Background: Arterial mechanics are crucial to cardiovascular functionality. The pressure–strain elastic modulus often delineates mechanical properties. Emerging methods use non-linear continuum mechanics and non-convex minimization to identify tissue-specific parameters in vivo. Reliability of these methods, particularly their accuracy in representing the in vivo stress state, is a significant concern. This study aims to compare the predicted stress state and the collagen-attributed load-bearing fraction with the stress state from in silico experiments. Methods: Our team has evaluated an in vivo parameter identification method through in silico experiments involving finite element models and demonstrated good agreement with the parameters of a healthy abdominal aorta. Results: The findings suggest that the circumferential stress state is well represented for an abdominal aorta with a low transmural stress gradient. Larger discrepancies are observed in the axial direction. The agreement deteriorates in both directions with an increasing transmural stress gradient, attributed to the membrane model’s inability to capture transmural gradients. The collagen-attributed load-bearing fraction is well predicted, particularly in the circumferential direction. Conclusions: These findings underscore the importance of investigating both isotropic and anisotropic aspects of the vessel wall. This evaluation advances the parameter identification method towards clinical application as a potential tool for assessing arterial mechanics.

This article demonstrates a large-scale 3D topology optimization problem formulation for components in need of internal cooling owing to surrounding hot gas flow. A conjugate heat transfer model is used and the goal of the optimization problem is to maximize the thermal performance subject to a coolant consumption limit. As a model problem, the interior design of a gas turbine guide-vane-like geometry is considered. High-quality finite element meshes are generated automatically by means of a voxelization method. A structural compliance constraint for thermo-mechanical loads, and a constraint for the suppression of free-floating structural parts, are included in the problem formulation. For the latter, an analytical expression for the constraint limit is derived. Several numerical examples indicate that the proposed problem formulation is able to generate interesting conceptual designs for interior-vane-cooling solutions.

A method is presented for obtaining topology optimized designs for internally cooled high temperature applications, using a flexible geometry description, by means of a voxelization methodology and a novel boundary detection algorithm. A conjugate heat transfer approach is taken; the physics is described by a Stokes-Brinkman model for the flow, weakly coupled with a convection-diffusion model for the heat transfer. A practically relevant optimization formulation, consisting of a maximum temperature objective with a mass flow constraint, is used, and applied to an industrial-relevant non-trivial geometry resembling a guide vane in a gas turbine. Temperatures and velocities from the optimized design are compared with the response from a Stokes flow model with body-fitted mesh and a high-fidelity Reynolds-averaged Navier-Stokes model. A comparison of the performance from a mixed and a penalty approach for solving the flow problem is included. The voxelization approach shows good promise for handling complex design domains.

We propose a topology optimization-based method for optimal design of cooling systems in the form of a mathematical game between two players trying to reach a compromise between limiting the amount of a cooling medium used and obtaining low temperatures in the design domain. The flow of the cooling medium is governed by a Stokes-Brinkman flow model with penalty, while the temperature is governed by a stationary convection-diffusion problem whose solution is approximated using a finite element method with consistent stabilization. Existence of solution for the continuum problems and finite element convergence are shown. The idea and performance of the proposed design method are illustrated by numerical examples based on a problem-setting inspired by an industrial design problem for a gas turbine part. The method exhibits good convergence and is able to generate meaningful design concepts representing various levels of compromise between limited use of cooling medium and low temperatures.

We propose a new deterministic robust design optimization method for composite laminate structures under worst-case material uncertainty. The method is based on a simultaneous parametrization of topology and material and combines a design problem and a material uncertainty problem into a single min–max optimization problem which provides an efficient approach to handle variation of material properties in stiffness driven design optimization problems. An analysis is performed using a design problem based on a failure criterion formulation to evaluate the ability of the proposed method to generate robust composite designs. The design problem is solved using various loads, boundary conditions and manufacturing constraints. The designs generated with the proposed method have improved objective responses compared to the worst-case response of designs generated with nominal material properties and are less sensitive to the variation of material properties. The analysis indicates that the proposed method can be efficiently applied in a robust structural optimization framework. © 2023 The Author(s)

We consider structural optimization (SO) under uncertainty formulated as a mathematical game between two players -- a "designer" and "nature". The first player wants to design a structure that performs optimally, whereas the second player tries to find the worst possible conditions to impose on the structure. Several solution concepts exist for such games, including Stackelberg and Nash equilibria and Pareto optima. Pareto optimality is shown not to be a useful solution concept. Stackelberg and Nash games are, however, both of potential interest, but these concepts are hardly ever discussed in the literature on SO under uncertainty. Based on concrete examples of topology optimization of trusses and finite element-discretized continua under worst-case load uncertainty, we therefore analyze and compare the two solution concepts. In all examples, Stackelberg equilibria exist and can be found numerically, but for some cases we demonstrate nonexistence of Nash equilibria. This motivates a view of the Stackelberg solution concept as the correct one. However, we also demonstrate that existing Nash equilibria can be found using a simple so-called decomposition algorithm, which could be of interest for other instances of SO under uncertainty, where it is difficult to find a numerically efficient Stackelberg formulation.

A method for identifying mechanical properties of arterial tissue in vivo is proposed in this paper and it is numerically validated for the human abdominal aorta. Supplied with pressure-radius data, the method determines six parameters representing relevant mechanical properties of an artery. In order to validate the method, 22 finite element arteries are created using published data for the human abdominal aorta. With these in silico abdominal aortas, which serve as mock experiments with exactly known material properties and boundary conditions, pressure-radius data sets are generated and the mechanical properties are identified using the proposed parameter identification method. By comparing the identified and pre-defined parameters, the method is quantitatively validated. For healthy abdominal aortas, the parameters show good agreement for the material constant associated with elastin and the radius of the stress-free state over a large range of values. Slightly larger discrepancies occur for the material constants associated with collagen, and the largest relative difference is obtained for the in situ axial prestretch. For pathological abdominal aortas incorrect parameters are identified, but the identification method reveals the presence of diseased aortas. The numerical validation indicates that the proposed parameter identification method is able to identify adequate parameters for healthy abdominal aortas and reveals pathological aortas from in vivo-like data.

We develop a topology optimization method including high-cycle fatigue as a constraint. The fatigue model is based on a continuous-time approach, which uses the concept of a moving endurance surface as a function of the stress history and back stress evolution. The development of damage only occurs when the stress state lies outside the endurance surface. Furthermore, an aggregation function, which approximates the maximum fatigue damage, is implemented. As the optimization workflow is sensitivity-based, the fatigue sensitivities are determined using an adjoint sensitivity analysis. The capabilities of the presented approach are tested on numerical models where the problem is to maximize the stiffness subject to high-cycle fatigue constraints.

The paper concerns robustness with respect to uncertain loading in topology optimization problems with essentially arbitrary objective functions and constraints. Using a game theoretic framework we formulate problems, or games, defining Nash equilibria. In each game a set of topology design variables aim to find an optimal topology, while a set of load variables aim to find the worst possible load. Several numerical examples with uncertain loading are solved in 2D and 3D. The games are formulated using global stress, mass and compliance as objective functions or constraints.

Many problems in structural optimization can be formulated as a minimization of the maximum eigenvalue of a symmetric matrix. In practise it is often observed that the maximum eigenvalue has multiplicity greater than one close to or at optimal solutions. In this note we give a sufficient condition for this to happen at extreme points in the optimal solution set. If, as in topology optimization, each design variable determines the amount of material in a finite element in the design domain then this condition essentially amounts to saying that the number of elements containing material at a solution must be greater than the order of the matrix.