This contribution presents a novel and versatile approach to geometrically nonlinear topology optimization by combining the level-set method with the element connectivity parameterization method or ECP. The combined advantages of both methods open up the possibility to treat a wide range of optimization problems involving complex physical and/or geometrical nonlinearities in a general and elegant manner. The level-set method features shape optimization on a fixed mesh, leading to intrinsically black-and-white designs. This approach allows a clear description of location and orientation of the interface, whereas topological changes can still be handled easily. A popular concept used in conventional level-set methods is to map the level-set function to volume-fraction design variables for every element of a finite element mesh. The resulting element density variables are then used to scale the Young¿s modulus in each element using the Ersatz material approach. In this work we employ a modified material interpolation method, in which the element density variables, based on a per-element integration of a regularized Heaviside operator applied to the level-set function, are used as element connectivity design variables. The resulting crisp boundary topology optimization method exploits the advantages of ECP in the field of complex nonlinearities and eliminates the need for penalization by the implicit level-set description of the design.@en

This paper presents the direct application of topology optimization to the design of shape memory alloy (SMA) thermal actuators. Because SMAs exhibit strongly nonlinear, temperature-dependent material behavior, designing effective multidimensional SMA actuator structures is a challenging task. We pursue the use of topology optimization to address this problem. Conventional material scaling topology optimization approaches are hampered by the complexity of the SMA constitutive behavior combined with large actuator deflections. Therefore, for topology optimization we employ the element connectivity parameterization approach, which offers improved analysis convergence and robustness, as well as an unambiguous treatment of nonlinear materials. A path-independent SMA constitutive model, aimed particularly at the NiTiR-phase transformation, is employed, allowing efficient adjoint sensitivity analysis. The effectiveness of the proposed SMA topology optimization is demonstrated by numerical examples of constrained and unconstrained formulations of actuator stroke maximization, which provide insight into the characteristics of optimal SMA actuators. Key words: shape memory alloys; NiTi; topology optimization; element connectivity parameterization; geometric nonlinearity; material nonlinearity@en

This contribution presents a novel and versatile approach to geometrically nonlinear topology optimization by combining the level-set method with the element-connectivity-parameterization method (ECP). The combined advantages of both methods open up the possibility to treat a wide range of optimization problems involving complex physical and/or geometrical nonlinearities in a general and elegant way. The level-set method features shape optimization on a fixed mesh, leading to intrinsically black-and-white designs. This approach allows a clear description of location and orientation of the interface, whereas topological changes can still be handled easily. A popular concept used in conventional level-set methods is to map the level-set function to volume-fraction design variables for every element of a finite element mesh using the Ersatz-material approach. In this work we employ a modified Ersatz-material formulation, in which the element-connectivity design variables are based on a per-element integration of a regularized Heaviside operator applied to the level-set function. The resulting crisp-boundary topology optimization method exploits the abilities of ECP in the field of complex nonlinearities and eliminates the need for penalization by the implicit level-set description of the design. Keywords: Topology optimization, level-set method, element-connectivity-parameterization method (ECP), geometrical nonlinearities.@en

This paper concerns itself with topological layout optimization of layered shell structures. Because shell structures have the capability to efficiently carry loads with a minimum amount of material, shells are widely used in major engineering structures such as aerospace structures, ship hulls, car bodies, etc. Given the importance of shell structures, many researchers have investigated the use of topology optimization techniques for this class of problems. The conventional approach is to use a density-based formulation. In various challenging topology optimization problems, the recently proposed element connectivity parameterization (ECP) method was found to have significant advantages over conventional density-based approaches. Examples are increased numerical robustness under large deflections, ease of including complex nonlinear materials, and improved accuracy in certain multi-physics settings. In order to exploit these benefits also in the important class of shell structure problems, the focus of this research is on the application of the ECP approach to topology optimization of shell structures. In our previous research, we developed an ECP-based formulation for the topology optimization of open shell structures, based on a decoupling of the bending and membrane modes of a given shell element. However, closed shell structures with local reinforcements are much more common in practice. In this contribution, we therefore extend the formulation to the reinforcement topology optimization of layered shell structures, considering both symmetric and asymmetric laminates, In addition to a detailed discussion of this new formulation, we demonstrate the effectiveness of our approach by various numerical examples. Keywords: Topology optimization, Shell structure, ECP method@en