Simultaneous Structural and Material Optimization

Research output: ThesisDoctoral Thesis

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Innovative and resource-efficient products are of great importance for a number of industries including automotive and aerospace. As a consequence, increased usage of lightweight materials in highly optimized structural designs is of highest priority. Structural optimization, in particular topology optimization, has seen accelerated deployment throughout all industries in the past decade, mainly due to the fact that significant efficiency gain can be achieved at the concept design level. In terms of extremely lightweight structures, composite structures are a key-player as they offer the possibility of tailoring the material to a specific application. Hence, the purpose of introducing composite materials as part of the design formulation for structural optimization requires both, to determine the optimal spatial distribution as well as the optimal local choice of material properties, i.e., the orientation and the anisotropy of the local material tensor which is controlled by the composite microstructure. Since a change in topology affects the local stress situation, it also affects the adjustment of material parameters (orientation, degree of anisotropy) and vice versa. As a consequence, it is essential to address the aspects of topology optimization and local material optimization simultaneously, which is contrary to the present design practice. The current work presents a new method for optimization of structural layout and material that simultaneously addresses the design of the global geometry (topology) and the more or less detailed design of the material itself in terms of orientation and anisotropy of the local material tensor. The concept, which is implemented for three-dimensional structures, is evaluated on simple pseudo two dimensional (academic) test cases. The global design objective is to minimize the compliance of a structure, subject to a volume constraint. The developed method is implemented in Python. The Python code takes advantage of the advanced FEM capacities of the Abaqus software and employs the Abaqus Scripting Interface (ASI) to communicate with Abaqus. The global geometry (topology) is determined using the Bi-Evolutionary Structural Optimization Algorithm (BESO), based on the use of sensitivity analysis and mathematical programming. Material optimization is achieved by adjusting the material orientation, based on the local loading conditions (i.e., principal stress directions). Furthermore, the optimized local anisotropy is determined by adjusting the respective volume fractions of continuous cylindrical inclusions, based on the relation of the absolute values of the principal stresses. The homogenized stiffness tensor is determined using a micromechanics mean field approach. Therefore, the method yields physically realistic material configurations and is based on a reasonable amount of design variables without adding unnecessary restrictions to the design space. The developed method is applicable to single as well as multiple loadcases. The numerical application of the method on simple pseudo two dimensional (academic) test cases shows its effectiveness and robustness. The material determined with this method goes beyond topology optimized quasi-isotropic and orientation optimized unidirectional material as it can be directly optimized for the functional needs at the structural scale. Therefore, the compliance is significantly reduced compared to a standard topology optimization with quasi-isotropic material. It is observed that the method is very robust, i.e. shows good convergence and little sensitivity to the startdesign and control parameters. Therefore, the proposed method opens up a wide range of interesting perspectives. Next steps include the generalization of the concept to three dimensional topologies as well as including manufacturing constraints such that the practical feasibility of the optimized design can be take
Translated title of the contributionKombinierte Optimierung von Bauteilstruktur und Material
Original languageEnglish
Awarding Institution
  • Montanuniversität
  • Schuecker, Clara, Assessor A (internal)
  • Elgeti, Stefanie, Assessor A (external), External person
Publication statusPublished - 2021

Bibliographical note

embargoed until null


  • Topology Optimization
  • Material Optimization
  • Bi-Evolutionary Structural Optimization (BESO)
  • Composite
  • Anisotropic Material
  • Finite Element Method
  • Mean Field Homogenization
  • Mori-Tanaka Method
  • Python

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