We develop a CAD-free geometry engine for shape optimization of complex, threedimensional geometries represented by surface discretizations. This method permits shape optimization of geometries for which no a-priori parametric CAD representation exists. The geometry engine consists of three parts: geometric preprocessing to improve discretization quality, parametric definition of deformation modes, and a physics-based deformation engine. The deformation engine proceeds by analogy to the elastic

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... behavior of thin plates and shells, mimicking the natural behavior of engineering materials under applied loads and strains. The parametric definition of the deformation modes is performed automatically by decomposing the initial geometry into patches upon which loads, strains, and constraints may be applied. These parameters are created hierarchically in order to allow both flexibility and efficiency during shape optimization. We provide example deformations using this geometry engine in conjunction with surfaces represented by tens and hundreds of thousands of triangles and timings on the order of several minutes using commodity hardware. I. Introduction A number of optimization techniques have been successfully employed to improve vehicle performance during the engineering design process. In order to reduce the amount of manual effort and expert knowledge required during problem formulation, we have developed a CAD-free geometry engine for shape optimization that combines the efficiency of parametric CAD with the flexibility of discrete surface representation. Geometry is often defined through parameters that specify the size, shape, and location of basic building blocks. This is the case when optimization is coupled with parametric Computer-Aided Design (CAD) packages, where parameters such as sweep, wing span, or fuselage diameter offer natural control over complex geometries. This approach to geometry definition offers a ready set of design variables for use during the shape optimization process. While this CAD-based approach is attractive, there are several situations in which a CAD-free option can ease problem setup and provide greater flexibility during design. First, parametric CAD models are not always easily obtainable for geometries of interest. Often, triangulated surface meshes are the only representation available for so-called legacy geometries, shapes derived during previous analysis or design studies. In order to compare such studies to contemporary design tools, a parametric model must be recreated in a current CAD package. Since this may require a large amount of manual effort, a geometry engine that operates on pre-existing surface triangulations alone becomes an attractive alternative. Additionally, the use of triangulated surfaces to represent geometry removes difficulties associated with conversion between different CAD packages and versions. It also eliminates compatibility issues associated with CAD packages that run on operating systems outside the high performance computing environment. Furthermore, the flexibility of CAD-based design tools to identify a global optimum is dependent upon the parametric definition of the initial geometry. Creating a good set of parameters for complicated geometries