Realization of a Framework for Simulation-Based Large-Scale Shape Optimization Using Vertex Morphing

There is a significant tendency in the industry for automation of the engineering design process. This requires the capability of analyzing an existing design and proposing or ideally generating an optimal design using numerical optimization. In this context, efficient and robust realization of such a framework for numerical shape optimization is of prime importance. Another requirement of such a framework is modularity, such that the shape optimization can involve different physics. This requires that different physics solvers should be handled in black-box nature. The current contribution discusses the conceptualization and applications of a general framework for numerical shape optimization using the vertex morphing parametrization technique. We deal with both 2D and 3D shape optimization problems, of which 3D problems usually tend to be expensive and are candidates for special attention in terms of efficient and high-performance computing. The paper demonstrates the different aspects of the framework, together with the challenges in realizing them. Several numerical examples involving different physics and constraints are presented to show the flexibility and extendability of the framework.

[1]  Thomas D. Economon,et al.  An Unsteady Continuous Adjoint Approach for Aerodynamic Design on Dynamic Meshes , 2014 .

[2]  Hideyuki Azegami,et al.  Shape optimization of running shoes with desired deformation properties , 2020 .

[3]  Kai-Uwe Bletzinger,et al.  The Vertex Morphing method for node-based shape optimization , 2014 .

[4]  Long Chen,et al.  A modified search direction method for inequality constrained optimization problems using the singular-value decomposition of normalized response gradients , 2019, Structural and Multidisciplinary Optimization.

[5]  Hans-Joachim Bungartz,et al.  preCICE – A fully parallel library for multi-physics surface coupling , 2016 .

[6]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2005, SIAM Rev..

[7]  Kai-Uwe Bletzinger,et al.  A consistent formulation for imposing packaging constraints in shape optimization using Vertex Morphing parametrization , 2017 .

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

[9]  Raphael T. Haftka,et al.  Accuracy Analysis of the Semi-Analytical Method for Shape Sensitivity Calculation∗ , 1990 .

[10]  J. Samareh Survey of Shape Parameterization Techniques for High-Fidelity Multidisciplinary Shape Optimization , 2001 .

[11]  Eugenio Oñate,et al.  An Object-oriented Environment for Developing Finite Element Codes for Multi-disciplinary Applications , 2010 .

[12]  Joaquim R. R. A. Martins,et al.  pyOpt: a Python-based object-oriented framework for nonlinear constrained optimization , 2011, Structural and Multidisciplinary Optimization.

[13]  Kai-Uwe Bletzinger,et al.  A consistent frame for sensitivity filtering and the vertex assigned morphing of optimal shape , 2014, Structural and Multidisciplinary Optimization.

[14]  Francisco Luna,et al.  Integrating a multi-objective optimization framework into a structural design software , 2014, Adv. Eng. Softw..

[15]  H. A. Eschenauer Shape optimization of satellite tanks for minimum weight and maximum storage capacity , 1989 .

[16]  P. Steinmann,et al.  On the formulation and implementation of geometric and manufacturing constraints in node–based shape optimization , 2016 .

[17]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[18]  Ole Sigmund,et al.  Large scale three-dimensional topology optimisation of heat sinks cooled by natural convection , 2015, ArXiv.

[19]  J. C. Newman,et al.  Discrete direct and adjoint sensitivity analysis for arbitrary Mach number flows , 2006 .

[20]  Joaquim R. R. A. Martins,et al.  OpenMDAO: an open-source framework for multidisciplinary design, analysis, and optimization , 2019, Structural and Multidisciplinary Optimization.

[21]  Jihong Zhu,et al.  Topology Optimization in Aircraft and Aerospace Structures Design , 2016 .

[22]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[23]  Yu Liu,et al.  An object-oriented MATLAB toolbox for automotive body conceptual design using distributed parallel optimization , 2017, Adv. Eng. Softw..

[24]  Ole Sigmund,et al.  Giga-voxel computational morphogenesis for structural design , 2017, Nature.

[25]  Carsten Othmer,et al.  Adjoint methods for car aerodynamics , 2014, Journal of Mathematics in Industry.