### L. Angela Mihai (University of Cambridge)

#### An adaptive multi-scale computational strategy for large-scale muti-body contact problems

*Joint work with Mark Ainsworh.*

*Wednesday 19 November 2008 at 15.30, JCMB 6206*

##### Abstract

For large-scale applications modelled as Partial Differential Equations (PDEs)
there is an increasing need to solve problems expressed in terms of equilibria
with constraints. For many of these problems, optimization methods that mimic
geometric considerations (e.g. in contact mechanics), thus preserving
feasibility by ensuring that iterates remain on the constraint manifold, are
particularly attractive. PDE constrained optimization has a strong impact on
various engineering and scientific applications (e.g. automotive and aerospace
industries, chemical processing, material science, biotechnology, etc.).
In turn, these applications lead to many exciting research problems for which
the appropriate mathematical treatment and the development of robust and
efficient solution strategies requires the integration of tools from several
mathematical subdisciplines (e.g. the theory of optimization and optimal
control in a functional analytic setting, the theory of PDEs, numerical
analysis, and scientific computing). A particular class of PDE constrained
optimization problems with many important practical applications arises in
structural mechanics, where there is a general need for more mathematically
rigorous and numerically accurate computational strategies. In this talk,
I will present an adaptive multi-scale approach for the computational modelling
of large-scale dynamic structures assembled from linear-elastic bodies in
mutual contact with friction. The adaptive multi-scale approach enables
us to carry out simulations at a complexity normally associated with the cost
of modelling the entire structure by a simple continuum model whilst
incorporating small scale effects, such as openings of gaps and slippage
between individual components, using a systematic and locally optimal
criterion. Comparisons of the numerical results with data from experimental
tests and from practical observations illustrate the capability of the
multi-scale algorithm in predicting the behaviour of large-scale masonry
structures.

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