Multi-scale topology optimization with graded microstructures

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Nyilvántartási szám: 
20/01
Témavezető neve: 
Témavezető e-mail címe:
logo.janos@emk.bme.hu
A témavezető teljes publikációs listája az MTMT-ben:
A téma rövid leírása, a kidolgozandó feladat részletezése: 
Topology optimization is a design tool that sketches lightweight components searching the design domain for the distribution of a limited amount of material that minimizes a prescribed objective function (generally compliance of the structure), given a set of constraints (such as equilibrium and volume).
Techniques such as additive manufacturing (AM) are well-suited to bring optimal layouts from concept to reality, since they considerably reduce restrictions imposed by traditional manufacturing techniques, see e.g. [1]. 
 
Adopting the conventional Solid Isotropic Model with Penalization (SIMP) to interpolate the elastic properties of the material with respect to its point-wise density, i.e. the minimization unknown, optimal layouts made of void and solid material are found. However, an improved overall performance can be achieved adopting alternative interpolation schemes with reduced penalization of the intermediate densities [2]. Extended grey regions arise in the optimal layouts, which can be handled as infill zones of porous material to be further optimized, see e.g. [3]. Alternatively, multi-scale topology optimization can be adopted to design both the macrostructure and the microstructure using a consistent material interpolation scheme, see e.g. [4]. A wide range of lattices is achieved, and it is not straightforward to effectively combine their different shapes.
 
In this proposal, topology optimization approaches will be investigated that distribute a limited amount of material by grading throughout the domain the main geometrical features of a selected set of microstructures of assigned shape. Reference is made in particular to [5] for an optimization problem that provides graded cells, but in case of a fixed macroscale. 
Numerical homogenization will be employed to derive the relevant material schemes that interpolate the elastic properties of isotropic and orthotropic lattices/microstructures both in 2D problems and 3D problems. The Cauchy model and the Cosserat model will be used at the macroscale depending on the reference size of the microstructure with respect to that of the macrostructure. 
Optimal shapes will be investigated considering manufacturability when using AM techniques. Continuity among adjacent microstructures with different material density will be sought, as well as shapes that avoid undesired overhangs. The latter point is crucial for printers that use Fused Deposition Modelling (FDM) to melt a plastic filament while positioning it layer-by-layer. At 45 degree, the newly printed layer is supported only by half of the previous layer, often still enough to build upon. For angles in excess of 45 degrees, some uneconomic support is generally required, at least for non-negligible “bridges”. 
The material laws derived from homogenization of the selected graded microstructures will be used, at first, to replace SIMP in the conventional volume-constrained minimum compliance problem. This is equivalent to a minimum volume problem with constraints on the displacement fields in case of identical boundary conditions. Hence, additional types of enforcement will be included in the formulation, such as stress-based constraints and eigenvalue-based constraints. The former topic addresses strength and fatigue requirement, whereas the second allows considering dynamic properties and buckling failure. Both topics have been widely investigated in the literature within the framework of the SIMP [6], whereas a lack of studies is reported for multiscale design based on porous microstructures.
The above problem will be investigated at first in the case of deterministic single loading. It will be investigated later the alternative loading and the multiple loading cases. The effect of probabilistic loads will be considered using first order (FORM), second order (SORM, )Monte Carlo approaches and ad hoc formulations [7,8,9].   
 
A téma meghatározó irodalma: 
[1] Liu J, Gaynor AT, Chen S, Kang Z, Suresh K, Takezawa A, et al. Current and future trends in topology optimization for additive manufacturing. Struct Mutltidiscip Opt 2018;57(6):2457-2483.
 
[2] Bendsøe MP, Sigmund O. Material interpolation schemes in topology optimization. Arch Appl Mech 1999;69(9-10):635-654. 
 
[3] Wu J, Aage N, Westermann R, Sigmund O. Infill Optimization for Additive Manufacturing-Approaching Bone-Like Porous Structures. IEEE Trans Visual Comput Graphics 2018;24(2):1127-1140.
 
[4] Sivapuram R, Dunning PD, Kim HA. Simultaneous material and structural optimization by multiscale topology optimization. Struct Multidiscip Opt 2016;54(5):1267-1281. 
 
[5] Cheng L, Bai J, To AC. Functionally graded lattice structure topology optimization for the design of additive manufactured components with stress constraints. Comput Methods Appl Mech Eng 2018;344:334-359.
 
[6] Deaton JD, Grandhi RV. A survey of structural and multidisciplinary continuum topology optimization: Post 2000. Struct Mutltidiscip Opt 2014;49(1):1-38.
 
[7] Lógó J. New type of optimality criteria method in case of probabilistic loading conditions. Mech Based Des Struct Mach 2007;35(2):147-162.
 
[8] Bence, Balogh ; Matteo, Bruggi ; Janos, Logo
Optimal design accounting for uncertainty in loading amplitudes: A numerical investigation
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES 46 : 5 pp. 552-566. , 15 p. (2018)
 
[9] János, Lógó ; Bence, Balogh ; Erika, Pintér
Topology Optimization Considering Multiple Loading
COMPUTERS & STRUCTURES 207 pp. 233-244. , 12 p. (2018)
 
A téma hazai és nemzetközi folyóiratai: 
1. ADVANCES IN ENGINEERING SOFTWARE 
2. COMPUTERS & STRUCTURES
3. MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
4. STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
5. PERIODICA POLYTECHNICA-CIVIL ENGINEERING
A témavezető utóbbi tíz évben megjelent 5 legfontosabb publikációja: 
1. Tauzowski, P. ; Blachowski, B. ; Lógó, J.
Functor-oriented topology optimization of elasto-plastic structures
ADVANCES IN ENGINEERING SOFTWARE 135  Paper: 102690 , 11 p. (2019)
 
2. Bence, Balogh ; Matteo, Bruggi ; Janos, Logo
Optimal design accounting for uncertainty in loading amplitudes: A numerical investigation
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES 46 : 5 pp. 552-566. , 15 p. (2018)
 
3. János, Lógó ; Bence, Balogh ; Erika, Pintér
Topology Optimization Considering Multiple Loading
COMPUTERS & STRUCTURES 207 pp. 233-244. , 12 p. (2018)
 
4. Bence, Balogh ; János, Lógó
The application of drilling degree of freedom to checkerboards in structural topology optimization
ADVANCES IN ENGINEERING SOFTWARE 107 pp. 7-12. , 6 p. (2017)
 
5. Lógó, J ; Ghaemi, M ; Movahedi, Rad M
Optimal topologies in case of probabilistic loading: The influence of load correlation
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES 37 : 3 pp. 327-348. , 22 p. (2009)
A témavezető fenti folyóiratokban megjelent 5 közleménye: 
1. A, Csébfalvi ; J, Lógó
A critical analysis of expected-compliance model in volume-constrained robust topology optimization with normally distributed loading directions, using a minimax-compliance approach alternatively
ADVANCES IN ENGINEERING SOFTWARE 120 pp. 107-115. , 9 p. (2018)
 
2. János, Lógó ; Bence, Balogh ; Erika, Pintér
Topology Optimization Considering Multiple Loading
COMPUTERS & STRUCTURES 207 pp. 233-244. , 12 p. (2018)
 
3. Blachowski, B. , Tauzowski, P. ; Lógó, J.
Yield Limited Optimal Topology Design of Elasto-Plastic Structures
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION (2019) elfogadva (DOI: 10.1007/s00158-019-02447-9)
 
4. Logo, J
New type of optimality criteria method in case of probabilistic loading conditions
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES 35 : 2 pp. 147-162. , 16 p. (2007)
 
5. Pintér, Erika ; Lengyel, András ; Lógó, János
Structural Topology Optimization with Stress Constraint Considering Loading Uncertainties
PERIODICA POLYTECHNICA-CIVIL ENGINEERING 59 : 4 pp. 559-565. , 7 p. (2015)
Megjegyzés: 
A téma Dr. Matteo Bruggi-val közösen vezetve. Szerződés szükséges a BME és Politecnico di Milano között.
 
Hallgató: 

A témavezető eddigi doktoranduszai

Balogh Bence (2014/2017/)
Pintér Erika (2012/2015/2019)
Merczel Dániel Balázs (2010/2013/2015)
Mohsen Ghaemi (2003//2010)
Movahedi Rad Majid (2007//2011)
Ismail Hussein (2020/2024/2024)
Tóth Bálint (2023//)
Ismail Hussein (2020/2024/2024)
Tóth Bálint (2023//)
Státusz: 
elfogadott