11,788 research outputs found
Measure of combined effects of morphological parameters of inclusions within composite materials via stochastic homogenization to determine effective mechanical properties
In our previous papers we have described efficient and reliable methods of
generation of representative volume elements (RVE) perfectly suitable for
analysis of composite materials via stochastic homogenization.
In this paper we profit from these methods to analyze the influence of the
morphology on the effective mechanical properties of the samples. More
precisely, we study the dependence of main mechanical characteristics of a
composite medium on various parameters of the mixture of inclusions composed of
spheres and cylinders. On top of that we introduce various imperfections to
inclusions and observe the evolution of effective properties related to that.
The main computational approach used throughout the work is the FFT-based
homogenization technique, validated however by comparison with the direct
finite elements method. We give details on the features of the method and the
validation campaign as well.
Keywords: Composite materials, Cylindrical and spherical reinforcements,
Mechanical properties, Stochastic homogenization.Comment: 23 pages, updated figures, version accepted to Composite Structures
201
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Converting a CAD Model into a Manufacturing Model for the Components Made of a Multiphase Perfect Material
To manufacture the component made of a multiphase perfect material (including homogeneous
and multi heterogeneous materials), it CAD model should be processed and converted into
layered manufacturing model for further transformation of numerical control (NC) coding. This
paper develops its detailed approaches and corresponding software. The process planning is made
first and includes: (1) determining the build orientation of the component; and (2) slicing the
component into layers adaptively according to different material regions since different materials
have different optimal layer thickness for manufacturing. After the process planning, the layered
manufacturing models with necessary information, including fabrication sequence and material
information of each layer, are fully generated.Mechanical Engineerin
Discrete Approximations of a Controlled Sweeping Process
The paper is devoted to the study of a new class of optimal control problems
governed by the classical Moreau sweeping process with the new feature that the polyhe-
dral moving set is not fixed while controlled by time-dependent functions. The dynamics of
such problems is described by dissipative non-Lipschitzian differential inclusions with state
constraints of equality and inequality types. It makes challenging and difficult their anal-
ysis and optimization. In this paper we establish some existence results for the sweeping
process under consideration and develop the method of discrete approximations that allows
us to strongly approximate, in the W^{1,2} topology, optimal solutions of the continuous-type
sweeping process by their discrete counterparts
On near-cloaking for linear elasticity
We make precise some results on the cloaking of displacement fields in linear
elasticity. In the spirit of transformation media theory, the transformed
governing equations in Cosserat and Willis frameworks are shown to be
equivalent to certain high contrast small defect problems for the usual Navier
equations. We discuss near-cloaking for elasticity systems via a regularized
transform and perform numerical experiments to illustrate our near-cloaking
results. We also study the sharpness of the estimates from [H. Ammari, H. Kang,
K. Kim and H. Lee, J. Diff. Eq. 254, 4446-4464 (2013)], wherein the convergence
of the solutions to the transmission problems is investigated, when the Lam\'e
parameters in the inclusion tend to extreme values. Both soft and hard
inclusion limits are studied and we also touch upon the finite frequency case.
Finally, we propose an approximate isotropic cloak algorithm for a symmetrized
Cosserat cloak.Comment: 7 figures, 7 tables; Note that the earlier version of this preprint
was titled 'Some results in near-cloaking for elasticity systems'. This new
version of the manuscript has also seen some major upgrade. We have added a
new section on 'Cloaking parameters and isotropic approximation'. In there,
we propose an approximate isotropic cloak algorithm for a symmetrized
Cosserat cloa
Optimality conditions and regularity results for time optimal control problems with differential inclusions
We study the time optimal control problem with a general target
for a class of differential inclusions that satisfy mild smoothness and
controllability assumptions. In particular, we do not require Petrov's
condition at the boundary of . Consequently, the minimum time
function fails to be locally Lipschitz---never mind
semiconcave---near . Instead of such a regularity, we use an
exterior sphere condition for the hypograph of to develop the
analysis. In this way, we obtain dual arc inclusions which we apply to show the
constancy of the Hamiltonian along optimal trajectories and other optimality
conditions in Hamiltonian form. We also prove an upper bound for the Hausdorff
measure of the set of all nonlipschitz points of which implies that
the minimum time function is of special bounded variation.Comment: 23 pages, 1 figur
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