Geometric optimization in the presence of contact singularities

T h e stress singularity of a sha rp wedge contacting a half p lane can b e avoided by changing t h e wedge shape. Shape optimization is accomplished wi th the geometric s t ra in method (GSM), an optimali ty criterion method. Several numerical examples a r e provided for different materials i n t h e wedge and half plane t o avoid stress singularity near t h e sha rp corner of t h e wedge. Opt imum wedge shapes are obtained a n d critical corner angles are compared wi th t h e angles f rom analytical contact mechanics. Numerical results a r e well matched t o analytical a n d experimental results. I t is shown t h a t shape optimization by G S M is a useful tool t o reshape t h e wedge a n d t o avoid a stress singularity. T h e method applies t o more general geometries where t h e singular behavior would b e difficult to avoid by classical means.