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Nonlinear bending of FG skew sandwich plates with temperature-dependent elastoplastic properties using an enhanced 3D meshless approach

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Abstract

This paper presents the three-dimensional (3D) nonlinear response of temperature-dependent thermo-elastoplastic bending of functionally graded (FG) skew sandwich plates with FG face sheets and FG core under a combination of mechanical and thermal loads. For this purpose, an enhanced and efficient truly meshless method based on the local radial point interpolation method (LRPIM) and a new radial basis function (RBF) has been developed in which the quality of the LRPIM shape functions is not affected by the shape parameter. The modified rule of mixtures is utilized to evaluate the effective temperature-dependent material parameters locally. To describe the plastic behavior of the plate, the Prandtl–Reuss flow rule and the von Mises yield criterion are adapted considering isotropic strain hardening. To prove the high accuracy and efficiency of the present method, the obtained results are compared and confirmed with other available numerical and analytical results. During the analysis of various examples, the effect of significant parameters such as material gradient, skew angle, plate thickness-to-length ratio, layer thickness ratio, and boundary conditions on the results is investigated.

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  1. Department of Mechanical Engineering, Fasa University, Fasa, Iran

    Reza Vaghefi

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Appendix 1

Appendix 1

The following variable changes convert Cartesian coordinates \((x,y,z)\) to skew coordinates \((\zeta ,\eta ,z)\):

$$\begin{gathered} x = \zeta + \eta \sin \theta ,\hfill \\ y = \eta cos\theta , \hfill \\ u_{\zeta } = ucos\theta - v\sin \theta , \hfill \\ v_{\eta } = u\sin \theta + vcos\theta , \hfill \\ \frac{\partial }{\partial x} = \frac{\partial }{\partial \zeta }, \hfill \\ \frac{\partial }{\partial y} = - tan\theta \frac{\partial }{\partial \zeta } + \frac{1}{cos\theta }\frac{\partial }{\partial \eta }. \hfill \\ \end{gathered}$$

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Vaghefi, R. Nonlinear bending of FG skew sandwich plates with temperature-dependent elastoplastic properties using an enhanced 3D meshless approach. Acta Mech 233, 1599–1631 (2022). https://doi.org/10.1007/s00707-022-03175-w

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