Shape optimization of mechanical contact elements for uniform stress distribution using isogeometric analysis

The optimization of the contact interface geometry plays a crucial role in achieving a uniform pressure distribution and reducing peak stresses in interacting components. This reduces the degree of wear of the components. The contact response is highly sensitive to small geometric variations, and identifying an optimal shape through the conventional finite element method (FEM) is challenging because the discrete analysis mesh differs from the underlying computer-aided design (CAD) geometry. During iterative optimization, node movements distort the mesh and require repeated remeshing, which increases the computational cost and reduces robustness. Moreover, derivative-based optimization demands sensitivity evaluation, which is difficult for nonlinear, nonsmooth contact behavior. These limitations can be overcome within the isogeometric analysis (IGA) framework, where geometry and analysis are unified through nonuniform rational B-splines (NURBS) representation, allowing direct modification of control points without remeshing. This study presents an integrated IGA-based contact shape optimization approach that combines a Gauss-point-to-surface (GPTS) contact formulation with the derivative-free Teaching–Learning-Based Optimization (TLBO) algorithm. The y-coordinates of the control points along the contact layer are used as design variables, and the objective is to minimize the standard deviation of the contact forces. The methodology is demonstrated through two plane strain problems: a concave–convex pair and a convex–flat pair. In both cases, small control point adjustments led to noticeable reductions in peak contact pressure and improved uniformity of the pressure field. The optimized responses are in close agreement with Abaqus simulations, demonstrating the effectiveness of the proposed IGA–TLBO framework for the investigated contact shape optimization problems.