Sentence examples for solutions can serve from inspiring English sources

These solutions can serve as generalized solutions for vibration and buckling of delaminated composites.

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

These analytical solutions can serve as a basis for establishing simplified theories and evaluating numerical solutions of functionally graded beams.

The derived solutions can serve as benchmark results to assess various approximate shell theories and numerical methods.

The present solutions can serve as benchmarks to various thick-plate theories and numerical methods, and could be further useful for designing layered composite structures involving small scale.

The results of model analytical solutions can serve engineers for design proposals or check analysis to determine the required thermal capacity of kang plate at the early design stage.

This exact solution can serve as a benchmark solution for various approximate solutions.

The presented solution can serve as a benchmark solution to the general problem of 3D acoustic scattering from axisymmetric inhomogeneities in ocean waveguides at low frequencies.

We discuss solution strategies for solving the encapsulation problem and the sufficient conditions under which the numerical solution can serve as a good estimator for capturing the effects of the epistemic uncertainty.

The proposed control solution can serve as a fail-safe measure in case of failure of the conventional attitude actuator, which triggered by automatic reconfiguration of the attitude control components.

This work is the first step towards understanding quasicrystals under intricate loading conditions such as indentation and impact, and the exact closed-form solution can serve as a reference in convergence studies of other numerical methods and for verification of existing or future plate theories.