Optimal location of additional supports for plastic cylindrical shells subjected to impulsive loading

Necessary optimality conditions for location of the additional supports, restricting the dynamic response of a rigid perfectly plastic cylindrical shell subjected to an initial transverse velocity, are deduced. Incorporating the concept of the mode-form motions the problem is treated as a self-conjugate problem of the optimal control theory with distributed parameters. We use the control technique, developed previously for the case in which the state variables (the bending moment, the shear force, the deflection and its rate) together with these derivatives, being continuous in certain subdomains, may have discontinuities on the boundaries of these subregions. A particular case. associated with the uniform initial impulse is examined in detail.