Non-probabilistic Reliability-based Topology Optimization Based On Ellisoid Set

Topology optimization plays an important role in the initial stage of conceptual design,and it can find the deficiency and redundancy of the original design scheme.In the engineering practice,the applied load,cross-section size and material properties can not determined,and their exact values will change randomly around nominal values.The structure designed by DTO may obtain smaller safety margin and more failure modes.In order to avoid the phenomenon of structural degradation caused by uncertainty of structural parameters,these parameter variabilities must be considered in topology optimization.The non-probabilisitic reliability-based topology optimization is a branch method of topology optimization,which combines the foresight of deterministic topology optimization strategy with the security of non-probabilistic reliability analysis.The research on NBRTO experiences a short development time until now that there are still many places to be perfected.Firstly,based on stiffness optimization problem,a new NRBTO method which taking BESO as the DTO strategy and adopting ellipsoid set model describing the variability and intrinsic relation of uncertain parameters is proposed.To solve the same problem of stiffness optimization,the results obtained by the method proposed in this paper is better than the results by the other NRBTO method.Compared with the results obtained by DTO method,the results obtained by new method take the risk caused by parameter uncertainty into consideration and is not overestimated,which is of greater value of guide and reference.Secondly,in order to help designers to choose rational non-probabilistic reliability index to avoiding unnecessary sacrifice of structural performanc in the stiffness optimization problem,the relative compliance for quantifying the value rationality is constructed under the research of relationship between the value of non-probabilistic reliability index and the increase of structure compliance.Finally,the research on structural topology optimization under multiple loading cases based on the problem of stiffness optimization has been fruitful,but no one takes the uncertainty of loading cases into NRBTO.In this paper,the NRBTO method under the consideration of uncertainty of loading cases is proposed.