This paper presents a numerical study on stress-constrained shell-lattice infill structural optimisation. This problem is inherently challenging for several reasons: (i) different stress measures have to be used for the solid shell and the porous lattice infill, and the two types of stress constraints make the problem extremely complex to solve and (ii) involvement of the shell layer further complicates the optimisation problem modelling and its solution. To address these challenges, two stress constraints were formulated, i.e. a von Mises stress-based constraint for the solid shell layer and a Tsai-Hill yield criteria-based constraint for the porous lattice. Then, level set function is adopted to represent the shape of the shell layer and the constant-thickness shell layer is modelled based on the signed distance feature. Then, a comprehensive and accurate sensitivity result is derived to guide the concurrent structural shape and lattice density optimisation. A few numerical examples will be studied to prove the effectiveness of the developed algorithm. Some interesting phenomena have been observed, such as the soft narrow band at the shell-lattice interface to mitigate stress concentration.

本文提出了应力约束壳晶格填料的结构优化的数值研究。由于以下几个原因，该问题具有固有的挑战性：（i）实心壳体和多孔晶格填充物必须使用不同的应力测量方法，并且两种应力约束条件使得该问题的解决极为复杂，并且（ii）壳层进一步使优化问题建模及其解决方案复杂化。为了应对这些挑战，制定了两个应力约束条件，即对固体壳层基于von Mises应力的约束条件和对多孔晶格基于Tsai-Hill屈服准则的约束条件。然后，采用水平集函数表示壳层的形状，并基于有符号距离特征对等厚壳层进行建模。然后，可以得出全面而准确的灵敏度结果，以指导同时进行的结构形状和晶格密度优化。将通过几个数值示例进行研究，以证明所开发算法的有效性。已经观察到一些有趣的现象，例如在壳-晶格界面处的柔软窄带以减轻应力集中。