Abstract: In this paper, we consider a geometric inverse source
problem for the heat equation with Dirichlet and Neumann boundary
data. We will reconstruct the exact form of the unknown source
term from additional boundary conditions. Our motivation is to
detect the location, the size and the shape of source support.
We present a one-shot algorithm based on the Kohn-Vogelius
formulation and the topological gradient method. The geometric
inverse source problem is formulated as a topology optimization
one. A topological sensitivity analysis is derived from a source
function. Then, we present a non-iterative numerical method for the
geometric reconstruction of the source term with unknown support
using a level curve of the topological gradient. Finally, we give
several examples to show the viability of our presented method.
Abstract: The aeration process via injectors is used to combat
the lack of oxygen in lakes due to eutrophication. A 3D numerical
simulation of the resulting flow using a simplified model is presented.
In order to generate the best dynamic in the fluid with respect to
the aeration purpose, the optimization of the injectors location is
considered. We propose to adapt to this problem the topological
sensitivity analysis method which gives the variation of a criterion
with respect to the creation of a small hole in the domain. The main
idea is to derive the topological sensitivity analysis of the physical
model with respect to the insertion of an injector in the fluid flow
domain. We propose in this work a topological optimization algorithm
based on the studied asymptotic expansion. Finally we present some
numerical results, showing the efficiency of our approach
Abstract: High precision in motion is required to manipulate the
micro objects in precision industries for micro assembly, cell
manipulation etc. Precision manipulation is achieved based on the
appropriate mechanism design of micro devices such as
microgrippers. Design of a compliant based mechanism is the better
option to achieve a highly precised and controlled motion. This
research article highlights the method of designing a compliant based
three fingered microgripper suitable for holding asymmetric objects.
Topological optimization technique, a systematic method is
implemented in this research work to arrive a topologically optimized
design of the mechanism needed to perform the required micro
motion of the gripper. Optimization technique has a drawback of
generating senseless regions such as node to node connectivity and
staircase effect at the boundaries. Hence, it is required to have post
processing of the design to make it manufacturable. To reduce the
effect of post processing stage and to preserve the edges of the image,
a cubic spline interpolation technique is introduced in the MATLAB
program. Structural performance of the topologically developed
mechanism design is tested using finite element method (FEM)
software. Further the microgripper structure is examined to find its
fatigue life and vibration characteristics.
Abstract: This work concerns the topological optimization
problem for determining the optimal petroleum refinery
configuration. We are interested in further investigating and
hopefully advancing the existing optimization approaches and
strategies employing logic propositions to conceptual process
synthesis problems. In particular, we seek to contribute to this
increasingly exciting area of chemical process modeling by
addressing the following potentially important issues: (a) how the
formulation of design specifications in a mixed-logical-and-integer
optimization model can be employed in a synthesis problem to enrich
the problem representation by incorporating past design experience,
engineering knowledge, and heuristics; and (b) how structural
specifications on the interconnectivity relationships by space (states)
and by function (tasks) in a superstructure should be properly
formulated within a mixed-integer linear programming (MILP)
model. The proposed modeling technique is illustrated on a case
study involving the alternative processing routes of naphtha, in which
significant improvement in the solution quality is obtained.