19,012 research outputs found
Linear matching method for design limits in plasticity
In this paper a state-of-the-art numerical method is discussed for the evaluation of the shakedown and ratchet limits for an elastic-perfectly plastic body subjected to cyclic thermal and mechanical load history. The limit load or collapse load, i.e. the load carrying capacity, is also determined as a special case of shakedown analysis. These design limits in plasticity have been solved by characterizing the steady cyclic state using a general cyclic minimum theorem. For a prescribed class of kinematically admissible inelastic strain rate histories, the minimum of the functional for these design limits are found by a programming method, the Linear Matching Method (LMM), which converges to the least upper bound. By ensuring that both equilibrium and compatibility are satisfied at each stage, a direct algorithm has also been derived to determine the lower bound of shakedown and ratchet limit using the best residual stress calculated during the LMM procedure. Three practical examples of the LMM are provided to confirm the efficiency and effectiveness of the method: the behaviour of a complex 3D tubeplate in a typical AGR superheater header, the behaviour of a fiber reinforced metal matrix composite under loading and thermal cycling conditions, and effects of drilling holes on the ratchet limit and crack tip plastic strain range fora centre cracked plate subjected to constant tensile loading and cyclic bending moment
Composite CDMA - A statistical mechanics analysis
Code Division Multiple Access (CDMA) in which the spreading code assignment
to users contains a random element has recently become a cornerstone of CDMA
research. The random element in the construction is particular attractive as it
provides robustness and flexibility in utilising multi-access channels, whilst
not making significant sacrifices in terms of transmission power. Random codes
are generated from some ensemble, here we consider the possibility of combining
two standard paradigms, sparsely and densely spread codes, in a single
composite code ensemble. The composite code analysis includes a replica
symmetric calculation of performance in the large system limit, and
investigation of finite systems through a composite belief propagation
algorithm. A variety of codes are examined with a focus on the high
multi-access interference regime. In both the large size limit and finite
systems we demonstrate scenarios in which the composite code has typical
performance exceeding sparse and dense codes at equivalent signal to noise
ratio.Comment: 23 pages, 11 figures, Sigma Phi 2008 conference submission -
submitted to J.Stat.Mec
Convergence of iterative methods based on Neumann series for composite materials: theory and practice
Iterative Fast Fourier Transform methods are useful for calculating the
fields in composite materials and their macroscopic response. By iterating back
and forth until convergence, the differential constraints are satisfied in
Fourier space, and the constitutive law in real space. The methods correspond
to series expansions of appropriate operators and to series expansions for the
effective tensor as a function of the component moduli. It is shown that the
singularity structure of this function can shed much light on the convergence
properties of the iterative Fast Fourier Transform methods. We look at a model
example of a square array of conducting square inclusions for which there is an
exact formula for the effective conductivity (Obnosov). Theoretically some of
the methods converge when the inclusions have zero or even negative
conductivity. However, the numerics do not always confirm this extended range
of convergence and show that accuracy is lost after relatively few iterations.
There is little point in iterating beyond this. Accuracy improves when the grid
size is reduced, showing that the discrepancy is linked to the discretization.
Finally, it is shown that none of the three iterative schemes investigated
over-performs the others for all possible microstructures and all contrasts.Comment: 41 pages, 14 figures, 1 tabl
A three dimensional calculation of elastic equilibrium for composite materials
A compact scheme is applied to three-dimensional elasticity problems for composite materials, involving simple geometries. The mathematical aspects of this approach are discussed, in particular the iteration method. A vector processor code implementing the compact scheme is presented, and several numerical experiments are summarized
A Simple and Efficient Algorithm for Nonlinear Model Predictive Control
We present PANOC, a new algorithm for solving optimal control problems
arising in nonlinear model predictive control (NMPC). A usual approach to this
type of problems is sequential quadratic programming (SQP), which requires the
solution of a quadratic program at every iteration and, consequently, inner
iterative procedures. As a result, when the problem is ill-conditioned or the
prediction horizon is large, each outer iteration becomes computationally very
expensive. We propose a line-search algorithm that combines forward-backward
iterations (FB) and Newton-type steps over the recently introduced
forward-backward envelope (FBE), a continuous, real-valued, exact merit
function for the original problem. The curvature information of Newton-type
methods enables asymptotic superlinear rates under mild assumptions at the
limit point, and the proposed algorithm is based on very simple operations:
access to first-order information of the cost and dynamics and low-cost direct
linear algebra. No inner iterative procedure nor Hessian evaluation is
required, making our approach computationally simpler than SQP methods. The
low-memory requirements and simple implementation make our method particularly
suited for embedded NMPC applications
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