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Item type:Publication, Access status: with files , Topology optimization considering contact and stress constraintsThis work advances stress-constrained topology optimization for frictionless unilateral contact problems involving large deformations and hyperelastic material behavior. The objective is to minimize the mass of a contact-constrained structure while enforcing stress constraints through local or global stress measures. Different contact coupling techniques based on Lagrange multipliers and penalty methods are investigated with respect to their applicability in stress-constrained optimization. The results show that stress-constrained optimization is considerably more sensitive to discretization errors at curved contact surfaces than common objectives such as compliance. Such errors may introduce artificial stresses that mislead the optimizer towards poorly performing designs. To address this issue, blending functions are used to retain the physical contact geometry during finite-element-based optimization, thereby avoiding the computational cost of very fine contact-surface discretizations. Furthermore, node-to-segment and segment-to-segment contact coupling are compared directly in stress-constrained topology optimization. The smoother contact-pressure and stress distributions provided by segment-to-segment coupling improve the optimization performance and lead to lighter feasible designs. Finally, local and global stress constraint formulations are compared, and an extension of the augmented Lagrangian approach is proposed to address convergence issues in challenging contact scenarios.Publicationtype: Journal Article54 12 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Adjoint shape optimization of blood flow applications under uncertainties(2025); This thesis aims to advance traditional gradient-based shape optimization techniques by incorporating blood-specific features. The work can be broadly classified into four main categories, (a) computational blood flow modeling, (b) parameter-free shape optimization, (c) the continuous adjoint method and (d) robust shape optimization. As regards (a), this work presents key aspects related to the computational fluid dynamics (CFD) or fluid-structure interaction (FSI) simulations employed for the solution of the blood flow problem (primal problem). The underlying primal problem is enhanced to account for blood damage (hemolysis) by the numerical solution of an additional partial differential equation (PDE). The minimization of hemolysis is one of the main objectives of interest in this work. In order to account for the shear-thinning behavior of blood, several non-Newtonian viscosity models are also employed. The numerical solution of the primal problem is verified against analytical solutions and literature-reported results when deemed necessary. The shape optimization problem is formulated based on a parameter-free approach. To this end, the identification of the shape gradient or at least, a suitable descent direction, based on the shape sensitivity is addressed. Several methods that compute the descent direction based on the solution of one (or two) additional PDE(s) are presented. Auxiliary aspects related to the optimization problem are also discussed in the context of (b). The thesis presents the novel derivation of continuous adjoint equation systems dual to the blood-specific problems. Specifically, contributions to (c) relate to the development of the continuous adjoint to the steady-state Navier-Stokes equations for an incompressible fluid with hemolysis modeling and with non-Newtonian viscosity properties. The accuracy of the novel systems in estimating the shape sensitivity is assessed against second-order accurate finite difference (FD) studies. On the topic of (d), this work focuses on the necessary uncertainty quantification techniques able to drive a robust shape optimization procedure. The problem is considered uncertain by means of the employed parameters or the boundary conditions thus rendering the objective functional a statistical quantity. The optimization targets the minimization of the statistical moments of the objective functional through the use of methods based on sampling or the method of moments. The biomedical applications studied in this thesis refer to an idealized medical device and an idealized bypass-graft.Publicationtype: Doctoral Thesis121 144 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Robust contact-constrained topology optimization considering uncertainty at the contact supportIn this paper, the general framework for contact-constrained topology optimization of Strömberg and Klarbring (2010) is extended to robust topology optimization. In doing so, a linear elastic design domain is considered and the augmented Lagrangian approach is used to model the unilateral contact. For topology optimization, the design space is parametrized with the SIMP-approach and the Sigmund’s filter is applied. Additionally, the robust framework considers uncertainties at the contact support such as deviations of the geometry of the contact surface and the friction coefficient. Both uncertainties are described by the first-order second-moment method which leads to minimal additional costs. In fact, only two additional linear equations must be solved to obtain the robust objective and its gradient with respect to the design variables. Having both the objective and the gradient, the design update is computed with the method of moving asymptotes. The robust framework is applied to 2D and 3D examples to prove its scalability for real-world applications.Publicationtype: Journal Article85 163 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Comparison of continuous and discrete adjoint methods for topology optimization in structural dynamicsSemi-analytic adjoint methods can be seen as breakthrough for deterministic topology optimization in structural dynamics since such methods have reduced the computational costs. Nevertheless, the costs are still very high, so that further improvements are crucial. In this work, the concept of the continuous and the discrete adjoint method are applied in structural dynamics. Additionally, a modified discrete method, which is independent of the time discretization of the primal problem, is proposed. This approach results in further numerical savings, while the quality of the gradient does not suffer.Publicationtype: Conference Paper137 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , An efficient and non-intrusive approach for robust design optimization with the first-order second-moment method(Elsevier, 2023-09-01); ; ; ; A modified robust design optimization approach is presented, which uses the first-order second-moment method to compute the mean value and the standard deviation for arbitrary objective functions. Existing approaches compute the gradient of the variance using the adjoint method, direct differentiation or finite differences, respectively. These approaches either access to the FE-code and/or have high computational cost. In this paper, a new approach for the computation of the gradient of the variance is provided. It can be easily implemented as a non-intrusive method, which behaves similar to finite differences with the cost of only one additional objective evaluation, independent of the number of variables. Here, a step-size has to be chosen carefully and therefore, a procedure to determine a problem-independent step-size is provided. As an alternative, the approach can be implemented as an analytic method with the same cost like the adjoint method, but providing wider applicability (e.g. eigenvalue problems). The provided approach is derived, analyzed and applied to several benchmark examples.Publicationtype: Journal Article164 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Adjoint shape sensitivities of blood flows considering non-newtonian propertiesThis article discusses the derivation and numerical implementation of an adjoint system, to the primal Navier–Stokes equations, for the computation of shape sensitivities of ducted blood flows considering non-Newtonian fluid properties. The ever-growing advancements in blood flow simulations are, naturally, accompanied by an increased interest in the optimization of related medical devices. In the majority of the computational studies, the Newtonian assumption is used to describe the rheology of blood. While this assumption has been shown to satisfactorily capture the flow when it is governed by high shear rates, it falls short at low shear rates. A rich variety of viscosity models has been proposed to tackle this shortcoming. In this article we show how such models can be incorporated into an adjoint system targeting to produce the shape sensitivity which can be used by a gradient-based optimization method for the minimization of an objective functional. A general formulation of the adjoint equations is proposed, in which contributions of the non-Newtonian properties explicitly occur. The numerical implementation is discussed and the validity of the method is assessed by means of numerical experiments of steady blood flows in a 2D stenosed duct, where results are compared against second-order finite-difference (FD) studies. The proposed methodology is then applied to CAD-free, gradient-based shape optimizations of an idealized 3D arterial bypass-graft operating at three relevant Reynolds numbers. It is observed that the impact of the adjoint viscosity treatment is amplified in low shear-rate flow regimes while fades for higher shear-rates, analogous to its primal counterpart.Publicationtype: Journal ArticleScopus© Citations 1 46 201 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , A scalable algorithm for shape optimization with geometric constraints in Banach spacesThis work develops an algorithm for PDE-constrained shape optimization based on Lipschitz transformations. Building on previous work in this field, the p-Laplace operator is utilized to approximate a descent method for Lipschitz shapes. In particular, it is shown how geometric constraints are algorithmically incorporated avoiding penalty terms by assigning them to the subproblem of finding a suitable descent direction. A special focus is placed on the scalability of the proposed methods for large scale parallel computers via the application of multigrid solvers. The preservation of mesh quality under large deformations, where shape singularities have to be smoothed or generated within the optimization process, is also discussed. It is shown that the interaction of hierarchically refined grids and shape optimization can be realized by the choice of appropriate descent directions. The performance of the proposed methods is demonstrated for energy dissipation minimization in fluid dynamics applications.Publicationtype: Journal ArticleScopus© Citations 1 100 144 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Adjoint node-based shape optimization of free-floating vesselsThe paper is concerned with a node-based, gradient-driven, continuous adjoint two-phase flow procedure to optimize the shapes of free-floating vessels and discusses three topics. First, we aim to convey that elements of a Cahn–Hilliard formulation should augment the frequently employed Volume-of-Fluid two-phase flow model to maintain dual consistency. It is seen that such consistency serves as the basis for a robust primal/adjoint coupling in practical applications at huge Reynolds and Froude numbers. The second topic covers different adjoint coupling strategies. A central aspect of the application is the floating position, particularly the trim and the sinkage, that interact with a variation of hydrodynamic loads induced by the shape updates. Other topics addressed refer to the required level of density coupling and a more straightforward—yet non-frozen—adjoint treatment of turbulence. The third part discusses the computation of a descent direction within a node-based environment. We will illustrate means to deform both the volume mesh and the hull shape simultaneously and at the same time obey technical constraints on the vessel’s displacement and its extensions. The Hilbert-space approach provides smooth shape updates using the established coding infrastructure of a computational fluid dynamics algorithm and provides access to managing additional technical constraints. Verification and validation follow from a submerged 2D cylinder case. The application includes a full-scale offshore supply vessel at Re = 3 × 10 8 and Fn = 0.37. Results illustrate that the fully parallel procedure can automatically reduce the drag of an already pre-optimized shape by 9–13% within ≈O(10,000-30,000) CPUh depending on the considered couplings and floatation aspects.Publicationtype: Journal ArticleScopus© Citations 8 93 547 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Robust topology optimization of static systems with unilateral frictional contactIn this paper a robust topology optimization algorithm for linear elastic structures in unilateral contact is presented. The deformation of the linear elastic structure is constrained by support structures that are modeled with the help of Signorini’s contact conditions. The contact conditions in turn are enforced with the augmented Lagrangian approach. Doing so, the robust optimization considers uncertainties at the support such as manufacturing tolerances and its local friction behavior. Due to high numerical costs in robust optimization, the first-order second-moment approach is used to approximate the mean and variance of the objective. This approximation results in minimal additional costs to approximate the mean, the variance and their gradients. Consequentially, a gradient-based optimization algorithm can be used to minimize a weighted sum of both. The results show that the presented approach indeed improves the robustness with respect to uncertain contact conditions compared to a deterministic optimization.Publicationtype: Conference PaperScopus© Citations 2 164 183 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Adjoint-based shape optimization for the minimization of flow-induced hemolysis in biomedical applicationsThis paper reports on the derivation and implementation of a shape optimization procedure for the minimization of hemolysis induction in biomedical devices. Hemolysis is a blood damaging phenomenon that may occur in mechanical blood-processing applications where large velocity gradients are found. An increased level of damaged blood can lead to deterioration of the immune system and quality of life. It is, thus, important to minimize flow-induced hemolysis by improving the design of next-generation biomedical machinery. Emphasis is given to the formulation of a continuous adjoint complement to a power-law hemolysis prediction model dedicated to efficiently identifying the shape sensitivity to hemolysis. The computational approach is verified against the analytical solutions of a benchmark problem and computed sensitivity derivatives are validated by a finite differences study on a generic 2D stenosed geometry. The application included addresses a 3D ducted geometry which features typical characteristics of biomedical devices. An optimized shape, leading to a potential improvement in hemolysis induction up to 22%, is identified. It is shown, that the improvement persists for different, literature-reported hemolysis-evaluation parameters.Publicationtype: Journal ArticleScopus© Citations 7 203 259