A critical assessment of the Simplified Hybrid Displacement Method
A critical assessment of the Simplified Hybrid Displacement Method
复制标题
对简化混合驱替法的严格评估
DOI：
10.1002/nme.1620110114
复制
发表时间：
1977
影响因子：
2.9
通讯作者：
R. Gallagher
中科院分区：
文献类型：
--
作者：
H. Mang;R. Gallagher
简化的杂交位移法，一个有吸引力的修改的原则之一的固定值的修改势能，严格审查和比较的另一种形式的变分原理和经典的最小势能原理。这三种方法研究从理论Vantage，并通过数值例子的媒介。利用经典的最小势能原理、修正势能驻值原理和简化杂交位移法，建立了一个非协调三角形有限板弯曲单元，并将其用于求解一些简单问题。
这种方法的吸引力来自于这样一个事实，即没有额外的独立的未知参数拉格朗日乘子从数学的角度来看，进入修改后的能量泛函，通常是混合方法的情况下。
数值分析表明，简化杂交位移法可能会失稳。它还表明，该方法的修改后的能量泛函的稳定值可能是不一致的经典势能的相应的最小值。此外，它表明，简化的混合位移法是，在一般情况下，无法“恢复”单元间的斜坡连续性的意义上的原则，固定值的修改势能，也就是说，至少在一个“积分意义上”。
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 modified 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 numcrically 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’.