中文摘要：

针对传统分步式结构优化设计的不足,提出一种同时进行结构拓扑、形状和尺寸统一优化的设计方法.首先采用水平集函数描述统一的结构优化模型和几何尺寸边界,通过引入紧支径向插值基函数将结构拓扑优化变量、形状优化变量和尺寸优化变量变换为基函数的扩展系数;然后取该扩展系数为设计变量,借助一种参数的变化表达3种优化要素对结构性能的影响,将复杂的多变量优化问题变换为相对简单的参数优化问题,有利于与相对成熟的优化算法相结合提高求解效率;进一步用R函数将其融合为一个整体,构造出统一优化模型,并用最优化准则法进行求解.最后通过数值案例证明了该方法的有效性和精确性.

英文摘要：

In order to solve the disadvantage of conventional step-type structural optimization,a unified optimization method which can carry out the structural topology,shape and sizing optimization concurrently is presented to realize the structural optimization for continuum structures.The unified structural optimization model and the structural geometry boundary are described with the level set function,by applying the compactly supported radial basis function with favorable smoothness and accuracy to interpolate it.The expansion coefficients of interpolants are regarded as the design variables which reflect the structural performance impacts of topology,shape and size.Accordingly,the original topology,shape and sizing optimization is now fully transformed into a relatively simple parameterization problem,namely,sizing optimization with the expansion coefficients of interpolants as a limited number of design variables.As a result,some efficient and matured optimization algorithms can be applied to improve the efficiency of optimization.Furthermore,the unified optimization model is constructed with the R function.Typical examples demonstrate that the method has achieved the unified optimization of continuum structures,with good efficiency and accuracy.