| 1. |
- Correa, Maicon Ribeiro, et al.
(author)
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A transient thermoelastic mathematical model for topology optimization of support structures in additive manufacturing
- 2024
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In: Structural and multidisciplinary optimization (Print). - : SPRINGER. - 1615-147X .- 1615-1488. ; 67:3
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Journal article (peer-reviewed)abstract
- This study presents a Topology Optimization (TO) methodology for determining the optimal distribution of support structures in the powder bed fusion Additive Manufacturing (AM) fabrication technology. The support structures enhance thermal dissipation, reducing distortion on overhang surfaces during the build process and improving printability. A novel transient thermoelastic layer-by-layer model simulates the AM process, evaluating temperature and displacement in partially built structures with supports. We propose two new objective functions related to part distortion, perform their adjoint sensitivity analysis, and present a comprehensive set of numerical experiments with different geometries and levels of overhang complexity. The numerical results show non-standard optimal support structures obtained using the proposed TO-AM methodology for different model parameters, including support volume, thermal anisotropy, time discretization method, and building times for each layer.
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| 2. |
- Gade, Jan-Lucas, et al.
(author)
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An in vivo parameter identification method for arteries : numerical validation for the human abdominal aorta
- 2019
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In: Computer Methods in Biomechanics and Biomedical Engineering. - : Taylor & Francis. - 1025-5842 .- 1476-8259. ; , s. 426-441
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Journal article (peer-reviewed)abstract
- 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.
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| 3. |
- Gade, Jan-Lucas, 1988-, et al.
(author)
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Identification of mechanical properties of arteries with certification of global optimality
- 2022
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In: Journal of Global Optimization. - : SPRINGER. - 0925-5001 .- 1573-2916. ; 82:1, s. 195-217
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Journal article (peer-reviewed)abstract
- In this study, we consider identification of parameters in a non-linear continuum-mechanical model of arteries by fitting the models response to clinical data. The fitting of the model is formulated as a constrained non-linear, non-convex least-squares minimization problem. The model parameters are directly related to the underlying physiology of arteries, and correctly identified they can be of great clinical value. The non-convexity of the minimization problem implies that incorrect parameter values, corresponding to local minima or stationary points may be found, however. Therefore, we investigate the feasibility of using a branch-and-bound algorithm to identify the parameters to global optimality. The algorithm is tested on three clinical data sets, in each case using four increasingly larger regions around a candidate global solution in the parameter space. In all cases, the candidate global solution is found already in the initialization phase when solving the original non-convex minimization problem from multiple starting points, and the remaining time is spent on increasing the lower bound on the optimal value. Although the branch-and-bound algorithm is parallelized, the overall procedure is in general very time-consuming.
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| 4. |
- Gade, Jan-Lucas, 1988-, et al.
(author)
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In vivo parameter identification in arteries considering multiple levels of smooth muscle activity
- 2021
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In: Biomechanics and Modeling in Mechanobiology. - : Springer Nature. - 1617-7959 .- 1617-7940. ; 20:4, s. 1547-1559
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Journal article (peer-reviewed)abstract
- In this paper an existing in vivo parameter identification method for arteries is extended to account for smooth muscle activity. Within this method a continuum-mechanical model, whose parameters relate to the mechanical properties of the artery, is fit to clinical data by solving a minimization problem. Including smooth muscle activity in the model increases the number of parameters. This may lead to overparameterization, implying that several parameter combinations solve the minimization problem equally well and it is therefore not possible to determine which set of parameters represents the mechanical properties of the artery best. To prevent overparameterization the model is fit to clinical data measured at different levels of smooth muscle activity. Three conditions are considered for the human abdominal aorta: basal during rest; constricted, induced by lower-body negative pressure; and dilated, induced by physical exercise. By fitting the model to these three arterial conditions simultaneously a unique set of model parameters is identified and the model prediction agrees well with the clinical data.
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| 5. |
- Gade, Jan-Lucas, 1988-
(author)
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Mechanical Properties of Arteries : Identification and Application
- 2019
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Licentiate thesis (other academic/artistic)abstract
- In this Licentiate of Engineering thesis, a method is proposed that identifies the mechanical properties of arteries in vivo. The mechanical properties of an artery are linked to the development of cardiovascular diseases. The possibility to identify the mechanical properties of an artery inside the human body could, thus, facilitate disease diagnostization, treatment and monitoring.Supplied with information obtainable in the clinic, typically limited to time- resolved pressure-radius measurement pairs, the proposed in vivo parameter identi- fication method calculates six representative parameters by solving a minimization problem. The artery is treated as a homogeneous, incompressible, residual stress- free, thin-walled tube consisting of an elastin dominated matrix with embedded collagen fibers referred to as the constitutive membrane model. To validate the in vivo parameter identification method, in silico arteries in the form of finite element models are created using published data for the human abdominal aorta. With these in silico arteries which serve as mock experiments with pre-defined material parameters and boundary conditions, in vivo-like pressure-radius data sets are generated. The mechanical properties of the in silico arteries are then determined using the proposed parameter identification method. By comparing the identified and the pre-defined parameters, the identification method is quantitatively validated. The parameters for the radius of the stress-free state and the material constant associated with elastin show high agreement in case of healthy arteries. Larger differences are obtained for the material constants associated with collagen, and the largest discrepancy occurs for the in situ axial prestretch. For arteries with a pathologically small elastin content, incorrect parameters are identified but the presence of a diseased artery is revealed by the parameter identification method.Furthermore, the identified parameters are used in the constitutive membrane model to predict the stress state of the artery in question. The stress state is thereby decomposed into an isotropic and an anisotropic component which are primarily associated with the elastin dominated matrix and the collagen fibers, respectively. In order to assess the accuracy of the predicted stress, it is compared to the known stress state of the in silico arteries. The comparison of the predicted and the in silico decomposed stress states show a close agreement for arteries exhibiting a low transmural stress gradient. With increasing transmural stress gradient the agreement deteriorates.The proposed in vivo parameter identification method is capable of identifying adequate parameters and predicting the decomposed stress state reasonably well for healthy human abdominal aortas from in vivo-like data.
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| 6. |
- Gade, Jan-Lucas, 1988-
(author)
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Mechanical Properties of Arteries : An In Vivo Parameter Identification Method
- 2021
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Doctoral thesis (other academic/artistic)abstract
- In this dissertation, a method is proposed that identifies the mechanical properties of arteries in vivo. The mechanical properties of an artery are linked to the development of cardiovascular diseases. The possibility to identify the mechanical properties of an artery inside the human body could, thus, facilitate disease diagnostization, treatment and monitoring. Supplied with information obtainable in the clinic, typically limited to time-resolved pressure-radius measurement pairs, the proposed in vivo parameter identification method solves a non-convex minimization problem to determine parameters related to the mechanical properties of the blood vessel. The artery is treated as a homogeneous, incompressible, residual stress-free, thin-walled tube consisting of an elastin dominated matrix with embedded collagen fibers. To validate the in vivo parameter identification method, in silico arteries in the form of finite element models are created using published data for the human abdominal aorta. With these in silico arteries which serve as mock experiments with pre-defined material parameters and boundary conditions, in vivo-like pressure-radius data sets are generated. The mechanical properties of the in silico arteries are then determined using the proposed parameter identification method. By comparing the identified and the pre-defined parameters, the identification method is quantitatively validated and it is shown that the parameters agree well for healthy arteries. Furthermore, the identified parameters are used to compare the stress state in the arterial model and in the in silico arteries. The stress state is thereby decomposed into an isotropic and an anisotropic component which are primarily associated with the elastin dominated matrix and the collagen fibers, respectively. The comparison of the decomposed stress states shows a close agreement for arteries exhibiting a physiological stress gradient.Another important aspect is the identification of parameters by solving a non-convex minimization problem. The non-convexity of the problem implies that incorrect parameter values, corresponding to local minima, may be found when common gradient-based solution techniques are employed. A problem-specific global algorithm based on the branch-and-bound method is, therefore, created which ensures that the global minimum and accordingly the correct parameters are obtained. It turns out that the gradient-based solution technique identifies the correct parameters if certain requirements are met, among others the use of the heuristic multi-start method.In a last step, the in vivo parameter identification method is extended to also identify parameters related to smooth muscle contraction. To prevent an overparameterization caused by the increased number of model parameters, the model is simultaneously fit to clinical data measured during three different arterial conditions: basal; constricted; and dilated. Despite the simple contraction model the extended method fits the clinical data well. Finally, in this dissertation it is shown that the proposed in vivo parameter identification method identifies the mechanical properties of arteries well. An open question for future research is how this method can be applied in a clinical setting to facilitate cardiovascular disease diagnostization, treatment and monitoring.
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| 7. |
- Haveroth, G. A., et al.
(author)
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Topology optimization including a model of the layer-by-layer additive manufacturing process
- 2022
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In: Computer Methods in Applied Mechanics and Engineering. - : ELSEVIER SCIENCE SA. - 0045-7825 .- 1879-2138. ; 398
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Journal article (peer-reviewed)abstract
- A topology optimization formulation including a model of the layer-by-layer additive manufacturing (AM) process is considered. Defined as a multi-objective minimization problem, the formulation accounts for the performance and cost of both the final and partially manufactured designs and allows for considering AM-related issues such as overhang and residual stresses in the optimization. The formulation is exemplified by stiffness optimization in which the overhang is limited by adding mechanical or thermal compliance as a measure of the cost of partially manufactured designs. Convergence of the model as the approximate layer-by-layer model is refined is shown theoretically, and an extensive numerical study indicates that this convergence can be fast, thus making it a computationally viable approach useful for including AM-related issues into topology optimization. The examples also show that drips and sharp corners associated with some geometry-based formulations for overhang limitation can be avoided. The codes used in this article are written in Python using only open sources libraries and are available for reference.
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| 8. |
- Hederberg, Hampus, et al.
(author)
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Topology optimization for fail-safe designs using moving morphable components as a representation of damage
- 2021
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In: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 64, s. 2307-2321
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Journal article (peer-reviewed)abstract
- Designs obtained with topology optimization (TO) are usually not safe against damage. In this paper, density-based TO is combined with a moving morphable component (MMC) representation of structural damage in an optimization problem for fail-safe designs. Damage is inflicted on the structure by an MMC which removes material, and the goal of the design problem is to minimize the compliance for the worst possible damage. The worst damage is sought by optimizing the position of the MMC to maximize the compliance for a given design. This non-convex problem is treated using a gradient-based solver by initializing the MMC at multiple locations and taking the maximum of the compliances obtained. The use of MMCs to model damage gives a finite element-mesh-independent method, and by allowing the components to move rather than remain at fixed locations, more robust structures are obtained. Numerical examples show that the proposed method can produce fail-safe designs with reasonable computational cost.
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| 9. |
- Holmberg, Erik, et al.
(author)
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Game theory approach to robust topology optimization with uncertain loading
- 2017
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In: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 55:4, s. 1383-1397
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Journal article (peer-reviewed)abstract
- 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.
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| 10. |
- Holmberg, Erik, et al.
(author)
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Worst-case topology optimization of self-weight loaded structures using semi-definite programming
- 2015
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In: Structural and multidisciplinary optimization (Print). - : Springer Science and Business Media LLC. - 1615-147X .- 1615-1488. ; 52:5, s. 915-928
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Journal article (peer-reviewed)abstract
- The paper concerns worst-case compliance optimization by finding the structural topology with minimum compliance for the loading due to the worst possible acceleration of the structure and attached non-structural masses. A main novelty of the paper is that it is shown how this min-max problem can be formulated as a non-linear semi-definite programming (SDP) problem involving a small-size constraint matrix and how this problem is solved numerically. Our SDP formulation is an extension of an eigenvalue problem seen previously in the literature; however, multiple eigenvalues naturally arise which makes the eigenvalue problem non-smooth, whereas the SDP problem presented in this paper provides a computationally tractable problem. Optimized designs, where the uncertain loading is due to acceleration of applied masses and the weight of the structure itself, are shown in two and three dimensions and we show that these designs satisfy optimality conditions that are also presented.
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