Linear Bending Analysis of Functionally Graded Sandwich Shells With the Meshless Method Based on the Layer-Wise Theory

CHEN Wei; TANG Zhihong; PENG Linxin

doi:10.21656/1000-0887.440262

Volume 45 Issue 5

May 2024

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Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(5): 539-553

CHEN Wei, TANG Zhihong, PENG Linxin. Linear Bending Analysis of Functionally Graded Sandwich Shells With the Meshless Method Based on the Layer-Wise Theory[J]. Applied Mathematics and Mechanics, 2024, 45(5): 539-553. doi: 10.21656/1000-0887.440262

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Linear Bending Analysis of Functionally Graded Sandwich Shells With the Meshless Method Based on the Layer-Wise Theory

doi: 10.21656/1000-0887.440262

1.
School of Civil Engineering, University of South China, Hengyang, Hunan 421001, P.R.China
2.
School of Civil Engineering and Architecture, Guangxi University, Nanning 530004, P.R.China

Received Date: 2023-08-29
Rev Recd Date: 2023-12-15
Publish Date: 2024-05-01

Abstract

Abstract

Based on the 3D continuous shell theory and the 1st-order shear deformation theory, a moving least squares meshless method was proposed for solving the linear bending problem of functionally graded sandwich shells with the layered method. With the mapping technology, the 2D meshless node information on the convected coordinate system was mapped on the 3D shell, and the shape function of moving least squares (MLS) approximation was formed on the convected coordinate system. Due to the inability of shell numerical solutions based on the 3D continuous shell theory to provide an explicit expression for the thickness direction of a specific shell, the portion of material parameter changes in the functionally graded sandwich material shell structure was divided into several layers, and the material parameters of each layer were obtained as constants. The governing meshless equation for linear bending of functionally graded sandwich shells was derived under the principle of minimum potential energy. Through introduction of a linear transformation in the thickness direction, the Gaussian integral in the thickness direction of each layer was bounded within the range of -1 to 1, without violation of the 1st-order shear deformation theory (FSDT). The essential boundary conditions were employed with the complete transformation method. Finally, the effects of different gradient coefficients, diameter to thickness ratios, and curvature radii on numerical results were discussed through examples of functionally graded sandwich plates, cylindrical shells, and hyperbolic shallow shells with classical geometric shapes. The calculated results were compared with the literature solutions. The results show that, the proposed method has the characteristics of good convergence and high computation accuracy in solving linear bending problems of functional graded sandwich shells with different shapes.
- layer-wise method,
- meshless method,
- mapping technology,
- functionally graded sandwich shell,
- linear bending

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References(39)

References

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