Читать книгу Multiscale Modelling and Optimisation of Materials and Structures - Tadeusz Burczynski - Страница 15

Solution of optimization problems in multiscale modelling allows finding structures with better performance or strength in one scale with respect to design variables in another scale. In this case, the typical situation is to find a vector of material or geometrical parameters on the micro‐level, which minimizes an objective function dependent on state fields on a macro‐level of the structure.

A special case of optimization problems associated with the multiscale approach is the optimization of atomic clusters for the minimization of the system's potential energy. This case has an important consequence, especially in the design of new 2D nanomaterials and nanostructures.

The identification problem is formulated as the evaluation of some geometrical or material parameters of structures in one scale having measured information in another scale. The important case of identification in multiscale modelling is to find material properties, the shape of the inclusions/fibres or voids in the microstructure having measurements of state fields made on the macro‐object. The identification problem is formulated and considered as a special optimization task.

The analysis methods of multiscale models based on computational homogenization are adopted for these classes of problems. To solve optimization and identification problems, global optimization methods based on bioinspired algorithms are used.