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Abstract: This paper presents an adaptive density point refinement approach for continuum topology optimization on the basis of an analysis-mesh separated material density field description based on nodal design variables. The Shepard interpolants are used to construct a strictly range-restricted density field over the design domain with the density design variables defined on a density point grid. Since the density points are defined independent of the finite element mesh, it is easy to refine the density point grid without remeshing the finite element model. A refinement criterion is given to identify the gray transitional regions to be adaptively refined in the subsequent optimization iterations. With such a refinement scheme, the topology optimization can start from a relatively coarse density point grid but still yields a desired higher resolution of the structural boundaries in the final design. Because refinements are only performed when and where necessary, this method is able to improve the boundary description quality of the optimal result with much less design variables as compared with the case of global refinement, and therefore can greatly reduce the computational burden involved in the sensitivity analysis and optimization process. Moreover, the percentage of transitional regions in the final solutions can also be reduced. Compared with using a uniformly globally-dense density point arrangement, this approach can achieve similar optimal designs but with much less computational cost. Numerical examples are given to demonstrate the effectiveness and efficiency of the present approach. [Copyright &y& Elsevier]

Abstract: A substructure-based finite element model updating technique is proposed in this paper. A few eigenmodes of the independent substructures and their associated derivative matrices are assembled into a reduced eigenequation to recover the eigensolutions and eigensensitivities of the global structure. Consequently, only the concerned substructures and the reduced eigenequation are re-analyzed in the optimization process, thus reducing the computational load of the traditional model updating methods which perform on the global structure. Applications of the proposed substructure-based model updating to a frame structure and a practical bridge demonstrate that the present method is computationally effective and efficient. [Copyright &y& Elsevier]

Abstract: A simple micro-mechanical model for the homogenised limit analysis of in-plane loaded masonry is proposed. Assuming brickwork under plane stress condition and adopting a polynomial expansion for the 2D stress field, a linear optimisation problem is derived on the elementary cell in order to recover the homogenised failure surface of the brickwork. Different models of higher accuracy are obtained by increasing the degree of the polynomial approximation. Several cases of technical interest are treated in detail, varying both the geometrical characteristics of the cell and the mechanical properties of the components. The model is validated through comparisons with experimental data and kinematic approaches; the comparison with experimental data has the aim to reproduce in a qualitative way the shape of the failure surface, since 3D effects and brittle behaviour of bricks can not be taken into consideration with the model proposed. In an accompanying paper, the homogenised failure surfaces here obtained are implemented in a finite element limit analysis code and relevant structural examples are treated both with a lower and an upper bound approach. [Copyright &y& Elsevier]