Level set topology optimization of problems with sliding contact interfaces

Abstract

This paper introduces a topology optimization method for the design of two-component structures and two-phase material systems considering sliding contact and separation along interfaces. The geometry of the contact interface is described by an explicit level set method which allows for both shape and topological changes in the optimization process. The mechanical model assumes infinitesimal strains, a linear elastic material behavior, and a quasi-static response. The contact conditions are enforced by a stabilized Lagrange multiplier method and an active set strategy. The mechanical model is discretized by the extended finite element method which retains the crispness of the level set geometry description and allows for the convenient integration of the weak form of the contact conditions at the phase boundaries. The formulation of the optimization problem is regularized by introducing a perimeter penalty into the objective function. The optimization problem is solved by a nonlinear programming scheme computing the design sensitivities by the adjoint method. The main characteristics of the proposed method are studied by numerical examples in two dimensions. Consideration of contact leads to the formation of barb-type features that increase the interface stiffness. The numerical results further demonstrate the significant difference in the optimized geometries when assuming perfect bonding versus considering contact.

Structural optimization of contact problems using Cahn–Hilliard model

“…This remark applies to the obtained optimal topology. In literature there are reported only a few examples dealing with topology optimization of contact problems [18][19][20]. In these papers considered contact phenomena are different then problem (10) and (11).…”

“…In [19] the topological derivative of the regularized cost functional has been used to find the solution to topology optimization problem for two-dimensional contact problem in elasticity. In [20][21][22][23] the level set approach has been used to solve numerically topology optimization problems for different unilateral boundary value problems.…”

“…Topology optimization of elastic bodies in contact has been considered in [18][19][20][21][22][23]. In [18] SIMP method has been used to solve optimization problem for frictionless contact.…”

Level set shape and topology optimization of finite strain bilateral contact problems

“…The optimization of unilateral contact surface geometries (similar to Figure B) have been achieved with a LSM for small strain theory problems; see, for example, Myťslinski . Topology optimization including the material interface geometry has been achieved in a few small strain theory studies, namely, for frictionless two‐phase problems and cohesive interface phenomena of multiphase problems . These 2 studies analyzed two‐dimensional problems and are comparable to option (D) and a combination of options (C) and (D) from Figure , respectively.…”

Multi-material topology optimization considering interface behavior via XFEM and level set method

“…[26] designed the shape of the interface between two-phase materials with a non-parametric shape optimization method, in which the positions of the nodes are treated as design variables. Lawry and Maute [27] used a parameterized level set function to describe the sliding contact surfaces between two-phase materials and optimizes the shapes of these contact surfaces. Hilchenbach and Ramm [28] considered the damage of the interface between the matrix and the inclusion by combining the XFEM and a cohesive model, and optimized the size/position of inclusions with user-specified shapes to improve the ductility of the design using parametric optimization techniques.…”