Sentence examples for the present analytical from inspiring English sources

The present analytical solutions include the effects of shear and interface deformations.

The high precision of the present analytical model is confirmed through simulations.

The present analytical theory and the supporting mathematical techniques are thoroughly verified.

The present analytical solutions are validated through comparisons with those available in open literature.

The present analytical method is also applicable to evaluating the misfit in other systems.

In the present analytical solution, a benchmark was also established for improving discretizing schemes in numerical works.

A numerical scheme followed by the finite difference method has been used to validate the present analytical result.

The present analytical solutions are compared with three-dimensional finite element analysis results and absolute agreements are found.

The present analytical solutions can serve as benchmarks for numerous simplified analyses and various numerical codes in the future.

The energy release rates predicted by the present analytical solutions are compared with those in the literatures.

Excellent agreement is observed between the present analytical partition theory and numerical results from finite element method (FEM) simulations.