A geometry projection method for the topology optimization of curved plate structures with placement bounds

作者：Zhang Shanglong; Gain Arun L; Norato Julian A^*

来源：International Journal for Numerical Methods in Engineering, 2018, 114(2): 128-146.

DOI：10.1002/nme.5737

• curved plate structures
• design for manufacturing
• placement constraint
• topology optimization

Single-curvature plates are commonly encountered in mechanical and civil structures. In this paper, we introduce a topology optimization method for the stiffness-based design of structures made of curved plates with fixed thickness. The geometry of each curved plate is analytically and explicitly represented by its location, orientation, dimension, and curvature radius, and therefore, our method renders designs that are distinctly made of curved plates. To perform the primal and sensitivity analyses, we use the geometry projection method, which smoothly maps the analytical geometry of the curved plates onto a continuous density field defined over a fixed uniform finite element grid. A size variable is ascribed to each plate and penalized in the spirit of solid isotropic material with penalization, which allows the optimizer to remove a plate from the design. We also introduce in our method a constraint that ensures that no portion of a plate lies outside the design envelope. This prevents designs that would otherwise require cuts to the plates that may be very difficult to manufacture. We present numerical examples to demonstrate the validity and applicability of the proposed method.

• 出版日期2018-4-13