This document discusses several papers on the topic of topology optimization. It summarizes the abstracts of three papers. The first paper discusses applying topology optimization and manufacturing simulations to aircraft component design. The second paper discusses designing smart composite materials using topology optimization to optimize properties like thermal expansion coefficients. The third paper surveys procedures for dealing with common numerical instabilities in topology optimization like checkerboards and mesh dependencies.

1. Topology Optimization
P Venkat Vijay Kumar
09101291

2. Application of Topology Optimization and
Manufacturing Simulations - A new trend
in design of Aircraft components
Waqas Saleem, Fan Yuqing, Wang
Yunqiao
IMECS 2008, 19-21 March, 2008, Hong Kong

3. Abstract…
• In this paper the way of application of topology
optimization is discussed and shown
• Nonparametric topology optimization has been
applied on a commercial aircraft vertical stabilizer
component using ANSYS software.
• Suitable loads and constraints are applied on the
initial design space of the component to
accommodate for fin gust, rudder deflection,
lateral gust, and other loads experienced by an
aircraft during actual flight maneuvering.

4. Abstract…
• Post machining distortions are also simulated by
using element deactivation technique first by
developing an initial residual stress field through
Sequential Coupled Field analysis.
• An integrated approach has also been developed
to verify the structural performance and to
overcome the problem of non-manufacturable
topology optimization results.
• CATIA is used to convert the optimized FE model
into geometry based CAD model and then virtual
machining is done.

5. Abstract…
• At the end topology assisted design model is
compared with the actual part that is being
manufactured for the aircraft. It is inferred
that topology optimization results in a better
and innovative product design with enhanced
structural performance and stability.

6. Conclusions…
• It is inferred that under the same loading
conditions, constraints and intended design
purposes, topology optimization results in
better and more reliable design.
• In this research, some features which
obtained in the topology optimization results
are omitted in the analysis model because
these do not affect the cutting simulations
largely and model can be simplified.

7. Design of smart composite
materials using topology
optimization
O Sigmund† and S Torquato‡
† Department of Solid Mechanics, Technical University of
Denmark, DK-2800 Lyngby,
Denmark
‡ Department of Civil Engineering and Operations Research and
Princeton Materials

8. Abstract…
• The topology optimization method is used to
find the distribution of material phases that
extremizes an objective function (e.g., thermal
expansion coefficient, piezoelectric coefficients
etc) subject to constraints, such as elastic
symmetry and volume fractions of the
constituent phases, within a periodic base cell.

9. Abstract…
• The effective properties of the material
structures are found using a numerical
homogenization method based on a finite-
element discretization of the base cell. The
optimization problem is solved using sequential
linear programming.

10. Conclusion
• We discussed two applications: design of
composites with extreme thermal expansion
coefficients and piezo composites with
optimal hydrophone characteristics. In the
case of the piezocomposites, we considered
fixed topology of the ceramic rods.

11. Numerical instabilities in topology
optimization: A survey on procedures
dealing with checkerboards, mesh-
dependencies and local minima
O. Sigmund
Department of Solid Mechanics, Technical University of
Denmark, DK-2800 Lyngby, Denmark
J. Petersson
Department of Mechanical Engineering, University of
Linkhping, S-58183 Linkhping, Sweden

12. Abstract…
• In this paper the current knowledge about
numerical instabilities such as checkerboards,
mesh-dependence and local minima occuring
in applications of the topology optimization
method are summarized.