Multiscale Optimisation of Resonant Frequencies for Lattice Based Additive Manufactured Structures

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.