Multiscale Optimisation of Resonant Frequencies for Lattice Based Additive Manufactured Structures

该项目正在进行的工作是实施多尺度优化方法，用于高度优化的增材制造（3D打印）结构的频率定制。对共振频率的理解和控制，即结构将自然振动的频率，在所有工程学科中起着重要作用。制造轻质结构也是航空和航天工业特别感兴趣的，因为它具有显著的成本节约效益。这两个目标都可以使用不断增长的增材制造领域来成功实现，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，在确定网格结构的材料特性时，可以通过使用尺度的抽象来进一步改进密集网格模型的振动响应和结构特性分析。这将通过优化具有参数化内部结构的空间变化网格来实现，该参数化内部结构由一系列均匀单元格表示。每个单胞都具有由小尺度参数定义的独特材料特性，这些小尺度参数在大尺度结构模拟中用作设计变量。这些材料的定义是来自预先计算的模拟的小尺度晶格充分描述的材料特性的小尺度参数的函数。通过对大型有限元模型的分析，得到了该结构在载荷作用下的静态响应、振动的共振频率及其各自的模态振型。结构的优化然后可以用传统的内点优化算法来实现，其目的是最大化刚度，同时还限制要使用的可用材料的量。频率定制是通过对频率范围施加限制来实现的，迫使优化器支持具有位于该范围内的谐振频率的设计。共振频率的排序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。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比传统的结构优化有了显着的改进。

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.