Level-set methods are domain classification techniques that are gaining popularity in the recent years for structural topology optimization. Level sets classify a domain into two or more categories (such as material and void) by examining the value of a scalar level-set function (LSF) defined in the entire design domain. In most level-set formulations, a large number of design variables, or degrees of freedom is used to define the LSF, which implicitly defines the structure. The large number of design variables makes non-gradient optimization techniques all but ineffective. Kriging-interpolated level sets (KLS) on the other hand are formulated with an objective to enable non-gradient optimization by defining the design variables as the LSF values at few select locations (knot points) and using a Kriging model to interpolate the LSF in the rest of the design domain. A downside of concern when adopting KLS, is that using too few knot points may limit the capability to represent complex shapes, while using too many knot points may cause difficulty for non-gradient optimization. This paper presents a study of the effect of number and layout of the knot points in KLS on the capability to represent complex topologies in single and multi-component structures. Image matching error metrics are employed to assess the degree of mismatch between target topologies and those best-attainable via KLS. Results are presented in a catalogue-style in order to facilitate appropriate selection of knot-points by designers wishing to apply KLS for topology optimization.

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