Geometric strain method for shape optimization.

The geometric strain method is developed to obtain an optimum (minimum weight) shape of a general elastic body subject to strength constraints using an optimality criterion method. The optimality criterion in this study are that the stress at every point in a designated domain should satisfy a yield condition or alternatively, a fatigue condition. The approach of this study is an iterative process and involves two phases of solution. In the first phase, the stress of the current shape is sought. In the second phase, the body is deformed, subject to proper boundary conditions, by an artificial strain which is calculated from the stress of the first phase. The deformed shape is the new design which is expected to lie closer to the optimum shape. The artificial strain is termed geometric strain, which is defined in principal stress axes, and then transformed to global coordinates. The geometric strain at a point is expected to deform an infinitesimal element at the point to satisfy the optimality criterion. Formulations of the geometric strain are set up for three- and two-dimensional shape optimization problems. Also, strength constraints of fatigue stress and yield criteria, such as maximum principal stress and von Mises stress, are considered. This method is applied to several two-dimensional and axisymmetric shape optimization problems. The shapes of a hole in a square plate, a cantilever beam, a fillet, and a bar under a body force and edge load are successfully determined. As an example of an axisymmetric problem, a spring retainer in the valve train of an engine is redesigned subject to the constraints of fatigue stress. Fast convergence is proven in example problems.PhDHealth care managementUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/162251/1/8920621.pd