A hierarchical design concept for shape optimization based on the interaction of CAGD and FEM

SUMMARYIn this paper, a new shape optimization approach is proposed to provide an e cient optimization solution of complex structures represented by polygonal meshes. Our approach consists of three main steps: (1) surface partitioning of polygonal meshes; (2) generation of shape design variables on the basis of partitioned surface patches; and (3) gradient-based shape optimization of the structures by reducing a weighted compliance among all load cases. The main contributions of this paper include (i) that our approach can be directly applied on polygonal meshes with the reduction of design variables or decision variables by 10 to 1000 times, compared to the conventional design variable scheme of using each mesh node; (ii) our perturbation scheme is mathematically proven with respect to maintaining the smoothness of each surface patch, except on its boundary; and (iii) overall, our approach can be used to automate time-consuming shape optimization of polygonal meshes to a greater extent. Numerical experiments have been conducted and the results indicate the e ectiveness of the approach.

Section: Propositionmentioning

confidence: 92%

“…(2) Optimization methods: gradient-based method [4,5], genetic method [6], dynamic simulation [7], heuristic evolution [3], etc. (3) Geometry: mesh-based [8], CAD-based [9,10].…”

Section: Introductionmentioning

confidence: 99%

A new scheme for efficient and direct shape optimization of complex structures represented by polygonal meshes

Shen

Yoon

2003

“…Two main considerations have evolved to bypass these conceptual shortcomings. On the one hand, a separate geometry model can be employed to govern the design update procedure [4][5][6][7]. By this mechanism, the inconvenient direct manipulation of nodal point coordinates within the corresponding finite element representation is avoided.…”

Section: Introductionmentioning

confidence: 99%

On structural shape optimization using an embedding domain discretization technique

Riehl

Steinmann

2016

Summary This contribution presents a novel approach to structural shape optimization that relies on an embedding domain discretization technique. The evolving shape design is embedded within a uniform finite element background mesh which is then used for the solution of the physical state problem throughout the course of the optimization. We consider a boundary tracking procedure based on adaptive mesh refinement to separate between interior elements, exterior elements, and elements intersected by the physical domain boundary. A selective domain integration procedure is employed to account for the geometric mismatch between the uniform embedding domain discretization and the evolving structural component. Thereby, we avoid the need to provide a finite element mesh that conforms to the structural component for every design iteration, as it is the case for a standard Lagrangian approach to structural shape optimization. Still, we adopt an explicit shape parametrization that allows for a direct manipulation of boundary vertices for the design evolution process. In order to avoid irregular and impracticable design updates, we consider a geometric regularization technique to render feasible descent directions for the course of the optimization. Copyright © 2016 John Wiley & Sons, Ltd.

“…A considerable amount of work in the area of shape optimization of structures has been conducted in the past. From the perspective of geometric representation, these approaches can be generally categorized as either CAD-based [1][2][3][4][5][6][7] or mesh-based [8][9][10][11][12][13]. For a more detailed classification, readers may refer to Reference [14], which contains an excellent review on different shape parameterization techniques.…”

Section: Introductionmentioning

confidence: 99%

A freeform shape optimization of complex structures represented by arbitrary polygonal or polyhedral meshes

Shen

Yoon

2004

SUMMARYIn this paper we propose a new scheme for freeform shape optimization on arbitrary polygonal or polyhedral meshes. The approach consists of three main steps: (1) surface partitioning of polygonal meshes into different patches; (2) a new freeform perturbation scheme of using the Cox-de Boor basis function over arbitrary polygonal meshes, which supports multi-resolution shape optimization and does not require CAD information; (3) freeform shape optimization of arbitrary polygonal or polyhedral meshes. Numerical experiments indicate the effectiveness of the proposed approach.