  This work introduces a topology optimization method for the design of structures composed of rectangular plates each of which is made of a predetermined anisotropic material. This work builds upon the geometry projection method with two notable additions. First, a novel geometric parameterization of plates represented by offset surfaces is formulated that is both simpler and more robust than the one used in previous works. This simplicity and robustness is achieved by avoiding the use of trigonometric functions and introducing an extra parameter for each plate. Second, the formulation presented herein adds support to the geometry projection method for geometric components with general anisotropic material properties.  

  A design-generation framework is formulated that produces optimal designs composed exclusively of rectangular plates that may be made of a predetermined, generally anisotropic material. Furthermore, the material properties at intersections of plates is determined as a linear combination of the materials of each intersecting plate, yet converges to the material of a singe plate for an optimal design. This ensures that the optimizer is able to produce meaningful designs which are composed of a single, optimal plate at any given point.

  The efficacy of the proposed method is demonstrated with a numerical example comparing optimal cantilever beam designs obtained using isotropic- and orthotropic-material plates. For this example, we maximize the stiffness of the structure for a fixed amount of material. The example reveals the importance of considering material anisotropy in the design of plate structures. Moreover, it is demonstrated that an optimally stiff design for plates made of an isotropic material can exhibit detrimental performance if the plates are naively replaced with an anisotropic material. Furthermore, it is found that the cantilever design problem makes little use of the transverse stiffness of the isotropic material; the optimal design obtained using plates whose stiffness is reduced in all but one direction performs similarly to the same design replaced with an isotropic material that is equally stiff in all directions. Unexpectedly, the example demonstrates that the use of a transversely-compliant orthotropic material is able to converge more quickly to a better local optimum than designing for a transversely-stiff isotropic material.

  Although the example given in this work is in the context of orthotropic plates, since the formulation presented in this work supports arbitrary anisotropic materials, it may be readily extended to support the design of each component's material anisotropy as a part of the optimization routine.


A Topology Optimization Method for the Design of Orthotropic Plate Structures

Division / Sponsors: 
Design Engineering Division and Computers & Information In Engineering Division


Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2020/volume/83907

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