Approximation, abstraction and decomposition in search and optimization

In this paper, I discuss four different areas of my research. One portion of my research has focused on automatic synthesis of search control heuristics for constraint satisfaction problems (CSPs). I have developed techniques for automatically synthesizing two types of heuristics for CSPs: Filtering functions are used to remove portions of a search space from consideration. Another portion of my research is focused on automatic synthesis of hierarchic algorithms for solving constraint satisfaction problems (CSPs). I have developed a technique for constructing hierarchic problem solvers based on numeric interval algebra. Another portion of my research is focused on automatic decomposition of design optimization problems. We are using the design of racing yacht hulls as a testbed domain for this research. Decomposition is especially important in the design of complex physical shapes such as yacht hulls. Another portion of my research is focused on intelligent model selection in design optimization. The model selection problem results from the difficulty of using exact models to analyze the performance of candidate designs

Generalized crystallography

X-ray crystal structure analysis can now be seen as a special kind of microscopy which is being extended to the recognition and examination of many kinds of ordered structure more general than crystals and which leads to their synthesis or construction by various methods. Electron microscopy and many other techniques now combine to give a coherent science of structure at the scale range of Ångstroms to microns, atoms to assemblies visible to the eye, which should continue to be called crystallography although it overlaps with nanotechnology, molecular biology, and solid state physics. Most generally, a crystal is a structure the description of which is much smaller than the structure itself and this view leads to the consideration of structures as carriers of information and on to wider concerns with growth, form, morphogenesis, and life itself

A hierarchic optimisation approach towards locking-free shell finite elements

A hierarchic optimisation approach is presented for relieving inaccuracies in conforming shell elements arising from locking phenomena. This approach introduces two sets of strain modes: (i) objective strain modes, defined in the physical coordinate system, and (ii) corrective strain modes, representing conforming strains enhanced with hierarchic strain modes. This leads to two alternative families of element, objective and corrective, both arising from minimising the difference between objective and corrective strains. Importantly, the proposed approach not only alleviates shear and membrane locking, but it also addresses locking arising from element distortion. The application of the proposed optimisation approach is demonstrated for a 9-noded quadrilateral Lagrangian shell element, where the membrane, bending and transverse shear strains are separately optimised, all within a local co-rotational framework that extends the element application to geometric nonlinear analysis. Several numerical examples, including cases with geometric and material nonlinearity, are finally presented to illustrate the effectiveness of the optimised 9-noded shell element in relieving the various sources of locking

A hierarchic optimisation approach towards locking-free shell finite elements

A hierarchic optimisation approach is presented for relieving inaccuracies in conforming shell elements arising from locking phenomena. This approach introduces two sets of strain modes: (i) objective strain modes, defined in the physical coordinate system, and (ii) corrective strain modes, representing conforming strains enhanced with hierarchic strain modes. This leads to two alternative families of element, objective and corrective, both arising from minimising the difference between objective and corrective strains. Importantly, the proposed approach not only alleviates shear and membrane locking, but it also addresses locking arising from element distortion. The application of the proposed optimisation approach is demonstrated for a 9-noded quadrilateral Lagrangian shell element, where the membrane, bending and transverse shear strains are separately optimised, all within a local co-rotational framework that extends the element application to geometric nonlinear analysis. Several numerical examples, including cases with geometric and material nonlinearity, are finally presented to illustrate the effectiveness of the optimised 9-noded shell element in relieving the various sources of locking

Bisector and zero-macrospin co-rotational systems for shell elements

A principal issue in any co-rotational approach for large displacement analysis of plates and shells is associated with the specific choice of the local reference system in relation to the current deformed element configuration. Previous approaches utilised local co-rotational systems, which are invariant to nodal ordering, a characteristic that is deemed desirable on several fronts; however, the associated definitions of the local reference system suffered from a range of shortcomings, including undue complexity, dependence on the local element formulation and possibly an asymmetric tangent stiffness matrix. In this paper, new definitions of the local co-rotational system are proposed for quadrilateral and triangular shell elements, which achieve the invariance characteristic to the nodal ordering in a relatively simple manner and address the aforementioned shortcomings. The proposed definitions utilise only the nodal coordinates in the deformed configuration, where two alternative definitions, namely, bisector and zero-macrospin definitions, are presented for each of quadrilateral and triangular finite elements. In each case, the co-rotational transformations linking the local and global element entities are presented, highlighting the simplicity of the proposed approach. Several numerical examples are finally presented to demonstrate the effectiveness and relative accuracy of the alternative definitions proposed for the local co-rotational system