Aircraft wings with passive load alleviation morph their shape to a configuration where the aerodynamic forces are reduced without the use of an actuator. In our research, we exploit geometric nonlinearities of the inner wing structure to maximize load alleviation. In order to find designs with the desired properties, we propose a topology optimization approach. Passive load alleviation is achieved through bending–torsion coupling. The wing twist will reduce the angle of attack, thus lowering the aerodynamic forces. Consequently, the objective function is to maximize the torsion angle. Since shape morphing should only affect loads that exceed normal maneuvering loads, a displacement constraint is enforced, preventing torsion at lower force levels. Maximizing the displacement will lead to topologies for which the finite element solver cannot find a solution. To circumvent this, we propose adding a compliance value to the objective function. This term has a weighting function, which controls how much influence the compliance value has: after a set number of iterations, the initially high level of influence will drop. We used a geometric nonlinear finite element formulation with a linear elastic material model. The addition of an energy interpolation scheme reduces mesh distortion. We successfully applied the proposed methodology to two different test cases resembling an aircraft wing box section. These test cases illustrate the methodology’s potential for designing new geometries with the desired nonlinear behavior. We discuss what design features can be deduced and how they achieve the nonlinear structural response.