„… finite cell method for geometrically nonlinear problems of solid mechanics. International Journal for …” „… hp-d-adaptive finite cell method for geometrically nonlinear problems of solid mechanics. International Journal …” „… Proceedings of the ECCOMAS Thematic Conference on Coupled Problems.(M. Papadrakakis, E. Onate), 2005. [73 …”

„… appears in almost all nonlinear problems where the stiffness matrix has to be computed several times …” „… this method for elastoplastic, hyperelastic and nonlinear problems as well. • The local enrichment …” „… 133 Chapter 6 Summary and Outlook The FCM offers a powerful discretization method for problems in …”

„… homogenization of cellular and foamed materials [66, 85, 86, 88], geometrically nonlinear problems [155, 157 …” „… applied numerical approach for solving boundary value problems. In this method, the geometry of the …” „… boundaries. In many cases, obtaining such meshes is straightforward – especially for 2D problems. For some …”

„… foamed materials [66, 85, 86, 159], multi-fields problems [182, 183], geometrically nonlinear problems …” „… 5 Chapter 2 Finite cell method for problems in solid mechanics In this chapter, we focus on the …” „… the governing equations In this thesis, we deal with the numerical simulation of problems in …”

„… problems using the FCM. Another class of numerical integration methods is based on constructing an …” „… integration points can be problematic, especially in nonlinear computations where several quantities like the …” „… position of the quadrature points The equation system (3.21) is nonlinear in terms of xi and linear in …”

„… problems with strongly non-linear characteristics for which a specialized optimization approach is …” „… replaces experience-based engineering practices. Many engineering problems can be addressed as optimization …” „… unavailable or unable to provide satisfactory results. Also problems that involve black-box simulations, in …”

„… topology optimization problems resides in the design freedom naturally reflected by an accordingly high …” „… representations are limited to small problems, geometric representations can provide a balance between design …” „… , currently reducing its applicability to problems with small to mediumsized simulation models. For the …”

„… convergence. It is expected that good results can be obtained mostly for moderately non-linear problems. Some …” „… interest in optimization is increasing. In sizing or shape design optimization problems a limited number of …” „… simplified problems and as a consequence, heuristic approaches for crashworthiness topology optimization have …”

„… the objective function, and especially when consideration of more challenging, non-linear problems …” „… The two-dimensional cantilever beam is one of the standard test problems agreed on in the topology …” „… is confirmed in the plot, while the relation is clearly non-linear for the nodal displacement LSFs …”

„… problems that can be addressed. This chapter contributes to the discourse by categorizing and by …” „… is that of a binary encoding for decision problems such as the Travelling Salesperson Problem …” „… purpose of engineering form optimization problems. The representation not only determines the …”

„… provide concept designs even for problems involving complex, black-box simulations. A self-contained …” „… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 C.1 Strain-stress curves for the non-linear material models used in the crash simulations …” „… optimization methods requires mathematical gradient information. However, when addressing optimization problems …”

„… . Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12:55–67, 1970. [84 …” „… . The Aeronautical Journal, 113:821–831, 2009. [105] Kuhn, H. W. and Tucker, A. W. Nonlinear programming …” „… . [130] Park, G.-J. Technical overview of the equivalent static loads method for non-linear static …”

„… anything but small-scaled problems. Furthermore, almost none of the existing evolutionary computation …” „… of optimization problems, yet a method that incorporates domain knowledge usually has better …” „… approaches in both industry and academia. The majority of topology optimization problems can be formulated as …”

„… nichtlineare Probleme COUENNE (Convex Over and Under ENvelopes for Nonlinear Estimation) [16]. Als direkt …” „… Problems exponentiell wachsende Rechenaufwand, auch Fluch der Dimensionalität [6] genannt, bildet eine …” „… konkurrierende Algorithmen haben wir SDPEN (Sequential Penalty Derivative-Free Method for Nonlinear Constrained …”

„… examined by performing a nonlinear finite element analysis. Such an analysis requires a realistic …” „… simulation of the lateral buckling behavior as well as an adapted safety concept for nonlinear methods in …” „… specifications in current design codes for simplified safety formats for nonlinear finite element calculations …”

„… Starrkörpermodell beschrieben werden können. Mit dem Informationsfusionsverfahrens NARGP (Nonlinear …” „… from multi-fidelity data: Application to function approximation and inverse PDE problems. Journal of …” „… Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations. Internet …”