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In this study, texture shape optimization is performed to minimize the friction coefficient based on the adjoint variable method under constant load. The shape update equation based on the gradient descent method is regarded as a differential equation, and in order to improve the accuracy of the solution of the differential equation, a new shape update equation is proposed that adapts the second-order Taylor expansion. Shape optimization is performed for four different textures, and the results are compared with those based on the gradient descent method and the proposed shape update equation. FreeFEM++ is used for the calculation.

Optimization of texture shape to minimize the friction coefficient and consideration of update equations for design variables