Searching for local Lorentz invariance violation (LIV) is a method to probe general relativity (GR), since local Lorentz invariance is a key ingredient for GR. Here, we first review the work we have done on LIV in the pure‐gravity sector involving quadratic couplings of Riemann curvature through short‐range pendulum experiments, especially focusing on the theoretical model we established for the transfer matrix linking the experimentally measured torque signal to the 14 LIV coefficients. Based on this model, we analyze the LIV effect in HUST‐2011 and HUST‐2015 experiments again, and give the constraints for the 14 measurable violating coefficients in both experiments. Furthermore, we propose a new experimental design aiming at exploring LIV, which may independently constrain the 14 LIV coefficients with higher sensitivity (improved by about an order of magnitude over earlier results) using the striped geometry.