Adding quadric fillets to quador lattice structures

Abstract

Gupta et al. [1, 2] describe a very beautiful application of algebraic geometry to lattice structures composed of quadric of revolution (quador) implicit surfaces. However, the shapes created have concave edges where the stubs meet, and such edges can be stress-raisers which can cause significant problems with, for instance, fatigue under cyclic loading. This note describes a way in which quadric fillets can be added to these models, thus relieving this problem while retaining their computational simplicity and efficiency.