In elasticity theory, harmonic holes are designed to leave the mean stress inside the surrounding material as a constant. In this paper, we present the design of periodic harmonic holes with surface tension in an elastic plane under a uniform remote loading. We identify the special shapes of such holes by solving a problem of the existence of a holomorphic function defined in a strip with one of the holes and satisfying specific boundary values. Several examples are given to illustrate the size-dependent effects of surface tension on the shapes of periodic harmonic holes.
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