Sensitizing according to Courant the Timoshenko beam finite element solution

Courant has presented in two articles from years 1923 and 1943 a formulation where a conventional variational principle is &sensitizedʹ by appending the variational expression with terms of higher order which vanish for the actual solution. The purpose of the article is to raise interest to this sensitizing idea. The idea is explained and applied in connection with the "nite element solution of the Timoshenko beam problem. A certain kind of patch test is employed for the determination of the sensitizing parameter values. Equal-order approximation for the beam axis de#ection and the cross-section rotation with linear two-noded elements is used. Sensitizing is found to remove the locking behaviour. Sensitizing without a variational principle and connections with the stabilized formulations in "nite element #uid mechanics problems are discussed. The concept of the sensitized principle of virtual work is introduced. References to applications of the patch test in more than one dimension are "nally given