Abstract
In this paper, a novel meshfree approach is proposed for the three-dimensional free vibration analysis of laminated composite combination shells. The three-dimensional theory of elasticity is applied to the formulation for free vibration analysis of thick laminated elliptical–cylindrical and conical–cylindrical combination shells, and the field functions are approximated by a novel meshfree Tchebychev-point interpolation method shape function using Tchebychev polynomials as the basis. The governing equation and boundary conditions for the individual layers of the substructures of the laminated combination shell are derived, and the equations of the whole system are obtained by combining them using a continuous condition. The boundary and continuous conditions are generalized by the introduction of an artificial spring technique, and the type of boundary conditions is selected according to the spring stiffness. The accuracy and reliability of the proposed method are verified by comparing the results of the proposed method with those of literature and finite element program ABAQUS. The free vibration characteristics including natural frequencies and mode shapes of thick combination shells with various geometries and boundary conditions are presented through numerical examples.
Highlights
With the development of science and technology, various composite materials with excellent performance are used in the manufacture of mechanical structures
The laminated combination shell is decomposed into individual layers of substructures, and the displacement components in the individual layers are approximated by the three-dimensional theory of elasticity and TPIM shape function
The governing equations and boundary conditions in a one-layer shell are obtained by Hamilton’s principle, and the equations of the whole system are determined by the compatibility conditions of displacement components for the nodes located on the interfaces between layers and substructures
Summary
With the development of science and technology, various composite materials with excellent performance are used in the manufacture of mechanical structures. Ye et al. developed a unified three-dimensional elasticity method for free vibration analysis of the thick cylindrical shells resting on elastic foundations In this method, the displacements of the shell are expanded as a standard Fourier cosine series. The governing equation and boundary conditions of the whole system are obtained by combining the equations in individual layers derived using the three-dimensional theory ofthe hottest areas in the research of mesh elasticity and Hamilton’s principle according to the continuity condition of displacement. Three-dimensional free vibration analysis of thick laminated conical–cylindrical and semi-elliptical–cylindrical combination shells is conducted using the proposed shape function. The displacement components are approximated using the proposed shape function, and the governing equation and boundary condition for individual layers of thick shells are derived by applying Hamilton’s principle. The effects of parameters such as material property, geometry, and lamination type on the free vibration of the laminated combination shell are presented through several numerical examples
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