Simultaneous optimization of shape and topology of free-form shells based on uniform parameterization model

In current optimization methods for free-form shells, the shape and topology are usually optimized separately. These methods are based on the assumption that the shape and topology of a shell influence each other only slightly, but this is not always correct. Moreover, different parameterization models are used in the shape optimization and topology optimization of free-form shells, which brings difficulties to carry out the integrated optimization. To solve this problem, an integrated method is proposed for simultaneously optimizing shape and topology for free-form shells. A uniform parameterization model based on NURBS solids is established to parameterize the free-form shells. In this model, only a small number of variables are used to describe both the shape and topology of the shell. In this way, the integrated optimization problem can be simplified, thus decrease the computational complexity. The integrated optimization of shape and topology is a complicated and large-scale optimization problem. Solving this problem requires a suitable optimization method. In this paper, the Method of Moving Asymptotes (MMA) is adopted. Finally, numerical examples are presented to address the importance of the optimization sequences and show the effectiveness and application of the proposed method.

[1]  John Rasmussen,et al.  An integrated approach for shape and topology optimization of shell structures , 2002 .

[2]  Toshio Honma,et al.  Structural shape optimization of free-form surface shell and property of solution search using firefly algorithm , 2015 .

[3]  Sergio Pellegrino,et al.  Multi-objective optimization of free-form grid structures , 2009 .

[4]  Chau H. Le,et al.  A gradient-based, parameter-free approach to shape optimization , 2011 .

[5]  E. Ramm,et al.  Form finding of shells by structural optimization , 1993, Engineering with Computers.

[6]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[7]  H. Ohmori,et al.  Computational Morphogenesis of Free Form Shells , 2009 .

[8]  Nathalie Labonnote,et al.  Additive construction: State-of-the-art, challenges and opportunities , 2016 .

[9]  Kenji Yamamoto,et al.  SHAPE OPTIMIZATION OF SHELL AND SPATIAL STRUCTURE FOR SPECIFIED STRESS DISTRIBUTION , 1998 .

[10]  Behrooz Hassani,et al.  Simultaneous shape and topology optimization of shell structures , 2013, Structural and Multidisciplinary Optimization.

[11]  Maan H. Jawad,et al.  Theory and design of plate and shell structures , 1994 .

[12]  J. Canales,et al.  On simultaneous shape and material layout optimization of shell structures , 2002 .

[13]  Claudio Borri,et al.  Two shape parametrizations for structural optimization of triangular shells , 2016 .

[14]  Frei Otto,et al.  Finding Form: Towards an Architecture of the Minimal , 1996 .

[15]  E. Ramm,et al.  Structural optimization and form finding of light weight structures , 2001 .

[16]  Jeong-ick Lee,et al.  An integrated design for double-layered structures , 2004 .

[17]  Ümit Uzman,et al.  Optimum shape design of shell structures , 2007 .

[18]  Antonio Tomás,et al.  Shape and size optimisation of concrete shells , 2010 .

[19]  I. Vizotto,et al.  Computational generation of free-form shells in architectural design and civil engineering , 2010 .

[20]  Ole Sigmund,et al.  On the (non-)optimality of Michell structures , 2016, Structural and Multidisciplinary Optimization.

[21]  Roland Wüchner,et al.  Optimal shapes of mechanically motivated surfaces , 2010 .

[22]  R. J. Yang,et al.  A three-dimensional shape optimization system—shop3D , 1989 .

[23]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[24]  Santiago Sánchez-Cervera Huerta,et al.  Structural Design in the Work of Gaudí , 2006 .

[25]  Yang Liu,et al.  A non-parametric free-form optimization method for shell structures , 2014 .

[26]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[27]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[28]  K. G. Mahmoud,et al.  Structural shape optimization using msc/nastran and sequential quadratic programming , 1999 .