We present a new design method, which we call design-by-morphing, for the optimal design of the shape of an object. The surface of one or more objects (or the sub-objects from which it is composed) is represented as a truncated series of exponentially-convergent spectral basis functions multiplied by spectral coefficients. A morphed object or sub-object is obtained from a new set of spectral coefficients, which are a weighted average of the spectral coefficients of the original objects or sub-objects from which it is morphed. Optimized designs are created by choosing the weights such that a cost function of the new morphed shape is minimized. The boundaries of an object and the interfaces between sub-objects can be forced to satisfy geometric constraints on their shapes, slopes, curvature, etc. With these constraints, sub-objects can be seamlessly attached to each other to create a complex object. Because design-by-morphing has the flexibility to adjust independently the weights of sub-objects, users or an automated algorithm can choose some subset of sub-objects to be optimized while preserving or restricting the changes of other sub-objects. Our design-by-morphing method can be automated and is computationally efficient, so it requires much less human input than traditional design methods and is therefore not only inexpensive but also free from human bias in finding optimal designs that are radical and non-intuitive.

We have applied optimization via design-by- morphing to aircraft and a turbine-99 draft tube, and reduced drag-to-lift ratio and maximized mean pressure recovery factor by 23.1% and 10.9%, respectively. We believe that this optimization method is applicable to a wide variety of engineering applications in which the performance of an object depends on the aerodynamic or hydrodynamic