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Optimization and Engineering

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02-01-2020 | Research Article

Numerical simulation of base-isolated buildings in collisions with surrounding moat walls during earthquakes: a nonsmooth mechanics approach

Authors: Shota Fukasawa, Yoshihiro Kanno

Published in: Optimization and Engineering | Issue 4/2020

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Abstract

In this paper, we present a formulation and a numerical simulation method for earthquake-induced collisions between a seismically base-isolated building structure and its surrounding moat walls. The base isolator is assumed to undergo plastic deformation. We use the conventional shear building model for a superstructure. Based on nonsmooth mechanics, we formulate a measure differential inclusion that describes the time evolution of the entire structure. For numerical computation, we apply Moreau’s time-stepping scheme to the presented formulation. As a consequence, we solve a quadratic programming problem for each time-step. Our preliminary numerical experiments demonstrate that the presented method is more robust and numerically stable compared with the conventional Newmark method. We also present two numerical examples of mid-rise base-isolated building structures.

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Since a collision can generate a velocity jump, we do not assume that \(\varvec{u}\) is continuous. However, \(\varvec{u}\) is of locally bounded variation on I. Then, at each t in the interior of I, \(\varvec{u}\) has a right limit \(\varvec{u}^{+}(t)\) and a left limit \(\varvec{u}^{-}(t)\) (Moreau 1988, section 7).

For a point \(\varvec{u} \in \mathbb {R}^{n}\), \(\partial \delta _{\varGamma (\varvec{q})}(\varvec{u})\) is nothing but the normal cone of \(\varGamma (\varvec{q})\) at \(\varvec{u}\); see Sect. 1.

See, e.g., Leine and van de Wouw (2008, section 3.5) and Monteiro Marques (1993, section 0.1) for the definition of the differential measure.

Particularly, for a shear building model, M is a diagonal matrix.

It should be clear that \(\sigma \) is not a stress but a force.

Our preliminary numerical experiments, summarized in Appendix A, demonstrate that the proposed time-stepping method allows a much larger time interval compared with naive implementation of the Newmark method.

Available online at https://www.data.jma.go.jp/svd/eqev/data/kyoshin/jishin/ (Accessed August 2019).

The results of our preliminary numerical experiments, including comparison with a conventional method, appear in Appendix A. There, it is also demonstrated that the time evolution of the mechanical energy stored in a structure is almost independent of a value of the coefficient of restitution.

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Title: Numerical simulation of base-isolated buildings in collisions with surrounding moat walls during earthquakes: a nonsmooth mechanics approach
Authors: Shota Fukasawa
Yoshihiro Kanno
Publication date: 02-01-2020
Publisher: Springer US
Published in: Optimization and Engineering / Issue 4/2020
Print ISSN: 1389-4420
Electronic ISSN: 1573-2924
DOI: https://doi.org/10.1007/s11081-019-09481-y

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