Optipization of clamped-clamped beam subjected to a concentrated load (Deflection criterion and strain energy density criterion)

For a both-ends-clamped beam that is subjected to a concentrated load, it had been shown that the actual most suitable form within the same volume exists only under a certain specific condition that a load was in a limited central region of the span. However, the most suitable form is supposed to exist at conditions outside the above. In this paper, we reconsider the optimization problem of a both-ends-clamped beam that is subjected to a concentrated load under the condition of volume constancy as minimization problems of functions related to displacement and as a problem of making the strain energy density uniform by GA.