This note considers two elastic quarter-planes perfectly bonded together on their common boundary and clamped on their other boundaries. Asymptotic analysis of the stresses in the corners of the quarter-planes identifies the power singularities present for a full range of elastic moduli. Configurations with nonsingular stresses at this juncture are also identified. These last results offer some means for removing stress singularities from clamped butt joints by perturbing elastic moduli.

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