Global and clustered approaches for stress constrained topology optimization and deactivation of design variables

Abstract We present a global (one constraint) version of the clustered approach previously developed for stress constraints, and also applied to fatigue constraints, in topology optimization. The global approach gives designs without large stress concentrations or geometric shapes that would cause stress singularities. For example, we solve the well known L-beam problem and obtain a radius at the internal corner. The main reason for using a global stress constraint in topology optimization is to reduce the computational cost that a high number of constraints impose. In this paper we compare the computational cost and the results obtained using a global stress constraint versus using a number of clustered stress constraints. We also present a method for deactivating those design variables that are not expected to change in the current iteration. The deactivation of design variables provides a considerable decrease of the computational cost and it is made in such a way that approximately the same final design is obtained as if all design variables are active. 2. Keywords: Topology optimization, Stress constraints, Global, Clustered, Deactivated variables Introduction In many industrial applications, the aim of structural optimization is to find the lightest design that meets the structural requirements. However, most commercial optimization software in industrial use are based on the traditional formulation of finding the stiffest structure for a prescribed amount of material: a formulation which does not necessarily yield a design that is feasible with respect to actual structural requirements, such as stress and fatigue. Furthermore, in many industrial applications, the stiffness does not necessarily have to be maximized and by allowing a slightly lower stiffness we might find a lighter and more mature design. The reason for using this stiffness based formulation is mostly computational efficiency: the optimization is driven by a global measure (compliance) and no extra (adjoint) system of equations needs to be solved in the sensitivity analysis. Stress constraints on the other hand give a much more expensive problem as stress is a local measure; i.e., a local (every stress evaluation point) quantity has to be constrained rather than a global, which increases the computational cost. However, minimizing the mass subjected to stress constraints has the potential of yielding a more mature and useful final design. Stress constraints have been discussed since the very first papers on topology optimization: Bendsøe and Kikuchi The clustered approach developed by Holmberg et al

http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-73555 Optimization of structures in frictional contact

This paper describes a new approach to optimization of linear elastic structures in frictional contact. It uses a novel method to determine an, in a specified sense, likely equilibrium state of the structure, using only the static equilibrium conditions. That is, no complex dynamic/quasi-static analyses have to be performed. The approach has the advantage that it is not necessary to know the complete load history, which is most often unknown for practical problems. To illustrate the theory, numerical results are given for the optimal design problem of sizing a truss to attain a more uniform normal contact force distribution

Design optimization based on state problem functionals

This paper presents a general mathematical structure for design optimization problems, where state problem functionals are used as design objectives.It extends to design optimization the general model of physical theories pioneered by Tonti (1972, 1976) and Oden and Reddy (1974, 1983). It turns out that the classical structural optimization problem of compliance minimization is a member of the treated general class of problems. Other particular examples, discussed in the paper, are related to Darcy-Stokes flow and pipe flow models. A main novel feature of the paper is the unification of seemingly different design problems, but the general mathematical structure also explains some previously not fully understood phenomena. For instance, the self-penalization property of Stokes flow design optimization receives an explanation in terms of minimization of a concave function over a convex set.Funding Agencies|Swedish Foundation for Strategic Research [AM13-0029]; Swedish Research Council [Dnr: 621-2012-3117]</p

optimization

systems and topology optimizatio