Geometrically Nonlinear Analysis of Plane Trusses and Frames

Galishnikova, Vera V.; Dunaiski, Peter; Pahl, Peter Jan

doi:10.18820/9781920109998

Cited by 7 publications

(1 citation statement)

References 10 publications

(42 reference statements)

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“…Previous studies on the behavior of the von Mises truss suggest that the structure undergoes a snap-through when loaded beyond a critical value with a vertical force at the apex [24,25]. As the double-helices are expected to introduce further nonlinearities, an iterative path-following algorithm is required to determine the load-displacement response of the structural assemblies.…”

Section: Path-following Methodsmentioning

confidence: 99%

Multistable Morphing Mechanisms of Nonlinear Springs

Aza

Pirrera

Schenk

2019

Journal of Mechanisms and Robotics

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Compliant mechanisms find use in numerous applications in both microscale and macroscale devices. Most of the current compliant mechanisms base their behavior on beam flexures. Their range of motion is thus limited by the stresses developed upon deflection. Conversely, the proposed mechanism relies on elastically nonlinear components to achieve large deformations. These nonlinear elements are composite morphing double-helical structures that are able to extend and coil like springs, yet, with nonlinear stiffness characteristics. A mechanism consisting of such structures, assembled in a simple truss configuration, is explored. A variety of behaviors is unveiled that could be exploited to expand the design space of current compliant mechanisms. The type of behavior is found to depend on the initial geometry of the structural assembly, the lay-up, and other characteristics specific of the composite components.

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Section: Path-following Methodsmentioning

confidence: 99%

Multistable Morphing Mechanisms of Nonlinear Springs

Aza

Pirrera

Schenk

2019

Journal of Mechanisms and Robotics

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Theoretical study of the geometrical non-linearity of the elastic properties of helical springs

Ivchenko

2020

American Journal of Physics

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We give a detailed derivation of the equation describing the elastic properties of the helical springs in the case of their large deformations. It is shown that the Taylor expansion for the restoring force contains, in addition to a linear term, a term quadratic in the strain. We discuss the physical consequences of this term. A surprising example of this is that for large values of the initial pitch angle during compression of spring, there may be an interval of strain values, for which the differential stiffness becomes negative. The issues outlined in this article will be useful for instructors and advanced undergraduates who deal with modern elasticity theory.

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Simple Planar Truss (Linear, Nonlinear and Stochastic Approach)

Frydrýšek

Jančo

2016

Strojnícky Casopis – Journal of Mechanical Engineering

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This article deals with a simple planar and statically determinate pin-connected truss. It demonstrates the processes and methods of derivations and solutions according to 1st and 2nd order theories. The article applies linear and nonlinear approaches and their simplifications via a Maclaurin series. Programming connected with the stochastic Simulation-Based Reliability Method (i.e. the direct Monte Carlo approach) is used to conduct a probabilistic reliability assessment (i.e. a calculation of the probability that plastic deformation will occur in members of the truss).

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Geometrically Nonlinear Analysis of Plane Trusses and Frames

Cited by 7 publications

References 10 publications

Multistable Morphing Mechanisms of Nonlinear Springs

Multistable Morphing Mechanisms of Nonlinear Springs

Theoretical study of the geometrical non-linearity of the elastic properties of helical springs

Simple Planar Truss (Linear, Nonlinear and Stochastic Approach)

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