中文摘要：

把自然邻近无网格法中控制方程的局部积分＂弱＂形式应用于连续型物质导数法灵敏度分析中,使用直接微分法导出了基于局部子域积分方程的连续型灵敏度分析公式,采用自然邻近无网格法对其离散求解,以获得各结点处的灵敏度信息。使用该灵敏度分析方法,把自然邻近无网格法与非线性规划理论相结合,采用约束变尺度序列二次规划法,构建了一种形状优化方法。算例表明,该灵敏度计算方法只使用离散结点信息,计算精度高,无需额外的背景积分网格,优化过程不需要网格重构,具有较高的收敛速度,使用较少的设计变量就可以获得良好的优化效果。

英文摘要：

Based on the material derivative concept and direct differentiation approach, a numerical method for shape design sensitivity analysis using meshless natural neighbor Petrov-Galerkin method （NNPG） is proposed. The local weak form of governing equation of NNPG is directly differentiated with respect to design variables and subsequently discretized with NNPG to obtain the sensitivities. Based on the mathematical programming method, a shape optimization method is proposed, and the natural neighbour Petrov-Galerkin method is used to calculate the structure responses and their sensitivities. The numerical example shows the proposed optimization method is totally automatic, efficient. Absolutely, no remeshing is needed.