Sentence examples for based on the variational principle from inspiring English sources

Based on the variational principle and power-based balance equation, the effective collapse mechanism is derived in closed form.

In phenomenological approach, one of the methods to describe the fractional nonlocal continua is based on the variational principle with Lagrangian density that contains fractional derivatives with respect to coordinates.

It is based on the variational principle.

An optimization procedure based on the variational principle is derived to develop an analytical formulation.

Governing equations and all boundary conditions of CNTs are derived based on the variational principle.

For the postbuckling analysis of VAT composite plates, an efficient tool based on the variational principle and the Rayleigh Ritz method is developed.

Based on the variational principles, this approach involves formulating the path planning problem as constrained minimization of a functional representing the total joint movement over the complete path.

A method based on the variational principles in conjunction with the finite difference technique is applied to examine the free vibration characteristics of isotropic rectangular plates of linearly varying thickness by including the effects of transverse shear deformation and rotary inertia.

And then, the constrained Hamiltonian canonical form is derived from the Lagrange governing equation based on the Hamiltonian variational principle.

Based on the second variational principle and nonlinear plate theory, the total potential energy of the channel beam including shear effect and beam bending twisting coupling is derived.

Based on the parametric variational principle (PVP), a unified constitutive equation of 3D bi-modulus materials is proposed to deal with the problem of numerical instability.