STRESS CONSTRAINED TOPOLOGY OPTIMIZATION VIA SEQUENTIAL SECOND ORDER CONE PROGRAMMING

The main objective of structural design is to determine a structure that can carry the applied loads providing safety and without undergoing excessive displacements. In general, it is not clear, a priori, what is the most efficient shape that satisfies the above criteria requiring the smallest amount of material. In order to obtain this optimal structure the topology optimization method can be applied. It consists in finding the best material distribution that minimizes some performance measure (e.g.,the structural compliance). However, in some applications the optimal structure fails to meet the safety criteria due to stress concentration. To overcome this problem, stress constraints must be taken into account during the topology optimization process. In this work a sequential second order cone programming method is proposed to efficiently incorporate the stress constraints into the optimization problem. This method is well known in the field of limit analysis and it has shown to provide optimal solutions with very low computational cost. Numerical examples are presented here to demonstrate the efficiency and applicability of the proposed second order cone programming method.

[1]  Arkadi Nemirovski,et al.  Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.

[2]  Stéphane Bordas,et al.  A cell‐based smoothed finite element method for kinematic limit analysis , 2010 .

[3]  A. Makrodimopoulos,et al.  Computational formulation of shakedown analysis as a conic quadratic optimization problem , 2006 .

[4]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[5]  Erik Holmberg,et al.  Stress constrained topology optimization , 2013, Structural and Multidisciplinary Optimization.

[6]  J. T. Pereira,et al.  Topology optimization of continuum structures with material failure constraints , 2004 .

[7]  Kai A. James,et al.  Structural and Multidisciplinary Optimization Manuscript No. Stress-constrained Topology Optimization with Design- Dependent Loading , 2022 .

[8]  Jaime Peraire,et al.  Mesh adaptive computation of upper and lower bounds in limit analysis , 2008 .

[9]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[10]  Stephen P. Boyd,et al.  Applications of second-order cone programming , 1998 .

[11]  Anders Clausen,et al.  Efficient topology optimization in MATLAB using 88 lines of code , 2011 .

[12]  Niels Olhoff,et al.  Topology optimization of continuum structures: A review* , 2001 .

[13]  Fred van Keulen,et al.  A unified aggregation and relaxation approach for stress-constrained topology optimization , 2017 .

[14]  Michael J. Todd,et al.  Self-Scaled Barriers and Interior-Point Methods for Convex Programming , 1997, Math. Oper. Res..

[15]  Donald Goldfarb,et al.  Second-order cone programming , 2003, Math. Program..

[16]  Erling D. Andersen,et al.  On implementing a primal-dual interior-point method for conic quadratic optimization , 2003, Math. Program..

[17]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[18]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[19]  F. Navarrina,et al.  Topology optimization of continuum structures with local and global stress constraints , 2009 .

[20]  Andrei V. Lyamin,et al.  Computational Cam clay plasticity using second-order cone programming , 2012 .

[21]  Knud D. Andersen,et al.  Computation of collapse states with von Mises type yield condition , 1998 .

[22]  Martin P. Bendsøe,et al.  Topology Optimization of Continuum Structures with Stress Constraints , 1997 .

[23]  Fred van Keulen,et al.  Damage approach: A new method for topology optimization with local stress constraints , 2016 .

[24]  George I. N. Rozvany,et al.  A critical review of established methods of structural topology optimization , 2009 .

[25]  C. D. Bisbos,et al.  Second-Order Cone and Semidefinite Representations of Material Failure Criteria , 2007 .

[26]  Sui Yun-kang,et al.  Topology Optimization Using Parabolic Aggregation Function with Independent-Continuous-Mapping Method , 2013 .

[27]  Michael L. Overton,et al.  Computing Limit Loads by Minimizing a Sum of Norms , 1998, SIAM J. Sci. Comput..