Optimization

Candela shell in Valencia: Shape optimization with implicit filters

Shape optimization with explicit filters of a shell with a point load

Shape optimization of a shell structure with CAD parameterization

Mass minimization of a structural joint via shape optimization

Bead pattern optimizations of a flat plate

Motivation

In mathematical terms, optimization deals with improving (minimizing) an objective function by selectively modifying the design variables. For differentiable objective functions, gradient-based methods can be applied, which utilize the gradients to determine a suitable update of the design variables. Optimization problems are applied in numerous disciplines. By appropriately choosing the objective function and the design variables, almost any problem can be formulated as an optimization problem.

In the context of structures, we focus on structural optimization. Depending on the problem formulation, structural optimization can be divided into three categories (see Figure 1):

Sizing optimization
Shape optimization
Topology optimization

Figure 1: Different types of structural optimization

In structural optimization, we address the question of the optimal design of a structure for a specific problem. An example of such a problem would be a structure subjected to a loading.

At the Chair of Structural Analysis, we focus on shape optimization, more specifically on node-based shape optimization. More information can be found under node-based structural optimization. Optimization is relevant to several research areas at the chair, such as the Form-Finding of membrane structures or System Identification and Digital Twins.

Research topics

Projects and cooperations

Kratos Multiphysics

Kratos Multiphysics is an open-source framwork for numerical simulation, especially for Finite-Element-Method applications. It contains two applications for optimization problems:

More details related to Kratos Multiphysics are available here.

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