Infill topology and shape optimisation of lattice-skin structures

Lattice-skin structures composed of a thin-shell skin and a lattice infill are widespread in nature and large-scale engineering due to their efficiency and exceptional mechanical properties. Recent advances in additive manufacturing, or 3D printing, make it possible to create lattice-skin structures of almost any size with arbitrary shape and geometric complexity. We propose a novel gradient-based approach to optimising both the shape and infill of lattice-skin structures to improve their efficiency further. The respective gradients are computed by fully considering the lattice-skin coupling while the lattice topology and shape optimisation problems are solved in a sequential manner. The shell is modelled as a Kirchhoff-Love shell and analysed using isogeometric subdivision surfaces, whereas the lattice is modelled as a pin-jointed truss. The lattice consists of many cells, possibly of different sizes, with each containing a small number of struts. We propose a penalisation approach akin to the SIMP (solid isotropic material with penalisation) method for topology optimisation of the lattice. Furthermore, a corresponding sensitivity filter and a lattice extraction technique are introduced to ensure the stability of the optimisation process and to eliminate scattered struts of small cross-sectional areas. The developed topology optimisation technique is suitable for non-periodic, non-uniform lattices. For shape optimisation of both the shell and the lattice, the geometry of the lattice-skin structure is parameterised using the free-form deformation technique. The topology and shape optimisation problems are solved in an iterative, sequential manner. The effectiveness of the proposed approach and the influence of different algorithmic parameters are demonstrated with several numerical examples.Comment: 20 pages, 17 figure

Boundary element based multiresolution shape optimisation in electrostatics

We consider the shape optimisation of high-voltage devices subject to electrostatic field equations by combining fast boundary elements with multiresolution subdivision surfaces. The geometry of the domain is described with subdivision surfaces and different resolutions of the same geometry are used for optimisation and analysis. The primal and adjoint problems are discretised with the boundary element method using a sufficiently fine control mesh. For shape optimisation the geometry is updated starting from the coarsest control mesh with increasingly finer control meshes. The multiresolution approach effectively prevents the appearance of non-physical geometry oscillations in the optimised shapes. Moreover, there is no need for mesh regeneration or smoothing during the optimisation due to the absence of a volume mesh. We present several numerical experiments and one industrial application to demonstrate the robustness and versatility of the developed approach.Web of Science29759858

Boundary element based multiresolution shape optimisation in electrostatics

We consider the shape optimisation of high-voltage devices subject to electrostatic field equations by combining fast boundary elements with multiresolution subdivision surfaces. The geometry of the domain is described with subdivision surfaces and different resolutions of the same geometry are used for optimisation and analysis. The primal and adjoint problems are discretised with the boundary element method using a sufficiently fine control mesh. For shape optimisation the geometry is updated starting from the coarsest control mesh with increasingly finer control meshes. The multiresolution approach effectively prevents the appearance of non-physical geometry oscillations in the optimised shapes. Moreover, there is no need for mesh regeneration or smoothing during the optimisation due to the absence of a volume mesh. We present several numerical experiments and one industrial application to demonstrate the robustness and versatility of the developed approach.We gratefully acknowledge the support provided by the EU commission through the FP7 Marie Curie IAPP project CASOPT (PIAP-GA-2008-230224). K.B. and F.C. thank for the additional support provided by EPSRC through #EP/G008531/1. J.Z. thanks for the support provided by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070) and by the project SPOMECH – Creating a Multidisciplinary R&D Team for Reliable Solution of Mechanical Problems, reg. no. CZ.1.07/2.3.00/20.0070 within the Operational Programme ‘Education for Competitiveness’ funded by the Structural Funds of the European Union and the state budget of the Czech Republic. Special thanks to Andreas Blaszczyk from the ABB Corporate Research Center Switzerland for fruitful discussions and for providing the industrial applications.This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.jcp.2015.05.01

A novel implementation of computational aerodynamic shape optimisation using Modified Cuckoo Search

This paper outlines a new computational aerodynamic design optimisation algorithm using a novel method of parameterising a computational mesh using `control nodes'. The shape boundary movement as well as the mesh movement is coupled to the movement of user--defined control nodes via a Delaunay Graph Mapping technique. A Modified Cuckoo Search algorithm is employed for optimisation within the prescribed design space defined by the allowed range of control node displacement. A finite volume compressible Navier--Stokes solver is used for aerodynamic modelling to predict aerodynamic design `fitness'. The resulting coupled algorithm is applied to a range of test cases in two dimensions including aerofoil lift--drag ratio optimisation intake duct optimisation under subsonic, transonic and supersonic flow conditions. The discrete (mesh--based) optimisation approach presented is demonstrated to be effective in terms of its generalised applicability and intuitiveness

Isogeometric Design, Analysis and Optimisation of Lattice-Skin Structures

The advancements in additive manufacturing techniques enable novel designs using lattice structures in mechanical parts, lightweight materials, biomaterials and so forth. Lattice-skin structures are a class of structures that couple thin-shells with lattices, which potentially combine the advantages of the thin-shell and the lattice structure. A new and systematic isogeometric analysis approach that integrates the geometric design, structural analysis and optimisation of lattice-skin structures is proposed in the dissertation. In the geometric design of lattice-skin structures, a novel shape interrogation scheme for splines, specifically subdivision surfaces, is proposed, which is able to compute the line/surface intersection efficiently and robustly without resorting to successive refinements or iterations as in Newton-Raphson method. The line/surface intersection algorithm involves two steps: intersection detection and intersection computation. In the intersection detection process, a bounding volume tree of k-dops (discrete oriented polytopes) for the subdivision surface is first created in order to accelerate the intersection detection between the line and the surface. The spline patches which are detected to be possibly intersected by the line are converted to Bézier representations. For the intersection computation, a matrix-based algorithm is applied, which converts the nonlinear intersection computation into solving a sequence of linear algebra problems using the singular value decomposition (SVD). Finally, the lattice-skin geometry is generated by projecting selected lattice nodes to the nearest intersection points intersected by the lattice edges. The Stanford bunny example demonstrates the efficiency and accuracy of the developed algorithm. The structural analysis of lattice-skin structures follows the isogeometric approach, in which the thin-shell is discretised with spline basis functions and the lattice structure is modelled with pin-jointed truss elements. In order to consider the lattice-skin coupling, a Lagrange multiplier approach is implemented to enforce the displacement compatibility between the coupled lattice nodes and the thin-shell. More importantly, the parametric coordinates of the coupled lattice nodes on the thin-shell surface are obtained directly from the lattice-skin geometry generation, which integrates the design and analysis process of lattice-skin structures. A sandwich plate example is analysed to verify the implementation and the accuracy of the lattice-skin coupling computation. In addition, a SIMP-like lattice topology optimisation method is proposed. The topology optimisation results of lattice structures are analysed and compared with several examples adapted from the benchmark examples commonly used in continuum topology optimisation. The SIMP-like lattice topology optimisation proposed is further applied to optimise the lattice in lattice-skin structures. The lattice-skin topology optimisation is fully integrated with the lattice-skin geometry design since the sensitivity analysis in the proposed method is based on lattice unit cells which are inherited from the geometry design stage. Finally, shape optimisation of lattice-skin structures using the free-form deformation (FFD) technique is studied. The corresponding shape sensitivity of lattice-skin structures is derived. The geometry update of the lattice-skin structure is determined by the deformation of the FFD control volume, and in this process the coupling between lattice nodes and the thin-shell is guaranteed by keeping the parametric coordinates of coupled lattice nodes which are obtained in the lattice-skin geometry design stage. A pentagon roof example is used to explore the combination of lattice topology optimisation and shape optimisation of lattice-skin structures