# Analytic solution of angle-ply laminated plates under extension, bending, and torsion

Shen Haw Ju, Wen Yu Liang, Hsin Hsiang Hsu, Jiann Quo Tarn

Research output: Contribution to journalArticle

### Abstract

This paper develops a Hamiltonian state space approach for analytic determination of deformation and stress fields in multilayered monoclinic angle-ply laminates under the combined action of extension, bending, and torsion. The present solution satisfies the equations of anisotropic elasticity, the end conditions, the traction-free boundary conditions on the four edge surfaces of the rectangular section, and the interfacial continuity conditions in multilayered laminates. The proposed method only requires the solutions of matrix and eigen equations, regardless of the number or lamination of the layers. The finite element analyses are used to validate the accuracy of the analysis. The analytical solution and the numerical solutions are in excellent agreement.

Original language English Journal of Composite Materials https://doi.org/10.1177/0021998319873025 Accepted/In press - 2019 Jan 1

### Fingerprint

Torsional stress
Laminates
Hamiltonians
Traction (friction)
Elasticity
Boundary conditions

### All Science Journal Classification (ASJC) codes

• Ceramics and Composites
• Mechanics of Materials
• Mechanical Engineering
• Materials Chemistry

### Cite this

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title = "Analytic solution of angle-ply laminated plates under extension, bending, and torsion",
abstract = "This paper develops a Hamiltonian state space approach for analytic determination of deformation and stress fields in multilayered monoclinic angle-ply laminates under the combined action of extension, bending, and torsion. The present solution satisfies the equations of anisotropic elasticity, the end conditions, the traction-free boundary conditions on the four edge surfaces of the rectangular section, and the interfacial continuity conditions in multilayered laminates. The proposed method only requires the solutions of matrix and eigen equations, regardless of the number or lamination of the layers. The finite element analyses are used to validate the accuracy of the analysis. The analytical solution and the numerical solutions are in excellent agreement.",
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Analytic solution of angle-ply laminated plates under extension, bending, and torsion. / Ju, Shen Haw; Liang, Wen Yu; Hsu, Hsin Hsiang; Tarn, Jiann Quo.

In: Journal of Composite Materials, 01.01.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Analytic solution of angle-ply laminated plates under extension, bending, and torsion

AU - Ju, Shen Haw

AU - Liang, Wen Yu

AU - Hsu, Hsin Hsiang

AU - Tarn, Jiann Quo

PY - 2019/1/1

Y1 - 2019/1/1

N2 - This paper develops a Hamiltonian state space approach for analytic determination of deformation and stress fields in multilayered monoclinic angle-ply laminates under the combined action of extension, bending, and torsion. The present solution satisfies the equations of anisotropic elasticity, the end conditions, the traction-free boundary conditions on the four edge surfaces of the rectangular section, and the interfacial continuity conditions in multilayered laminates. The proposed method only requires the solutions of matrix and eigen equations, regardless of the number or lamination of the layers. The finite element analyses are used to validate the accuracy of the analysis. The analytical solution and the numerical solutions are in excellent agreement.

AB - This paper develops a Hamiltonian state space approach for analytic determination of deformation and stress fields in multilayered monoclinic angle-ply laminates under the combined action of extension, bending, and torsion. The present solution satisfies the equations of anisotropic elasticity, the end conditions, the traction-free boundary conditions on the four edge surfaces of the rectangular section, and the interfacial continuity conditions in multilayered laminates. The proposed method only requires the solutions of matrix and eigen equations, regardless of the number or lamination of the layers. The finite element analyses are used to validate the accuracy of the analysis. The analytical solution and the numerical solutions are in excellent agreement.

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