• Structural Engineering and Mechanics
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• v.91 no.5
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• pp.527-538
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• 2024

The standard numerical approximation of structural displacement field leads to the thickness-wise transverse shear stress distributions which are quite different from the exact ones. To overcome this inherent problem, an effective and reliable post-processing method is presented based on the strain recovery and the stress equilibrium, particularly for functionally graded cylindrical and conical elastic panels. The present method is developed in the framework of locking-free 2-D natural element method. Through the recovery of displacement component-wise derivatives, the element-wise discontinuous in-plane strain distributions are enhanced to be globally continuous and smoothened. And, using the continuous in-plane strains, the troublesome poor transverse shear stress distributions are enhanced through the thickness-wise integration of static equilibrium equations. The validity of present post-processing method is verified through the comparison with the reference solutions. In addition, the comparative experiments are also performed to investigate the difference between the present method and other available post-processing methods. The numerical results confirm that the present method provides the accurate transverse shear stress distributions which are consistent with the reference solutions and much better than other available methods.

• Structural Engineering and Mechanics
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• v.88 no.5
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• pp.439-449
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• 2023

Non-linear vibration characteristics of functionally graded CNT-reinforced composite (FG-CNTRC) cylindrical shell panel on elastic foundation have not been sufficiently examined. In this situation, this study aims at the profound numerical investigation of the non-linear vibration response of FG-CNTRC cylindrical panels on Winkler-Pasternak foundation by introducing an accurate and effective 2-D meshfree-based non-linear numerical method. The large-amplitude free vibration problem is formulated according to the first-order shear deformation theory (FSDT) with the von Karman non-linearity, and it is approximated by Laplace interpolation functions in 2-D natural element method (NEM) and a non-linear partial derivative operator H_NL. The complex and painstaking numerical derivation on the curved surface and the crucial shear locking are overcome by adopting the geometry transformation and the MITC3+ shell elements. The derived nonlinear modal equations are iteratively solved by introducing a three-step iterative solving technique which is combined with Lanczos transformation and Jacobi iteration. The developed non-linear numerical method is estimated through the benchmark test, and the effects of foundation stiffness, CNT volume fraction and functionally graded pattern, panel dimensions and boundary condition on the non-linear vibration of FG-CNTRC cylindrical panels on elastic foundation are parametrically investigated.