Sentence examples for by using the governing from inspiring English sources

Then, a system of complete algebraic nonlinear equations can be constructed to calculate out the final point-values of the mid-plane displacements by using the governing equations and relative boundary conditions with HDQ method.

The scheme provides for a more balanced sharing of communication load over index nodes by using the governing property that the wider the spatial extent known to an index node, the more constrained is the value range covered by that node.

The displacement fields used in the analytical formulation are coupled by using the homogeneous governing static axial equilibrium equation of the beam.

By using the hybrid governing equation in the response analysis and sensitivity analysis, the convoluted algorithm can be avoided in sensitivity analysis, and the response quantities and the sensitivity coefficients can be obtained simultaneously.

Basis functions for the transverse and the in-plane displacements are related by using the nonlinear equation governing the plate in-plane motion.

Basis functions for the transverse and the in-plane displacements are related by using the nonlinear equation governing the plate's in-plane motion.

By using the above transformations, the governing partial differential equations are transformed into a system of non-dimensional nonlinear and coupled ordinary differential equations as follows: f ‴ + f f ″ − f ′ 2 − A ( f ′ + 1 2 η f ″ ) − M 1 + m 2 ( f ′ + m g ) = 0, (10).

The mapped nodal displacements can be determined using the governing equations established by means of the virtual work principle.

By using the Timoshenko beam theory, the governing differential equations are expressed in terms of the adherend displacements and then analytically solved for the force boundary conditions prescribed at both overlap ends.

By using the Hamilton's principle, governing equations of motion for coupled axial shear flexural stretching response are derived.

Free vibration analysis of laminated conical shells is presented by using the numerical solution of governing differential equations of motion based on transverse shear deformation theory.