Sentence examples for use of variational principles from inspiring English sources
We are promoting the use of variational principles as some generalizing idea that allows us to create consistent approximations of mathematical models.
The basic constitutive equations and equations of motion are derived for anisotropic porous piezoelectric materials by making use of variational principle.
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.
A survey of variational principles in stability analysis of composite structures is first given, followed by a brief introduction of the theoretical background of variational principles in elasticity.
The evolution equation of the beam spot size is derived and solved by making use of the variational principle approach method.
The applications of the finite element method to the dynamic problem rely on the use of a variational principle to derive the necessary element properties or equations.
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.
As application examples, the local and global buckling of FRP thin-walled composite structural shapes is analyzed using the variational principles of total potential.
In the general case, we should use the variational principles that are represented by non-holonomic variational equations.
The model is derived by means of the "second-order" homogenization theory, which makes use of suitably designed variational principles utilizing the idea of a "linear comparison composite".
The proposed model is generated by means of the "second-order" homogenization method, which makes use of suitably designed variational principles utilizing the idea of a "linear comparison composite".
