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2015•Unpublished venueOpen access

Expansive Periodic Mechanisms

Ciprian S. Borcea, Ileana Streinu

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Abstract

A one-parameter deformation of a periodic bar-and-joint framework is expansive when all distances between joints increase or stay the same.In dimension two, expansive behavior can be fully explained through our theory of periodic pseudo-triangulations.However, higher dimensions present new challenges.In this paper we study a number of periodic frameworks with expansive capabilities in dimension d ≥ 3 and register both similarities and contrasts with the two-dimensional case.

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A one-parameter deformation of a periodic bar-and-joint framework is expansive when all distances between joints increase or stay the same.In dimension two, expansive behavior can be fully explained through our theory of periodic pseudo-triangulations.However, higher dimensions present new challenges.In this paper we study a number of periodic frameworks with expansive capabilities in dimension d ≥ 3 and register both similarities and contrasts with the two-dimensional case.

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Available abstract

A one-parameter deformation of a periodic bar-and-joint framework is expansive when all distances between joints increase or stay the same.In dimension two, expansive behavior can be fully explained through our theory of periodic pseudo-triangulations.However, higher dimensions present new challenges.In this paper we study a number of periodic frameworks with expansive capabilities in dimension d ≥ 3 and register both similarities and contrasts with the two-dimensional case.

Key concepts: Expansive, Dimension (graph theory), Bar (unit), Mathematics, Joint (building), Pure mathematics, Physics, Structural engineering

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