Topology optimization of continuum structures for the uniformity of contact pressures

In this paper, a topology optimization method is developed for elastic continuum structures in frictionless contact to improve the uniformity of contact pressures. The variance constraint of contact pressures is introduced into the standard volume-constrained compliance minimization problem and combined with the three-field SIMP (Solid Isotropic Material with Penalization) model. Two geometric constraints are also incorporated to achieve optimization solutions with desired minimum length scales and clear boundaries without intermediate densities. To ensure a correct evaluation of contact pressure variance, a density threshold method is proposed to assign each contact node pair a certain density value according to the physical densities of its adjacent elements and further to exclude the contact node pairs with density values smaller than the threshold value. The effectiveness of the proposed method is validated through a series of numerical examples including elastic-rigid and elastic-elastic frictionless contact problems. The influence of the variance constraint of contact pressures on the optimization result is discussed in comparison with the standard maximum stiffness design. It concludes that the variance of contact pressures can be reduced at the cost of the structural stiffness, which implies that a trade-off exists between the structural stiffness and the uniformity of contact pressures.