Method Rayleigh-Ritz approximation

Geometrical nonlinearity due to in-plane stress should be considered when the deflection of the plate reaches the order of the plate thickness or that of the delaminated portions. This order of the deflection is often realized in composite materials when the propagation of multiple delaminations takes place. The clamped circular plate with multiple penny-shape delaminations of the same radius a is considered again. The boundary and the continuity conditions are the same as those in Section 2.1. Since no exact solution is available, the Rayleigh-Ritz approximation method is adopted. The total potential energy fl = f/- T is written as the sum of the total strain energy... 

MacDonald J K L 1933 Successive approximations by the Rayleigh-Ritz variation method Phys. Rev4Z 830-3... 

In quantum calculations, the Rayleigh-Ritz variational method is widely used to approximate the solution of the Schrodinger equation [86], To obtain exact results, one should expand the exact wave function in a complete basis set... 

Figure 1 A family tree of quantum chemistry DFT, density functional theory QMC, quantum Monte Carlo RRV, Rayleigh-Ritz variational theory X-a, X-alpha method KS, Kohn-Sham approach LDA, BP, B3LYP, density functional approximations VQMC, variational QMC DQMC, diffusion QMC FNQMC, fixed-node QMC PIQMC, path integral QMC EQMC, exact QMC HF, Hartree-Fock EC, explicitly correlated functions P, perturbational MP2, MP4, Maller-Plesset perturbational Cl, configuration interaction MRCI, multireference Cl FCI, full Cl CC, CCSD(T), coupled-cluster approaches. Other acronyms are defined in the text.

The Rayleigh-Ritz variational theory is the basis for so-called variational methods in which an estimate of the energy of a system is calculated for an approximate trial wavefunction usually assembled from combinations of atomic orbitals. Expectation values of the energy may be calculated accurately for many trial wavefunctions and are upper bounds to the true energy. If the parameters of the trial wavefunctions are varied systematically, the lowest upper bound to the energy for a particular form of trial wavefunction may be determined (thus the term variational ). The trial functions must satisfy certain restrictions such... 

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