51 research outputs found

    Application of discontinuity layout optimization to plane plasticity problems

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    A new and potentially widely applicable numerical analysis procedure for continuum mechanics problems is described. The procedure is used here to determine the critical layout of discontinuities and associated upper-bound limit load for plane plasticity problems. Potential discontinuities, which interlink nodes laid out over the body under consideration, are permitted to crossover one another giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology. Highly efficient linear programming solvers can be employed when certain popular failure criteria are specified (e. g. Tresca or Mohr Coulomb in plane strain). Stress/velocity singularities are automatically identified and visual interpretation of the output is straightforward. The procedure, coined 'discontinuity layout optimization' (DLO), is related to that used to identify the optimum layout of bars in trusses, with discontinuities (e. g. slip-lines) in a translational failure mechanism corresponding to bars in an optimum truss. Hence, a recently developed adaptive nodal connection strategy developed for truss layout optimization problems can advantageously be applied here. The procedure is used to identify critical translational failure mechanisms for selected metal forming and soil mechanics problems. Close agreement with the exact analytical solutions is obtained

    An Extension and Efficient Calculation of the Horner’s Rule for Matrices

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    Potential use of structural layout optimization at the conceptual design stage

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    Despite recent developments in computer-aided design in architecture, both in terms of form generation techniques and performance-based design tools, there still appears to be polarization between the 'visual' and the 'technical' elements of design. Two causes of this are discussed: long-standing tradition within the discipline and perception of design as primarily a visual exercise. Structural layout optimization is a technique which enables automatic identification of optimal arrangements of structural elements in frames. As the technique appears to have the potential to help reduce the polarization between the visual and the technical elements of design, it can be considered as an 'integrative' form generation tool. Applications of the technique are considered via three design examples, demonstrating both its potential and areas where refinement is required before it is suitable for application in practice
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