We have systematically studied the effects of in-plane uniaxial pressure $p$ on the superconducting transition temperature $T_c$ in many iron-based superconductors. The change of $T_c$ with $p$ is composed of linear and nonlinear components. The latter can be described as a quadratic term plus a much smaller fourth-order term. In contrast to the linear component, the nonlinear $p$ dependence of $T_c$ displays a pronounced in-plane anisotropy, which is similar to the anisotropic response of the resistivity to $p$. As a result, it can be attributed to the coupling between the superconducting and nematic orders, in accordance with the expectations of a phenomenological Landau theory. Our results provide direct evidences for the interplay between nematic fluctuations and superconductivity, which may be a common behavior in iron-based superconductors.
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