Keywords: fully stressed structure, ranked bidirectional evolutionary.

Evolutionary Structural Optimization(ESO) method [1,2,3,4] was developed as an alternative to simplify traditional mathematical programming approaches. It is based on a simple concept that by systematically removing the material from the under- utilized regions or adding the material onto the over-utilized regions, the resulting structure evolves towards an optimum. Compared with other existing methods, it can be easily implemented into many general purpose finite element analysis(FEA) program.

In this study, Ranked Bidrectional ESO(R-BESO) method is introduced to search the topology of a fully stressed structure under several mechanical environments. By R-BESO method an optimum topology can be obtained throughout less iteration number than one required in BESO method. R-BESO method includes the displacement sensitivity analysis using nodal displacement to determine a rank onto each free edge or free surface of candidate elements having any free edge or free surface. Ranks onto the edge or surface based on the displacement sensitivity are classified into three level and added element types are used 3 types corresponding to a rank. The number of added elements is 7, 4, 3 for 2 dimensional problem and 19, 10, 1 for 3 dimensional problem by the rank, respectively.

R-BESO method is consist of the fast evolution module in which elements are added corresponding to the determined rank and some of existing elements are removed, and the normal evolution module in which elements are added onto all edges or surfaces due to the added element type corresponding to rank 3 and some are removed. So, volume growth of a structure is sharply made within fast evolution module and then the model produced in the fast evolution module shrinks in the normal evolution module until a current model arrives at the optimum.

Fully stressed structure design using R-BESO method is obtained under various mechanical boundary conditions. Performance for fully stress state of a structure can be estimated by the Performance Index(PI) defined by stress ratio and weight ratio. Optimal model can be obtained at the maximum of PI in a current model corresponding to each iteration number.

Considered models are several nozzles as a 2 dimensional axi-symmetric problem and a bracket design as a 3 dimensional problem. For nozzle design, load conditions are radial compression, shear force and torque and are applied to a branch pipe. Design domain within which elements can be added through all iterations is chosen the inner and outer region, which is said the full design domain, and only the inner region, which is said the inner design domain. For the full design domain, optimal nozzles have 45° between an vessel and a branch pipe on all load conditions and a cavity is created on the shear force case, especially. For the inner design domain, optimal nozzles have different topologies from each other depending on load conditions. An optimal nozzle is identical to the initial model for torque condition on the inner design domain.

1

O.M. Querin, G.P. Steven and Y.M. Xie, "Evolutionary Structural Optimisation (ESO) Using a Bidirectional Algorithm," Engineering Computations, 15(8), 1031-1048, 1998. doi:10.1108/02644409810244129

2

X.Y. Yang and Y.M. Xie, G.P. Steven and O.M. Querin, "Bidirectional Evolutionary Method for Stiffness Optimization," AIAA Journal, 37(11), 1483-1488, 1999. doi:10.2514/2.626

3

O.M. Querin, V. Young, G.P. Steven and Y.M. Xie, "Computational Efficiency and Validation of Bi-directional Evolutionary Structural Optimisation," Computer Methods in Applied Mechanics and Engineering, 189(2), 559-573, 2000. doi:10.1016/S0045-7825(99)00309-6

4

D. Nha Chu, Y.M. Xie, A. Hira and G.P. Steven, "On Various Aspects of Evolutionary Structural Optimization for Problems with Stiffness Constraints," Finite Elements in Analysis and Design, 24, 197-212, 1997. doi:10.1016/S0168-874X(96)00049-2

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