Two-scale structural design optimization for the simultaneous design of material and structure, has been a topic of research interest during the last decade. This paper is based on the approach presented in  and considers two scales, macro and micro, identified with the design domains of the structure and its material (cellular or composite material), respectively. Structure and material evolve for their optimal layouts as a result of updating the density based design variables such that the global compliance is minimized and a global resource volume constraint is satisfied. Here the class of cellular or composite materials, is restricted to single scale periodic materials, with the unit cell topology locally optimized for the given objective function and constraints. Asymptotic homogenization theory is used to compute equivalent elastic properties at the macroscopic level. The design model may include local constraints for the material microstructure depending on the applications. For instance, some constraints may be related with material manufacture requirements as minimum thicknesses as well as mass transport properties and so forth . The structure design domain is usually discretized using a conforming finite element mesh and then each finite element is associated with a cellular material design region matching a proper global volume fraction or density assumed constant in the element. This type of design model leads in general to a very high number of local problems identified with the material microstructure characterization across the whole structure domain. Eventually, the number of local problems is equal to the number of finite elements discretizing the structure domain. Fortunately, parallel processing techniques may be easily applied to this approach ensuring solutions within reasonable computational times . Although the resulting designs obtained with the described methodology are mechanically very efficient, they are hard to manufacture because the changes in material microstructure occur almost from "point-to-point" over the structural domain. Alternatively, the model described so far may be reformulated assuming that the microstructure remains equal in a structural region (design element) defined not based on each finite element but from larger sub-regions consistent with manufacture constraints or structural uniformity. Such a design element may group several finite elements and may be for example one layer in a typical layered composite structure (e.g. laminates or sandwiches panels). The scope of structural applications in the present work is layered composite structures where typically fiber mats are embedded in a polymeric (resin) matrix covering a large area of the structure domain to form a laminate. This fiber reinforced polymers are usually stacked in a number of layers (laminates) each one having proper fiber orientations. Integer optimization has been applied to determine optimal ply angles and stacking sequences playing with fixed two-material mixing proportions/rules and fiber layouts. The main contribution given in this work is to investigate and eventually improve the optimality of this type of bi-material composites by applying the reformulated multiscale approach described above. This approach is intended to be lesser restrictive than common design approaches applied to laminated composites. Therefore, macroscopic design sub-regions are here assigned to enclose laminates of a composite structure. A single variable can govern the orientation of the fiber material even though it covers several finite elements in the discretized model (lamina domain). The design space is explored in terms of material directionality (fiber orientation), proper choice of materials and their volume fractions (fiber and resin phases design), stacking sequence, laminate thicknesses, fiber and resin cross-section lay-outs. Optimal composite laminated structures are achieved for maximum stiffness (minimum compliance) with a global material resource constraint that imposes a limit on the total amount of the fiber material. The optimal orientation, volume fraction and cross-section layout of the fiber in each lamina (ply) of the structure is determined by density and angle based design variables. Three-dimensional examples involving laminated beams and plates are shown to demonstrate the relevance of the proposed design methodology and also to recognize the optimality of this type of bi-material composite structures.
|Title of host publication||CST|
|Publication status||Published - 1 Jan 2012|
|Event||The Eleventh International Conference on Computational Structures Technology - |
Duration: 1 Jan 2012 → …
|Conference||The Eleventh International Conference on Computational Structures Technology|
|Period||1/01/12 → …|