SUMMARYA new upper bound formulation of limit analysis of two-and three-dimensional solids is presented. In contrast to most discrete upper bound methods the present one is formulated in terms of stresses rather than velocities and plastic multipliers. However, by means of duality theory it is shown that the formulation does indeed result in rigorous upper bound solutions. Also, kinematically admissible discontinuities, which have previously been shown to be very efficient, are given an interpretation in terms of stresses. This allows for a much simpler implementation and, in contrast to existing formulations, extension to arbitrary yield criteria in two and three dimensions is straightforward. Finally, the capabilities of the new method are demonstrated through a number of examples.

International audienceThis paper aims to improve knowledge on the suitability of the discrete element method (DEM) to simulate the in-plane and out-of-plane behaviour of different in-configuration structural masonry walls constructed with dry joints. The study compares the results obtained from laboratory tests against those predicted using the three-dimensional distinct element 3DEC software. Significant features of the structural behaviour shown by the walls are discussed and conclusions on their ultimate capacity and failure mechanisms are addressed. A key feature of the DEM is the important role that brick discontinuities, i.e. joints, play in the mechanics of masonry. Within DEM, the bricks were modelled as continuum rigid elements while the joints were modelled by line interface elements represented by the Mohr-Coulomb law. The analysis of the results showed that the model developed is capable of representing the crack development and load carrying capacity of masonry structures constructed with dry joints with sufficient accuracy. Moreover, a collection of experimentally verified material parameters is provided to be used by other researchers and engineers and to develop a reliable model to solve engineering challenges worldwide. © 2017 Elsevier Lt

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International audienceThe corotational method is an attractive approach to derive non-linear finite beam elements. In a number of papers, this method was employed to investigate the non-linear dynamic analysis of 2D beams. However, most of the approaches found in the literature adopted either a lumped mass matrix or linear local interpolations to derive the inertia terms (which gives the classical linear and constant Timoshenko mass matrix), although local cubic interpolations were used to derive the elastic force vector and the tangent stiffness matrix. In this paper, a new corotational formulation for dynamic nonlinear analysis is presented. Cubic interpolations are used to derive both the inertia and elastic terms. Numerical examples show that the proposed approach is more efficient than using lumped or Timoshenko mass matrices

SUMMARYThe objective of this work is to present an adaptive remeshing procedure for lower bound limit analysis with application to soil mechanics. Unlike conventional finite element meshes, a lower bound grid incorporates statically admissible stress discontinuities between adjacent elements. These discontinuities permit large stress jumps over an infinitesimal distance and reduce the number of elements needed to predict the collapse load accurately. In general, the role of the discontinuities is crucial as their arrangement and distribution has a dramatic influence on the accuracy of the lower bound solution (Limit Analysis and Soil Plasticity, 1975). To ensure that the discontinuities are positioned in an optimal manner requires an error estimator and mesh adaptation strategy which accounts for the presence of stress singularities in the computed stress field.Recently, Borges et al. (Int. J. Solids Struct. 2001; 38:1707-1720) presented an anisotropic mesh adaptation strategy for a mixed limit analysis formulation which used a directional error estimator. In the present work, this strategy has been tailored to suit a discontinuous lower bound formulation which employs the stresses and body forces as primary unknowns. The adapted mesh has a maximum density of discontinuities in the direction of the maximum rate of change in the stress field. For problems involving strong stress singularities in the boundary conditions (e.g. a strip footing), the automatic generation of discontinuity fans, centred on the singular points, has been implemented.The efficiency of the proposed technique is demonstrated by analysis of two classical soil mechanics problems; namely the bearing capacity of a rigid strip footing and the collapse of a vertical cut.

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