A scalable implementation of the ground structure method for solving large scale topology optimization problems in GPU
Arturo E. Cubas1; Ivan F. M. Menezes1
1 Pontifical Catholic University of Rio de Janeiro / PUC-Rio
doi:10.20906/CPS/COB-2015-1077
Resumo
Topology optimization aims to find the most efficient distribution of material in a specified domain without violating user-defined design constraints. When applied to continuum structures, topology optimization is usually performed by means of well-known density methods. In this study, we focus on the application of its discrete formulation in which a given domain is discretized into a ground structure, i.e., a finite spatial distribution of nodes that are connected using truss members. The ground structure method provides an approximation to optimal Michell-type structures, which are composed of an infinite number of members, using a reduced number of truss members. The optimal least-weight truss with a single load under linear elastic conditions and subjected to stress constraints can be posed as a linear programming problem. The aim of this work is to provide a scalable implementation for the optimization of least-weight trusses embedded in a domain with any type of geometry. The method removes unnecessary members from a truss that has a user-defined degree of connectivity while keeping the locations of nodes fixed. We detail the scalable implementation of the ground structure method using an efficient and robust interior point algorithm in a parallel computing environment that involves graphics processing units (GPUs). The capabilities of the proposed implementation are illustrated by means of large-scale applications to practical problems with millions of members in both 2D and 3D structures.
Palavras-chave: topology optimization; interior point algorithm; ground structure method; parallel computing; GPU