Multiscale Optimisation of Resonant Frequencies for Lattice Based Additive Manufactured Structures

该项目正在进行的工作是实现用于高度优化的添加剂制造(3D打印)结构的频率裁剪的多尺度优化方法。对共振频率的理解和控制，即结构自然振动的频率，在所有工程学科中都发挥着重要作用。制造轻质结构也是航空和航空航天行业特别感兴趣的，因为它节省了大量的成本。这两个目标都可以通过使用不断增长的添加制造领域来成功地实现，以生产复杂和非均匀的晶格结构。随着有限元模拟能力的提高，在确定格子结构的材料特性时，通过使用尺度抽象，可以进一步改进密集网格模型的振动响应和结构特性的分析。这将通过优化具有参数化内部结构的空间变化的格子来实现，该格子由一系列均匀的单胞表示。每个单元格都具有由小尺度参数定义的独特材料属性，这些参数被用作大型结构模拟的设计变量。这些材料定义来自对小尺度晶格的预计算模拟，该模拟充分描述了材料性质作为小尺度参数的函数。通过对大型有限元模型的分析，得到了结构在荷载作用下的静力响应、振动的共振频率及其振型。然后，可以使用传统的内点优化算法来实现结构的优化，目标是最大化刚度，同时限制可用材料的数量。频率定制是通过施加频率范围的限制来实现的，迫使优化器偏爱共振频率在此范围内的设计。共振频率的分类方法允许在忽略其他模式的同时优化特定模式，从而允许工程师更好地控制结构。与传统的结构优化相比，多尺度网格方法在结构的可制造性以及限制优化和制造阶段之间所需的后处理量方面产生了显著的改进。

The work being undertaken in this project is towards the implementation of a multiscale optimisation method for use in frequency tailoring of highly optimised additive manufactured (3D-printed) structures. The understanding and control over resonant frequencies, the frequency at which a structure will natural vibrates, plays a major role in all engineering disciplines. Creating light weight structures is also of particular interest to both the aviation and aerospace industries due to profound cost saving benefits. Both of these objectives can be successfully achieved using the growing field of additive manufacturing to produce complicated and non-uniform lattice structures. Alongside the increasing capability of finite element modelling, the analysis of vibrational response and structural properties of densely meshed models can be further improved upon by using the abstraction of scales when determining material properties of the lattice structure.This will be achieved by optimising a spatially-varying lattice with a parameterised internal structure, represented by a series of homogenised unit cells. Each unit cell has unique material properties defined by the small-scale parameters which are used as the design variables in the large-scale structural simulations. These material definitions are derived from precomputed simulations of the small-scale lattice which fully describe the material properties as functions of the small-scale parameters. The static response to loading as well as resonant frequencies of vibration and their respective mode shapes are obtained through the analysis of the large-scale finite element model. The optimisation of the structure can then be implemented with traditional interior point optimisation algorithms with the objective of maximising the stiffness whilst also restricting the amount of available material to be used. Frequency tailoring is achieved by imposing constraints of frequency ranges, forcing the optimiser to favour designs with resonant frequencies that lie within this range. A sorting method for the resonant frequencies allows for specific modes to be optimised whilst ignoring others, allowing for greater control of the structure by the engineer. The multiscale lattice method has yielded significant improvements over traditional structural optimisation regarding the manufacturability of the structure as well as limiting the amount of post processing required between the optimisation and manufacturing stage.