Sentence examples for using the variational principle from inspiring English sources
Using the variational principle, the governing equations of the magnetoelectroelastic plate are derived.
In addiThen, the neutral axis and zero-stress axis no longoverningidequationsch other, and the results of boundaryd beam gradually approaconditions of monolarer beam as the height of one layer is becoming much greater than that of the other layer.
The governing equations are derived with the corresponding boundary conditions using the variational principle.
Dynamical equations for the optimal transition paths are derived using the variational principle.
The governing equation for the composite element containing both fractures and drainage holes is established using the variational principle.
Equations of motion and the conjugate parameters for the impedance and admittance matrices are derived using the variational principle.
As application examples, the local and global buckling of FRP thin-walled composite structural shapes is analyzed using the variational principles of total potential.
The total potential energy of the beam-soil system is minimized, and the governing differential equations and boundary conditions describing the equilibrium configuration of the system are obtained using the variational principles of mechanics.
In summary, the application of variational principles as a viable tool in buckling analysis of FRP thin-walled composite structures is illustrated, and the present explicit formulations using the variational principles of the Ritz method can be applied to determine buckling capacities of composite structures and facilitate the buckling analysis, design, and optimization of FRP structural profiles.
In the general case, we should use the variational principles that are represented by non-holonomic variational equations.
Using the variational Hamilton's principle, the equations for free motion of a simple two-bar frame carrying a concentrated mass with rotational inertia at its joint are established.
