Multiscale Optimisation of Resonant Frequencies for Lattice Based Additive Manufactured Structures

该项目正在进行的工作是实现一种多尺度优化方法，用于高度优化的增材制造（3d打印）结构的频率定制。理解和控制共振频率，即结构自然振动的频率，在所有工程学科中都起着重要作用。创造轻质结构也特别感兴趣的航空和航天工业，因为深刻的成本节约效益。利用不断发展的增材制造领域，可以成功地实现这两个目标，以生产复杂和不均匀的晶格结构。随着有限元建模能力的不断提高，在确定晶格结构的材料性能时，采用尺度抽象可以进一步改进密网格模型的振动响应和结构性能分析。这将通过优化具有参数化内部结构的空间变化晶格来实现，该内部结构由一系列均质单元格表示。每个单元格都具有独特的材料特性，这些特性由小尺度参数定义，这些小尺度参数在大尺度结构模拟中用作设计变量。这些材料定义是从预先计算的小尺度晶格模拟中推导出来的，它充分描述了材料的性质作为小尺度参数的函数。通过对大尺度有限元模型的分析，得到了结构对载荷的静响应、振动的共振频率及其振型。然后可以使用传统的内部点优化算法来实现结构的优化，其目标是最大化刚度，同时限制可用材料的使用量。频率裁剪是通过施加频率范围的限制来实现的，迫使优化器偏向于在该范围内的谐振频率的设计。谐振频率的分类方法允许优化特定模式，同时忽略其他模式，从而允许工程师更好地控制结构。与传统结构优化相比，多尺度点阵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取得了重大改进。

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.