Topology optimization without volume constraint – the new paradigm for lightweight design

In the paper the new paradigm for structural optimization without volume constraint is presented. Since the problem of stiffest design (compliance minimization) has no solution without additional assumptions, usually the volume of the material in the design domain is limited. The biomimetic approach, based on trabecular bone remodeling phenomenon is used to eliminate the volume constraint from the topology optimization procedure. Instead of the volume constraint, the Lagrange multiplier is assumed to have a constant value during the whole optimization procedure. Well known MATLAB topology based optimization code, developed by Ole Sigmund, was used as a tool for the new approach testing. The code was modified and the comparison of the original and the modified optimization algorithm is also presented. With the use of the new optimization paradigm, it is possible to minimize the compliance by obtaining different topologies for different materials. It is also possible to obtain different topologies for different load magnitudes. Both features of the presented approach are crucial for the design of lightweight structures, allowing the actual weight of the structure to be minimized. The final volume is not assumed at the beginning of the optimization process (no material volume constraint), but depends on the material’s properties and the forces acting upon the structure. The cantilever beam example, the classical problem in topology optimization is used to illustrate the presented approach