The paper deals with the minimum-weight design of elastic grillages in which the absolute value of the axial stresses nowhere exceeds a prescribed value. After discussing optimality conditions for this problem, a geometrical method for obtaining the optimal beam directions is presented. Considering quadrilateral grillages, the effect of translation and rotation of sides on the optimal layout is investigated. Finally, the concept of “beam weaves” is introduced and the optimal layout of beams near a free edge is discussed.
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Prager et al. (1977) studied this question.
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