capacities going beyond what is currently available. Moreover, fabrication-specific constraints need to be considered to enable printability. To address these challenges, we present a scalable system for generating 3D objects using topology optimization, which allows to efficiently evolve the topology of high-resolution solids towards printable and light-weight-high-resistance structures. To achieve this, the system is equipped with a high-performance GPU solver which can efficiently handle models comprising several millions of elements. A minimum thickness constraint is built into the optimization process to automatically enforce printability of the resulting shapes. We further shed light on the question how to incorporate geometric shape constraints, such as symmetry and pattern repetition, in the optimization process. We analyze the performance of the system and demonstrate its potential by a variety of different shapes such as interior structures within closed surfaces, exposed support structures, and surface models.
We present a hexahedral finite element method for simulating cuts in deformable bodies using the corotational formulation of strain at high computational efficiency. Key to our approach is a novel embedding of adaptive element refinements and topological changes of the simulation grid into a geometric multigrid solver. Starting with a coarse hexahedral simulation grid, this grid is adaptively refined at the surface of a cutting tool until a finest resolution level, and the cut is modeled by separating elements along the cell faces at this level. To represent the induced discontinuities on successive multigrid levels, the affected coarse grid cells are duplicated and the resulting connectivity components are distributed to either side of the cut. Drawing upon recent work on octree and multigrid schemes for the numerical solution of partial differential equations, we develop efficient algorithms for updating the systems of equations of the adaptive finite element discretization and the multigrid hierarchy. To construct a surface that accurately aligns with the cuts, we adapt the splitting cubes algorithm to the specific linked voxel representation of the simulation domain we use. The paper is completed by a convergence analysis of the finite element solver and a performance comparison to alternative numerical solution methods. These investigations show that our approach offers high computational efficiency and physical accuracy, and that it enables cutting of deformable bodies at very high resolutions.
Virtual cutting of deformable bodies has been an important and active research topic in physically based modelling and simulation for more than a decade. A particular challenge in virtual cutting is the robust and efficient incorporation of cuts into an accurate computational model that is used for the simulation of the deformable body. This report presents a coherent summary of the state of the art in virtual cutting of deformable bodies, focusing on the distinct geometrical and topological representations of the deformable body, as well as the specific numerical discretizations of the governing equations of motion. In particular, we discuss virtual cutting based on tetrahedral, hexahedral and polyhedral meshes, in combination with standard, polyhedral, composite and extended finite element discretizations. A separate section is devoted to meshfree methods. Furthermore, we discuss cutting-related research problems such as collision detection and haptic rendering in the context of interactive cutting scenarios. The report is complemented with an application study to assess the performance of virtual cutting simulators.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.