This study is focused on the multi-scale modelling strategy for complex and heterogeneous microstructures of real materials by automatic image-based modelling and finite element mesh superposition method. The synergetic application of the conventional asymptotic homogenization method and the authors' mesh superposition method has been proposed to obtain the microscopic responses under high gradient of macroscopic fields at the macroscopic crack tip and/or interface, for instance. For complex and random microstructures, automatic image-based voxel meshing by means of x-ray CT is commonly required; however, it cannot always adapt to the mathematical theory of microscopic modelling in the mesh superposition method. Therefore, a modelling technique for mesh refinement is proposed in this paper using additional elements for insulation in consideration of the theoretical background of the mesh superposition method.In this paper, we provide the modelling procedure and its theoretical consideration of mesh refinement for flexible modelling of real materials. To demonstrate the technique, a numerical example of a porous ceramic component with random microstructure and macroscopic crack is illustrated.
MEMS structures and machines fabricated by photolithography and/or etching have often repeated unit microstructure. We need to design not only the global parameters but also microscopic and local parameters. In pursuit of this, a dynamic analysis of global/local problem is essential, and especially fast computational method and convenient modeling technique are both required for the MEMS design. Hence, this paper presents the application of model order reduction (MOR) for fast dynamic analysis combined with the finite element mesh superposition (FEMS) technique for practical and convenient modeling of the above-mentioned microstructures. Through two examples, the accuracy is carefully investigated for both global and local responses associated with the base vectors in MOR algorithm. The first example is analyzed by a kind of homogenization technique and MOR. The number of DOFs was finally reduced by a factor of approximately 1/6 (47,362/296,268). In addition, MOR enabled us to reduce the coefficient matrix size to only 300. The second example is analyzed by both FEMS and MOR, and it was found that MOR is also applicable to an unusual matrices generated by FEMS.
In shape optimization, an optimal shape is generated by moving some nodes of an initial mesh. But there are many cases that meshes can not follow the movement of nodes. In this paper, the shape optimization technique using mesh superposition method is proposed. In the present technique, the shape of design domain is represented by local mesh to allow flexible shape control.
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