Abstract In this paper, a study on non-probabilistic reliability-based topology optimization (NRBTO) scheme for continuum structures based on the parameterized Level-Set method (PLSM) is conducted, in which the unknown-but-bounded (UBB) uncertainties of material and external loads are taken into account simultaneously. By interpolating the level set function (LSF) with the compactly supported radial basis functions (CSRBFs), the partial differential equation (PDE) is transformed into an ordinary differential equation (ODE). Based on the interval-set model, the displacement constraint is transformed into the non-probabilistic reliability-based scheme and the reliability is evaluated by the optimization feature distance (OFD). Moreover, the interval parametric vertex approach, the concept of shape derivative and the adjoint vector method are employed to obtain the sensitivity between the optimization model and the pseudo time to obtain the evolution velocity field of LSF. By utilizing the optimization criterion (OC) method, the optimization problem can be solved iteratively. To verify the validity and applicability of the proposed NRBTO method, three examples are presented, and numerical results show that taking the UBB uncertainties effects into account during the topology optimization may have a significant influence on the final structural configurations.

中文翻译：

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基于参数化水平集方法和区间数学的连续结构非概率可靠性拓扑优化（NRBTO）方案

摘要 本文研究了基于参数化水平集方法（PLSM）的连续结构非概率可靠性拓扑优化（NRBTO）方案，其中未知但有界（UBB）的不确定性同时考虑材料和外部载荷。通过用紧支撑径向基函数 (CSRBF) 对水平集函数 (LSF) 进行插值，将偏微分方程 (PDE) 转换为常微分方程 (ODE)。基于区间集模型，将位移约束转化为基于非概率可靠性的方案，并通过优化特征距离（OFD）来评估可靠性。此外，区间参数顶点法，利用形状导数的概念和伴随向量法得到优化模型与伪时间之间的灵敏度，得到LSF的演化速度场。通过利用优化准则（OC）方法，可以迭代地解决优化问题。为了验证所提出的 NRBTO 方法的有效性和适用性，给出了三个例子，数值结果表明，在拓扑优化过程中考虑 UBB 不确定性影响可能对最终结构配置产生重大影响。