H.A. Mang, R.H. Gallagher:
"A Critical Assessment of the Simplified Hybrid Displacement Method";
International Journal for Numerical Methods in Engineering, 11 (1977), 145 - 167.
The Simplified Hybrid Displacement Method, an attractive modification of one of the principles of stationary value of modified potential energy, is examined critically and compared to another form of such variational principles and to the classical principle of minimum of potential energy. The three methods are studied from a theoretical vantage point and through the medium of numerical examples. A non-conforming triangular finite plate bending element serves as the vehicle to solve a number of simple problems, utilizing the classical principle of minimum potential energy, a principle of stationary value of modiefied potential energy and the Simplified Hybrid Displacement Method.The attraction of this method derives from the fact that no additional independent unknown parameters - Lagrangian multipliers from a mathematical standpoint - enter into the modified energy functional, as is usually the case with hybrid methods.
It is demonstrated numerically that the Simplified Hybrid Displacement Method may become unstable. It is also shown that the stationary values of the modified energy functional for this method may be inconsistent with the corresponding minima of the classical potential energy. Furthermore, it is demonstrated that the Simplified Hybrid Displacement method is, in general, incapable of 'restoring' interelement slope continuity in the sense of a principle of stationary value of modified potential energy, that is, at least in an 'integral sense'.