Geometrically Nonlinear Analysis of Functionally Graded Timoshenko Curved Beams with Variable Curvatures

Ze-Qing Wan,Shi-Rong Li,Hong-Wei Ma

doi:10.1155/2019/6204145

Ze-Qing Wan, Shi-Rong Li + Show 1 more

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https://doi.org/10.1155/2019/6204145

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Abstract

In this paper, geometrically nonlinear analysis of functionally graded curved beams with variable curvatures based on Timoshenko beam theory is presented. Considering the axial extension and the transversal shear deformation, geometrically nonlinear governing equations for the FGM curved beams with variable curvatures subjected to thermal and mechanical loads are formulated. Material properties of the curved beams are assumed to vary arbitrarily in the thickness direction and be independent on the temperature change. By using the numerical shooting method to solve the coupled ordinary differential equations, the nonlinear response of static thermal bending of a FGM semielliptic beams subjected to transversely nonuniform temperature rise is obtained numerically. The effects of material gradient, shear deformation, and temperature rise on the response of the curved beam are discussed in detail. Nonlinear bending of a closed FGM elliptic structure subjected to two pinching concentrated loads is also analyzed. This paper presents some equilibrium paths and configurations of the elliptic curved beam for different pinching concentrated loads.

Highlights

Curved beams have been widely applied in many engineering disciplines such as civil, mechanical, and aerospace [1]
Golf shafts and fishing rods have apparently deformed shapes during use, both of which can be analyzed by curved beam theory. e analysis of static, stability, and dynamic behavior of curved beam structures was frequently performed by researchers
Numerical results for thermal and mechanical bending of functionally graded material (FGM) elliptic curved beam composed of ceramic (ZrO2) and metal (Al) are presented. e outer surface of the curved beam is fully ceramic and the inner surface is fully metal. e material properties of the two constituents are listed in Table 1. e effective material properties of the FGM curved beam are given by equations (1) and (2)

Summary

Introduction

Curved beams have been widely applied in many engineering disciplines such as civil, mechanical, and aerospace [1]. Based on the static bending and free vibration analysis of FG microbeams by using isogeometric approach in combination with the quasi-3D beam theory, the research work about analyzing mechanical behavior of FG curved beams employing the same method is attracting great attention [23, 24]. From the previously cited references, one can note that despite extensive research for the static and dynamical behaviors of the curved beams, to the knowledge of authors, not much work has been devoted to the geometrically nonlinear analysis of functionally graded curved beams with variable curvature. By considering axial extension and transversely shearing, the nonlinear governing equations of FGM Timoshenko curved beams with variable curvatures subjected to thermomechanical loads will be presented. Some equilibrium paths and configurations of FGM elliptic curved beams under different pinching concentrated loads are presented

Theoretical Formations

Numerical Examples

Conclusions