Static and dynamic analysis of thin functionally graded shell with in-plane material inhomogeneity

The static and dynamic problems of thin functionally graded shells (FGSs) with in-plane material inhomogeneity are investigated in this work. Governing equations are derived based on the first-order shear deformation shell theory. A meshfree radial basis collocation method (RBCM) which employs infinitely continuous radial basis functions (RBFs) as the approximation and utilizes collocation method for the solution is introduced for the static and dynamic eigenvalue analysis. Comparison studies with the analytical solutions of the homogeneous shell problems demonstrate that this method can achieve high accuracy and spectral convergence. FGSs with three representative gradient distributions are studied. Numerical simulations reveal that material inhomogeneity can shift the dangerous positions of maximum displacements or stresses in statics, and has prominent influences on the natural frequencies and mode shapes in dynamics. These observations can be utilized for the design of material properties of shell structures in the engineering applications.

Automated summary

This work investigates the static and dynamic problems of thin functionally graded shells with in-plane material inhomogeneity, introducing a new meshfree radial basis collocation method for solution. Numerical simulations show that material inhomogeneity can shift dangerous positions in statics and affect natural frequencies and mode shapes in dynamics. These findings can be used for material property design in engineering applications.