A point interpolation method for two-dimensional solids

A Point Interpolation Method for Two-dimesional Solids

A Point Interpolation Method (PIM) is presented for stress analysis for two-dimensional solids. In the PIM, the problem domain is represented by properly scattered points. A technique is proposed to construct polynomial interpolants with delta function property based only on a group of arbitrarily distributed points. The PIM equations are then derived using variational principles. In the PIM, t...

A meshfree radial point interpolation method (RPIM) for three-dimensional solids

A meshfree radial point interpolation method (RPIM) is developed for stress analysis of threedimensional (3D) solids, based on the Galerkin weak form formulation using 3D meshfree shape functions constructed using radial basis functions (RBFs). As the RPIM shape functions have the Kronecker delta functions property, essential boundary conditions can be enforced as easily as in the finite elemen...

Lagrange Two-Dimensional Interpolation Method for Modeling Nanoparticle Formation During RESS Process

VII.D Two Dimensional Solids

The rotational invariance of energy is ensured by the implicit sum over the indices (i, j) in the above expression. In the Fourier representation, the energy depends on the quantities q, |u|, and (q · u) which are clearly independent of rotations. For other lattices, there are more elastic coefficients, since the energy should only be invariant under lattice rotations. For example, the symmetry...

VII.D Two Dimensional Solids

The rotational invariance of energy is ensured by the implicit sum over the indices (i, j) in the above expression. In the Fourier representation, the energy depends on the quan­ tities q , |u|, and (q · u) which are clearly independent of rotations. For other lattices, there are more elastic coefficients, since the energy should only be invariant under lattice rotations. For example, the symme...