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Geometric and material nonlinearities of sandwich beams under static loads

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Abstract

A new theory developed from extended high-order sandwich panel theory (EHSAPT) is set up to assess the static response of sandwich panels by considering the geometrical and material nonlinearities simultaneously. The geometrical nonlinearity is considered by adopting the Green–Lagrange-type strain for the face sheets and core. The material nonlinearity is included as a piecewise function matched to the experimental stress–strain curve using a polynomial fitting technique. A Ritz technique is applied to solve the governing equations. The results show that the stress stiffening feature is well captured in the geometric nonlinear analysis. The effect of the geometric nonlinearity in the face sheets on the displacement response is more significant when the stiffness ratio of the face sheets to the core is large. The geometric nonlinearity decreases the shear stress and increases the normal stress in the sandwich core. By comparison with open literature and finite element simulations, the present nonlinear EHSAPT is shown to be sufficiently precise for estimating the nonlinear static response of sandwich beams by considering the geometric and material nonlinearities simultaneously.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant 11432004).

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Authors and Affiliations

  1. Center for Composite Materials, Harbin Institute of Technology, Harbin, 150001, China

    Guangtao Wei, Yang Jin & Linzhi Wu

  2. Center for Advanced Vessels Materials and Mechanics, College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, 150001, China

    Linzhi Wu

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  1. Guangtao Wei
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  2. Yang Jin
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Correspondence to Linzhi Wu.

Appendix

Appendix

$$A = {\text{diag}}\left( {\begin{array}{*{20}c} {\chi_{1} } & {\chi_{1} } & {\chi_{1} } & {\chi_{1} } & {\chi_{3} } & {\chi_{4} } & {\chi_{3} } & {\chi_{4} } & {\chi_{3} } & {\chi_{4} } \\ \end{array} } \right),$$
$$B = {\text{diag}}\left( {\begin{array}{*{20}c} {\chi_{2} } & {\chi_{2} } & {\chi_{2} } & {\chi_{2} } & {\chi_{5} } & {\chi_{6} } & {\chi_{5} } & {\chi_{4} } & {\chi_{6} } & {\chi_{6} } \\ \end{array} } \right),$$

with

$$\begin{aligned} & \chi_{1} = \frac{{x - x_{i + 1} }}{{x_{i} - x_{i + 1} }},\chi_{2} = \frac{{x - x_{i} }}{{x_{i + 1} - x_{i} }},\\ & \chi_{3} = \left( {1 + 2\frac{{x - x_{i} }}{{x_{i + 1} - x_{i} }}} \right)\left( {\frac{{x - x_{i + 1} }}{{x_{i} - x_{i + 1} }}} \right)^{2} , \end{aligned}$$
$$\begin{aligned} & {\chi} _{4} = \left( {x - x_{i} } \right)\left( {\frac{{x - x_{{i + 1}} }}{{x_{i} - x_{{i + 1}} }}} \right)^{2}, \\ & {\chi} _{5} = \left( {1 + 2\frac{{x - x_{{i + 1}} }}{{x_{i} - x_{{i + 1}} }}} \right)\left( {\frac{{x - x_{i} }}{{x_{{i + 1}} - x_{i} }}} \right)^{2}, \\ & {\chi} _{6} = \left( {x - x_{{i + 1}} } \right)\left( {\frac{{x - x_{i} }}{{x_{{i + 1}} - x_{i} }}} \right)^{2}\end{aligned}$$

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Wei, G., Jin, Y. & Wu, L. Geometric and material nonlinearities of sandwich beams under static loads. Acta Mech. Sin. 36, 97–106 (2020). https://doi.org/10.1007/s10409-019-00899-2

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