Abstract

. We develop and test an algorithmic approach for the boundary design of elastic structures. The goal of our approach is two-fold. First, to develop a method which allows one to rapidly solve the two-dimensional Lame equations in abitrary domains and compute for example the stresses, and second, to develop a systematic way of modifying the design towards optimizing chosen properties. At the core, our approach relies on two distinct steps. Given a design, we rst apply an Explicit Jump Immersed Interface Method for computing the stresses for a given design shape. We then use a narrow band level set method to perturb this shape and progress towards an improved design. The equations of 2D linear elastostatics in the displacement formulation on arbitrary domains are solved quickly by domain embedding and the use of fast elastostatic solvers. This eectively reduces the dimensionality of the problem by one. Once the stresses are found, the level set method, which represents the...