These slides were presented at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

Non-parametric stiffness, strength and/or weight optimization of nonlinear structures is challenging due to the many various potential physical and numerical instabilities for the primal solutions during the optimization iterations. A common approach is to simplify the physics and ignore the non-linear effects of the realistic physical modeling. However, such simplifications often fails when the linear optimized structures are validated using full non-linear modeling including large deformations, imperfections, elastic-plastic material, large sliding contact with friction etc. This potentially leads to additional required redesign work and lost time, and a high likelihood for sub-optimal designs. There is a tradeoff between more time spent in understanding physics, setting up nonlinear analysis, running longer optimizations versus simplified physics with faster optimizations but at the risk of less accurate results which potentially fail in validation. We will demonstrate for a number of applications that sensitivity based optimization approaches using various recent stabilization techniques can successfully address optimizations where severe non-linear phenomenon are present in the structural modeling. The stabilization techniques are utilized depending upon problem type and degree of nonlinearity. These stabilization techniques are independent from each other and can be applied separately or in various combinations. Initially, implicit dynamic procedure can be used in dynamic or quasi-static events for the primal solution modeling and corresponding adjoint sensitivities. The inertia of the system acts as an additional damping procedure for the primal solution. Secondly, a hyper-elastic stabilization scheme has been implemented to address artificial local buckling due to numerical singularities in geometrical nonlinear modeling caused by distorted void elements in topology optimization. The implementation adds artificial stiffness in a non-intrusive manner and only affects otherwise numerical unstable regions which normally cause the primal solution to fail. Thirdly, an artificial added stabilization force scheme in post-buckling region for force-driven problems is implemented. This ensures a full solution for a global buckling analysis being force driven which would often be numerical unstable in post-buckling range. Finally, it is also found that using imperfections help stabilize the optimization iteration convergence as well as ensure that design is robust. Three different nonlinear structural optimization cases are used as demonstrators of above described techniques covering Topology-, Sizing- and Shape optimization. Each problem contains different types of nonlinearities including large deformations, elastic-plastic material constitutive behavior and large sliding frictional contact. In each case a successful optimization has resulted in improved performance of the nonlinear structures.