Nonlinear behaviour of different flexible size-dependent beams models based on the modified couple stress theory. Part 1

Governing equations and static analysis of flexible beams

A. V. Krysko, J. Awrejcewicz, M. V. Zhigalov, S. P. Pavlov, V. A. Krysko

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

In the first part of the paper we employ the Sheremetev-Pelekh-Reddy-Levinson hypotheses, which yield a non-linear mathematical model of a beam taking into account geometric and physical non-linearity as well as transverse shear based on the modified couple stress theory. The general model includes both Bernoulli-Euler and Timoshenko models with/without geometric/physical non-linearity, and the size-dependent beam behaviour. In addition, we present results of the development of the relaxation method for solution to numerous static problems. The influence of the size-dependent coefficient on the load-deflection and stress-strain states of the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Reddy-Levinson mathematical models has been also studied.

Original languageEnglish
Pages (from-to)96-105
Number of pages10
JournalInternational Journal of Non-Linear Mechanics
Volume93
DOIs
Publication statusPublished - 1 Jul 2017

Fingerprint

Flexible Beam
Couple Stress
Static analysis
Static Analysis
Bernoulli
Euler
Governing equation
Nonlinearity
Mathematical Model
Mathematical models
Model-based
Dependent
Relaxation Method
Deflection
Nonlinear Model
Loads (forces)
Transverse
Coefficient
Model
Influence

Keywords

  • Beam models
  • Chaos
  • Nano-mechanics
  • Vibrations

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

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abstract = "In the first part of the paper we employ the Sheremetev-Pelekh-Reddy-Levinson hypotheses, which yield a non-linear mathematical model of a beam taking into account geometric and physical non-linearity as well as transverse shear based on the modified couple stress theory. The general model includes both Bernoulli-Euler and Timoshenko models with/without geometric/physical non-linearity, and the size-dependent beam behaviour. In addition, we present results of the development of the relaxation method for solution to numerous static problems. The influence of the size-dependent coefficient on the load-deflection and stress-strain states of the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Reddy-Levinson mathematical models has been also studied.",
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T2 - Governing equations and static analysis of flexible beams

AU - Krysko, A. V.

AU - Awrejcewicz, J.

AU - Zhigalov, M. V.

AU - Pavlov, S. P.

AU - Krysko, V. A.

PY - 2017/7/1

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N2 - In the first part of the paper we employ the Sheremetev-Pelekh-Reddy-Levinson hypotheses, which yield a non-linear mathematical model of a beam taking into account geometric and physical non-linearity as well as transverse shear based on the modified couple stress theory. The general model includes both Bernoulli-Euler and Timoshenko models with/without geometric/physical non-linearity, and the size-dependent beam behaviour. In addition, we present results of the development of the relaxation method for solution to numerous static problems. The influence of the size-dependent coefficient on the load-deflection and stress-strain states of the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Reddy-Levinson mathematical models has been also studied.

AB - In the first part of the paper we employ the Sheremetev-Pelekh-Reddy-Levinson hypotheses, which yield a non-linear mathematical model of a beam taking into account geometric and physical non-linearity as well as transverse shear based on the modified couple stress theory. The general model includes both Bernoulli-Euler and Timoshenko models with/without geometric/physical non-linearity, and the size-dependent beam behaviour. In addition, we present results of the development of the relaxation method for solution to numerous static problems. The influence of the size-dependent coefficient on the load-deflection and stress-strain states of the Bernoulli-Euler, Timoshenko, and Sheremetev-Pelekh-Reddy-Levinson mathematical models has been also studied.

KW - Beam models

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KW - Nano-mechanics

KW - Vibrations

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