Meshfree Radial Point Interpolation Research Articles

Free vibration analysis of sandwich structure via point interpolation meshfree method based on polynomial basic function

The stability of circular and annular sector plate structures under aerodynamic pressure in supersonic conditions is crucial for aircraft components. Conventional uniform materials lead to heavy structures, which are undesirable for aircraft. This study explores the use of functionally graded materials to enhance flutter stability. It employs a refined logarithmic shear deformation theory to describe plate displacement, classical elasticity theory for constitutive equations, and Hamilton’s principle for equations of motion. Two methods, finite element, and Meshfree radial point interpolation, are used to solve these equations and verify the results. Parameter studies are conducted to assess the effects of grading index, Biot’s coefficient, span angle, and geometrical aspect ratio, revealing unexpected adverse effects of grading material on stability.

Free vibrations and buckling analysis of cross-ply composite nanoplates by means of a Mesh Free Radial Point Interpolation Method

The paper deals with the dynamic analysis of composite simply supported nanoplates modelled according to the second order strain gradient theory. Numerical results are obtained by means of a Mesh Free Radial Point Interpolation Method. Both uniaxial and biaxial buckling as well as free vibration analysis are considered. The buckling analysis is performed on plates with different aspect ratio a/b and variable E1/E2 ratio. For the vibration analysis, the geometry and mechanical properties of the plate are kept constant while different lamination sequences are accounted for. Moreover, different values of the nonlocal parameter ℓ are considered for both analyses. Finally, the numerical results are compared against the analytical results find in the literature, the comparison being made in terms of percentage error between the two.

On the analysis of a kind of nonlinear Sobolev equation through locally applied pseudo‐spectral meshfree radial point interpolation

AbstractIn this study, we develop an approximate formulation for two‐dimensional nonlinear Sobolev problems by focusing on pseudospectral meshless radial point interpolation (PSMRPI) which is a kind of locally applied radial basis function interpolation and truthfully a meshless approach. In the PSMRPI method, the nodal points do not need to be regularly distributed and can even be quite arbitrary. It is easy to have high order derivatives of unknowns in terms of the values at nodal points by constructing operational matrices. The convergence and stability of the technique in some sense are studied via some examples to show the validity and trustworthiness of the PSMRPI technique.