Optimal design of shells with FE based parameterization

In a finite element (FE) based parameterization, data of the FE mesh are used as design variables, such as nodal coordinates and nodal thickness. During shape and thickness optimization, this approach provides much design freedom for a limited modeling effort. Stress results are, however, very sensitive to the local shape changes that can occur during FE based optimization. When stress results are used as response function, this irregularity can complicate the optimization. As a solution, the KreisselmeierSteinhauser function for the stresses is introduced as a response function for FE based optimization. In this function, the local stress results are aggregated to obtain a global measure of stress in a structure. This measure can be used as an objective to reduce the overall stress in the structure or as a constraint to limit the stress in the structure to a maximum allowable value. As a result, the optimal structures are smooth and material efficient. Several examples are presented in this paper to illustrate the use of the FE based design approach in combination with the stress response function. Keywords— shape and size optimization, parameter free optimization, shell structures

[1]  J. Sobieszczanski-Sobieski,et al.  A technique for locating function roots and for satisfying equality constraints in optimization , 1992 .

[2]  M. E. Botkin,et al.  Structural shape optimization with geometric description and adaptive mesh refinement , 1985 .

[3]  Fujio Yamaguchi,et al.  Curves and Surfaces in Computer Aided Geometric Design , 1988, Springer Berlin Heidelberg.

[4]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[5]  Julián A. Norato,et al.  Stress-based topology optimization for continua , 2010 .

[6]  Sigrid Adriaenssens,et al.  Shape optimization of small span textile reinforced cementitious composite shells , 2009 .

[7]  A. Schumacher.  Optimierung mechanischer Strukturen , 2013 .

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

[9]  M. Imam.  Three‐dimensional shape optimization , 1982 .

[10]  Weihong Zhang,et al.  Truss shape optimization with multiple displacement constraints , 2002 .

[11]  K. J. Chang.  Optimality criteria methods usingK-S functions , 1992 .

[12]  Geert Lombaert,et al.  The optimal design of a barrel vault in the conceptual design stage , 2012 .

[13]  Roland Wüchner,et al.  Regularization of shape optimization problems using FE-based parametrization , 2013 .

[14]  Marko Kegl,et al.  Shape optimization of truss-stiffened shell structures with variable thickness , 2006 .

[15]  Kai-Uwe Bletzinger,et al.  Parameter free shape design of thin shells : Efficient and effective , parallel solution techniques for very large design problems , 2010 .

[16]  Manolis Papadrakakis,et al.  Optimum Design of Shell Structures with Stiffening Beams , 2004 .

[17]  Martin P. Bendsøe,et al.  An interpretation for min-max structural design problems including a method for relaxing constraints , 1984 .

[18]  V. Braibant,et al.  Shape optimal design using B-splines , 1984 .

[19]  Roland Wüchner,et al.  Stress‐adapted numerical form finding of pre‐stressed surfaces by the updated reference strategy , 2005 .

[20]  Jasbir S. Arora,et al.  Guide to structural optimization , 1997 .

[21]  M. Shimoda,et al.  Optimal Shape Design of Shell Structures , 2010 .

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

[23]  Nikos D. Lagaros,et al.  Optimum design of shell structures with random geometric, material and thickness imperfections , 2006 .

[24]  J. L. Walsh,et al.  Efficient structural optimization for multiple load cases using adjoint sensitivities , 2001 .

[25]  J. Martins,et al.  Brazil On Structural Optimization Using Constraint Aggregation , 2005 .

[26]  Niels Leergaard Pedersen,et al.  Optimization of practical trusses with constraints on eigenfrequencies, displacements, stresses, and buckling , 2003 .

[27]  E. Hinton,et al.  Dangers inherited in shells optimized with linear assumptions , 2000 .

[28]  G. Qiu,et al.  A note on the derivation of global stress constraints , 2009 .

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

[30]  Mustafa Özakça,et al.  An integrated approach to structural shape optimization of linearly elastic structures. Part I: General methodology , 1991 .

[31]  F. Navarrina,et al.  Stress constraints sensitivity analysis in structural topology optimization , 2010 .